1039 lines
29 KiB
Fortran
1039 lines
29 KiB
Fortran
!moduleMesh2DCyl: 2D axial symmetric extension of generic mesh from GMSH format.
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! x == z
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! y == r
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! z == theta (unused)
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MODULE moduleMesh2DCyl
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USE moduleMesh
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USE moduleMeshBoundary
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IMPLICIT NONE
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!Values for Gauss integral
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REAL(8), PARAMETER:: corQuad(1:3) = (/ -DSQRT(3.D0/5.D0), 0.D0, DSQRT(3.D0/5.D0) /)
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REAL(8), PARAMETER:: wQuad(1:3) = (/ 5.D0/9.D0, 8.D0/9.D0, 5.D0/9.D0 /)
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REAL(8), PARAMETER:: xi1Tria(1:4) = (/ 1.D0/3.D0, 1.D0/5.D0, 3.D0/5.D0, 1.D0/5.D0 /)
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REAL(8), PARAMETER:: xi2Tria(1:4) = (/ 1.D0/3.D0, 1.D0/5.D0, 1.D0/5.D0, 3.D0/5.D0 /)
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REAL(8), PARAMETER:: wTria(1:4) = (/ -27.D0/96.D0, 25.D0/96.D0, 25.D0/96.D0, 25.D0/96.D0 /)
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TYPE, PUBLIC, EXTENDS(meshNode):: meshNode2DCyl
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!Element coordinates
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REAL(8):: r = 0.D0, z = 0.D0
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CONTAINS
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PROCEDURE, PASS:: init => initNode2DCyl
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PROCEDURE, PASS:: getCoordinates => getCoord2DCyl
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END TYPE meshNode2DCyl
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TYPE, PUBLIC, EXTENDS(meshEdge):: meshEdge2DCyl
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!Element coordinates
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REAL(8):: r(1:2) = 0.D0, z(1:2) = 0.D0
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!Connectivity to nodes
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CLASS(meshNode), POINTER:: n1 => NULL(), n2 => NULL()
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CONTAINS
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PROCEDURE, PASS:: init => initEdge2DCyl
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PROCEDURE, PASS:: getNodes => getNodes2DCyl
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PROCEDURE, PASS:: intersection => intersection2DCylEdge
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PROCEDURE, PASS:: randPos => randPosEdge
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END TYPE meshEdge2DCyl
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TYPE, PUBLIC, ABSTRACT, EXTENDS(meshVol):: meshVol2DCyl
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CONTAINS
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PROCEDURE, PASS:: detJac => detJ2DCyl
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PROCEDURE, PASS:: invJac => invJ2DCyl
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PROCEDURE(fPsi_interface), DEFERRED, NOPASS:: fPsi
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PROCEDURE(dPsi_interface), DEFERRED, NOPASS:: dPsi
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PROCEDURE(partialDer_interface), DEFERRED, PASS:: partialDer
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END TYPE meshVol2DCyl
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ABSTRACT INTERFACE
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PURE FUNCTION fPsi_interface(xi) RESULT(fPsi)
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REAL(8), INTENT(in):: xi(1:3)
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REAL(8), ALLOCATABLE:: fPsi(:)
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END FUNCTION fPsi_interface
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PURE FUNCTION dPsi_interface(xi) RESULT(dPsi)
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REAL(8), INTENT(in):: xi(1:3)
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REAL(8), ALLOCATABLE:: dPsi(:,:)
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END FUNCTION dPsi_interface
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PURE SUBROUTINE partialDer_interface(self, dPsi, dz, dr)
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IMPORT meshVol2DCyl
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CLASS(meshVol2DCyl), INTENT(in):: self
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REAL(8), INTENT(in):: dPsi(1:,1:)
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REAL(8), INTENT(out), DIMENSION(1:2):: dz, dr
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END SUBROUTINE partialDer_interface
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END INTERFACE
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!Quadrilateral volume element
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TYPE, PUBLIC, EXTENDS(meshVol2DCyl):: meshVol2DCylQuad
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!Element coordinates
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REAL(8):: r(1:4) = 0.D0, z(1:4) = 0.D0
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!Connectivity to nodes
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CLASS(meshNode), POINTER:: n1 => NULL(), n2 => NULL(), n3 => NULL(), n4 => NULL()
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!Connectivity to adjacent elements
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CLASS(*), POINTER:: e1 => NULL(), e2 => NULL(), e3 => NULL(), e4 => NULL()
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REAL(8):: arNodes(1:4) = 0.D0
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CONTAINS
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PROCEDURE, PASS:: init => initVolQuad2DCyl
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PROCEDURE, PASS:: randPos => randPosVolQuad
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PROCEDURE, PASS:: area => areaQuad
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PROCEDURE, NOPASS:: fPsi => fPsiQuad
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PROCEDURE, NOPASS:: dPsi => dPsiQuad
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PROCEDURE, NOPASS:: dPsiXi1 => dPsiQuadXi1
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PROCEDURE, NOPASS:: dPsiXi2 => dPsiQuadXi2
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PROCEDURE, PASS:: partialDer => partialDerQuad
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PROCEDURE, PASS:: elemK => elemKQuad
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PROCEDURE, PASS:: elemF => elemFQuad
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PROCEDURE, NOPASS:: weight => weightQuad
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PROCEDURE, NOPASS:: inside => insideQuad
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PROCEDURE, PASS:: scatter => scatterQuad
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PROCEDURE, PASS:: gatherEF => gatherEFQuad
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PROCEDURE, PASS:: getNodes => getNodesQuad
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PROCEDURE, PASS:: phy2log => phy2logQuad
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PROCEDURE, PASS:: nextElement => nextElementQuad
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END TYPE meshVol2DCylQuad
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!Triangular volume element
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TYPE, PUBLIC, EXTENDS(meshVol2DCyl):: meshVol2DCylTria
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!Element coordinates
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REAL(8):: r(1:3) = 0.D0, z(1:3) = 0.D0
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!Connectivity to nodes
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CLASS(meshNode), POINTER:: n1 => NULL(), n2 => NULL(), n3 => NULL()
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!Connectivity to adjacent elements
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CLASS(*), POINTER:: e1 => NULL(), e2 => NULL(), e3 => NULL()
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REAL(8):: arNodes(1:3) = 0.D0
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CONTAINS
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PROCEDURE, PASS:: init => initVolTria2DCyl
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PROCEDURE, PASS:: randPos => randPosVolTria
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PROCEDURE, PASS:: area => areaTria
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PROCEDURE, NOPASS:: fPsi => fPsiTria
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PROCEDURE, NOPASS:: dPsi => dPsiTria
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PROCEDURE, NOPASS:: dPsiXi1 => dPsiTriaXi1
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PROCEDURE, NOPASS:: dPsiXi2 => dPsiTriaXi2
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PROCEDURE, PASS:: partialDer => partialDerTria
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PROCEDURE, PASS:: elemK => elemKTria
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PROCEDURE, PASS:: elemF => elemFTria
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PROCEDURE, NOPASS:: weight => weightTria
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PROCEDURE, NOPASS:: inside => insideTria
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PROCEDURE, PASS:: scatter => scatterTria
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PROCEDURE, PASS:: gatherEF => gatherEFTria
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PROCEDURE, PASS:: getNodes => getNodesTria
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PROCEDURE, PASS:: phy2log => phy2logTria
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PROCEDURE, PASS:: nextElement => nextElementTria
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END TYPE meshVol2DCylTria
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CONTAINS
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!NODE FUNCTIONS
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!Inits node element
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SUBROUTINE initNode2DCyl(self, n, r)
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USE moduleSpecies
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USE moduleRefParam
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IMPLICIT NONE
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CLASS(meshNode2DCyl), INTENT(out):: self
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INTEGER, INTENT(in):: n
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REAL(8), INTENT(in):: r(1:3)
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self%n = n
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self%z = r(1)/L_ref
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self%r = r(2)/L_ref
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!Node volume, to be determined in mesh
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self%v = 0.D0
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!Allocates output:
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ALLOCATE(self%output(1:nSpecies))
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END SUBROUTINE initNode2DCyl
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!Get coordinates from node
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PURE FUNCTION getCoord2DCyl(self) RESULT(r)
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IMPLICIT NONE
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CLASS(meshNode2DCyl), INTENT(in):: self
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REAL(8):: r(1:3)
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r = (/self%z, self%r, 0.D0/)
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END FUNCTION getCoord2DCyl
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!EDGE FUNCTIONS
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!Inits edge element
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SUBROUTINE initEdge2DCyl(self, n, p, bt, physicalSurface)
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USE moduleSpecies
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USE moduleBoundary
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USE moduleErrors
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IMPLICIT NONE
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CLASS(meshEdge2DCyl), INTENT(out):: self
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INTEGER, INTENT(in):: n
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INTEGER, INTENT(in):: p(:)
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INTEGER, INTENT(in):: bt
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INTEGER, INTENT(in):: physicalSurface
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REAL(8), DIMENSION(1:3):: r1, r2
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INTEGER:: s
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self%n = n
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self%n1 => mesh%nodes(p(1))%obj
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self%n2 => mesh%nodes(p(2))%obj
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!Get element coordinates
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r1 = self%n1%getCoordinates()
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r2 = self%n2%getCoordinates()
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self%z = (/r1(1), r2(1)/)
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self%r = (/r1(2), r2(2)/)
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!Normal vector
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self%normal = (/ self%r(2)-self%r(1), &
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self%z(2)-self%z(1), &
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0.D0 /)
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self%normal = self%normal/NORM2(self%normal)
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!Boundary index
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self%boundary => boundary(bt)
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ALLOCATE(self%fboundary(1:nSpecies))
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!Assign functions to boundary
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DO s = 1, nSpecies
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CALL pointBoundaryFunction(self, s)
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END DO
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!Physical surface
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self%physicalSurface = physicalSurface
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END SUBROUTINE initEdge2DCyl
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!Get nodes from edge
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PURE FUNCTION getNodes2DCyl(self) RESULT(n)
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IMPLICIT NONE
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CLASS(meshEdge2DCyl), INTENT(in):: self
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INTEGER, ALLOCATABLE:: n(:)
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ALLOCATE(n(1:2))
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n = (/self%n1%n, self%n2%n /)
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END FUNCTION getNodes2DCyl
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PURE FUNCTION intersection2DCylEdge(self, r0, v0) RESULT(r)
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IMPLICIT NONE
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CLASS(meshEdge2DCyl), INTENT(in):: self
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REAL(8), DIMENSION(1:3), INTENT(in):: r0, v0
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REAL(8), DIMENSION(1:3):: r
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REAL(8), DIMENSION(1:3):: rS !base point of surface
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REAL(8):: d
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rS = (/ self%z(1), self%r(1), 0.D0 /)
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d = DOT_PRODUCT((rS - r0), self%normal)/DOT_PRODUCT(v0, self%normal)
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r = r0 + v0*d
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END FUNCTION intersection2DCylEdge
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!Calculates a random position in edge
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FUNCTION randPosEdge(self) RESULT(r)
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USE moduleRandom
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IMPLICIT NONE
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CLASS(meshEdge2DCyl), INTENT(in):: self
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REAL(8):: rnd
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REAL(8):: r(1:3)
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REAL(8):: p1(1:2), p2(1:2)
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rnd = random()
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p1 = (/self%z(1), self%r(1) /)
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p2 = (/self%z(2), self%r(2) /)
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r(1:2) = (1.D0 - rnd)*p1 + rnd*p2
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r(3) = 0.D0
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END FUNCTION randPosEdge
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!VOLUME FUNCTIONS
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!QUAD FUNCTIONS
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!Inits quadrilateral element
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SUBROUTINE initVolQuad2DCyl(self, n, p)
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USE moduleRefParam
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IMPLICIT NONE
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CLASS(meshVol2DCylQuad), INTENT(out):: self
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INTEGER, INTENT(in):: n
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INTEGER, INTENT(in):: p(:)
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REAL(8), DIMENSION(1:3):: r1, r2, r3, r4
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self%n = n
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self%n1 => mesh%nodes(p(1))%obj
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self%n2 => mesh%nodes(p(2))%obj
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self%n3 => mesh%nodes(p(3))%obj
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self%n4 => mesh%nodes(p(4))%obj
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!Get element coordinates
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r1 = self%n1%getCoordinates()
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r2 = self%n2%getCoordinates()
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r3 = self%n3%getCoordinates()
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r4 = self%n4%getCoordinates()
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self%z = (/r1(1), r2(1), r3(1), r4(1)/)
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self%r = (/r1(2), r2(2), r3(2), r4(2)/)
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!Assign node volume
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CALL self%area()
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self%n1%v = self%n1%v + self%arNodes(1)
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self%n2%v = self%n2%v + self%arNodes(2)
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self%n3%v = self%n3%v + self%arNodes(3)
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self%n4%v = self%n4%v + self%arNodes(4)
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self%sigmaVrelMax = sigma_ref/L_ref**2
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CALL OMP_INIT_LOCK(self%lock)
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END SUBROUTINE initVolQuad2DCyl
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!Computes element area
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PURE SUBROUTINE areaQuad(self)
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USE moduleConstParam, ONLY: PI8
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IMPLICIT NONE
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CLASS(meshVol2DCylQuad), INTENT(inout):: self
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REAL(8):: r, xi(1:3)
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REAL(8):: detJ
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REAL(8):: fPsi(1:4)
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self%volume = 0.D0
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self%arNodes = 0.D0
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!2D 1 point Gauss Quad Integral
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xi = 0.D0
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detJ = self%detJac(xi)*PI8 !4*2*pi
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fPsi = self%fPsi(xi)
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r = DOT_PRODUCT(fPsi,self%r)
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self%volume = r*detJ
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self%arNodes = fPsi*r*detJ
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END SUBROUTINE areaQuad
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!Computes element functions in point xi
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PURE FUNCTION fPsiQuad(xi) RESULT(fPsi)
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IMPLICIT NONE
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REAL(8),INTENT(in):: xi(1:3)
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REAL(8), ALLOCATABLE:: fPsi(:)
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ALLOCATE(fPsi(1:4))
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fPsi(1) = (1.D0-xi(1))*(1.D0-xi(2))
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fPsi(2) = (1.D0+xi(1))*(1.D0-xi(2))
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fPsi(3) = (1.D0+xi(1))*(1.D0+xi(2))
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fPsi(4) = (1.D0-xi(1))*(1.D0+xi(2))
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fPsi = fPsi*0.25D0
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END FUNCTION fPsiQuad
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!Derivative element function at coordinates xi
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PURE FUNCTION dPsiQuad(xi) RESULT(dPsi)
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IMPLICIT NONE
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REAL(8), INTENT(in):: xi(1:3)
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REAL(8), ALLOCATABLE:: dPsi(:,:)
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ALLOCATE(dPsi(1:2,1:4))
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dPsi(1,:) = dPsiQuadXi1(xi(2))
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dPsi(2,:) = dPsiQuadXi2(xi(1))
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END FUNCTION dPsiQuad
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!Derivative element function (xi1)
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PURE FUNCTION dPsiQuadXi1(xi2) RESULT(dPsiXi1)
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IMPLICIT NONE
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REAL(8),INTENT(in):: xi2
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REAL(8):: dPsiXi1(1:4)
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dPsiXi1(1) = -(1.D0-xi2)
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dPsiXi1(2) = (1.D0-xi2)
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dPsiXi1(3) = (1.D0+xi2)
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dPsiXi1(4) = -(1.D0+xi2)
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dPsiXi1 = dPsiXi1*0.25D0
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END FUNCTION dPsiQuadXi1
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!Derivative element function (xi2)
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PURE FUNCTION dPsiQuadXi2(xi1) RESULT(dPsiXi2)
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IMPLICIT NONE
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REAL(8),INTENT(in):: xi1
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REAL(8):: dPsiXi2(1:4)
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dPsiXi2(1) = -(1.D0-xi1)
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dPsiXi2(2) = -(1.D0+xi1)
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dPsiXi2(3) = (1.D0+xi1)
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dPsiXi2(4) = (1.D0-xi1)
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dPsiXi2 = dPsiXi2*0.25D0
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END FUNCTION dPsiQuadXi2
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!Partial derivative in global coordinates
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PURE SUBROUTINE partialDerQuad(self, dPsi, dz, dr)
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IMPLICIT NONE
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CLASS(meshVol2DCylQuad), INTENT(in):: self
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REAL(8), INTENT(in):: dPsi(1:,1:)
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REAL(8), INTENT(out), DIMENSION(1:2):: dz, dr
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dz(1) = DOT_PRODUCT(dPsi(1,:),self%z)
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dz(2) = DOT_PRODUCT(dPsi(2,:),self%z)
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dr(1) = DOT_PRODUCT(dPsi(1,:),self%r)
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dr(2) = DOT_PRODUCT(dPsi(2,:),self%r)
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END SUBROUTINE partialDerQuad
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!Random position in quadrilateral volume
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FUNCTION randPosVolQuad(self) RESULT(r)
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USE moduleRandom
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IMPLICIT NONE
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CLASS(meshVol2DCylQuad), INTENT(in):: self
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REAL(8):: r(1:3)
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REAL(8):: xii(1:3)
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REAL(8), ALLOCATABLE:: fPsi(:)
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xii(1) = random(-1.D0, 1.D0)
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xii(2) = random(-1.D0, 1.D0)
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xii(3) = 0.D0
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fPsi = self%fPsi(xii)
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r(1) = DOT_PRODUCT(fPsi, self%z)
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r(2) = DOT_PRODUCT(fPsi, self%r)
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r(3) = 0.D0
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END FUNCTION randposVolQuad
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!Computes element local stiffness matrix
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PURE FUNCTION elemKQuad(self) RESULT(ke)
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USE moduleConstParam, ONLY: PI2
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IMPLICIT NONE
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CLASS(meshVol2DCylQuad), INTENT(in):: self
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REAL(8):: r, xi(1:3)
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REAL(8):: fPsi(1:4), dPsi(1:2,1:4)
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REAL(8):: ke(1:4,1:4)
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REAL(8):: invJ(1:2,1:2), detJ
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INTEGER:: l, m
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ke=0.D0
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xi=0.D0
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!Start 2D Gauss Quad Integral
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DO l=1, 3
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xi(2) = corQuad(l)
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dPsi(1,:) = self%dPsiXi1(xi(2))
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DO m = 1, 3
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xi(1) = corQuad(m)
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dPsi(2,:) = self%dPsiXi2(xi(1))
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fPsi = self%fPsi(xi)
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detJ = self%detJac(xi,dPsi)
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invJ = self%invJac(xi,dPsi)
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r = DOT_PRODUCT(fPsi,self%r)
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ke = ke + MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)), &
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MATMUL(invJ,dPsi))* &
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r*wQuad(l)*wQuad(m)/detJ
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END DO
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END DO
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ke = ke*PI2
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END FUNCTION elemKQuad
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!Computes the local source vector for a force f
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PURE FUNCTION elemFQuad(self, source) RESULT(localF)
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USE moduleConstParam, ONLY: PI2
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylQuad), INTENT(in):: self
|
|
REAL(8), INTENT(in):: source(1:)
|
|
REAL(8), ALLOCATABLE:: localF(:)
|
|
REAL(8):: r, xi(1:3)
|
|
REAL(8):: fPsi(1:4)
|
|
REAL(8):: detJ, f
|
|
INTEGER:: l, m
|
|
|
|
ALLOCATE(localF(1:4))
|
|
localF = 0.D0
|
|
xi = 0.D0
|
|
DO l=1, 3
|
|
xi(1) = corQuad(l)
|
|
DO m = 1, 3
|
|
xi(2) = corQuad(m)
|
|
detJ = self%detJac(xi)
|
|
fPsi = self%fPsi(xi)
|
|
r = DOT_PRODUCT(fPsi,self%r)
|
|
f = DOT_PRODUCT(fPsi,source)
|
|
localF = localF + r*f*fPsi*wQuad(l)*wQuad(m)*detJ
|
|
|
|
END DO
|
|
END DO
|
|
localF = localF*PI2
|
|
|
|
END FUNCTION elemFQuad
|
|
|
|
!Computes weights in the element nodes
|
|
PURE FUNCTION weightQuad(xi) RESULT(w)
|
|
IMPLICIT NONE
|
|
|
|
REAL(8), INTENT(in):: xi(1:3)
|
|
REAL(8):: w(1:4)
|
|
|
|
w = fPsiQuad(xi)
|
|
|
|
END FUNCTION weightQuad
|
|
|
|
!Checks if a particle is inside a quad element
|
|
PURE FUNCTION insideQuad(xi) RESULT(ins)
|
|
IMPLICIT NONE
|
|
|
|
REAL(8), INTENT(in):: xi(1:3)
|
|
LOGICAL:: ins
|
|
|
|
ins = (xi(1) >= -1.D0 .AND. xi(1) <= 1.D0) .AND. &
|
|
(xi(2) >= -1.D0 .AND. xi(2) <= 1.D0)
|
|
|
|
END FUNCTION insideQuad
|
|
|
|
!Scatter properties of particle into element nodes
|
|
SUBROUTINE scatterQuad(self, part)
|
|
USE moduleOutput
|
|
USE moduleSpecies
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylQuad), INTENT(in):: self
|
|
CLASS(particle), INTENT(in):: part
|
|
TYPE(outputNode), POINTER:: vertex
|
|
REAL(8):: w_p(1:4)
|
|
REAL(8):: tensorS(1:3,1:3)
|
|
|
|
w_p = self%weight(part%xi)
|
|
tensorS = outerProduct(part%v, part%v)
|
|
|
|
vertex => self%n1%output(part%sp)
|
|
vertex%den = vertex%den + part%weight*w_p(1)
|
|
vertex%mom(:) = vertex%mom(:) + part%weight*w_p(1)*part%v(:)
|
|
vertex%tensorS(:,:) = vertex%tensorS(:,:) + part%weight*w_p(1)*tensorS
|
|
|
|
vertex => self%n2%output(part%sp)
|
|
vertex%den = vertex%den + part%weight*w_p(2)
|
|
vertex%mom(:) = vertex%mom(:) + part%weight*w_p(2)*part%v(:)
|
|
vertex%tensorS(:,:) = vertex%tensorS(:,:) + part%weight*w_p(2)*tensorS
|
|
|
|
vertex => self%n3%output(part%sp)
|
|
vertex%den = vertex%den + part%weight*w_p(3)
|
|
vertex%mom(:) = vertex%mom(:) + part%weight*w_p(3)*part%v(:)
|
|
vertex%tensorS(:,:) = vertex%tensorS(:,:) + part%weight*w_p(3)*tensorS
|
|
|
|
vertex => self%n4%output(part%sp)
|
|
vertex%den = vertex%den + part%weight*w_p(4)
|
|
vertex%mom(:) = vertex%mom(:) + part%weight*w_p(4)*part%v(:)
|
|
vertex%tensorS(:,:) = vertex%tensorS(:,:) + part%weight*w_p(4)*tensorS
|
|
|
|
END SUBROUTINE scatterQuad
|
|
|
|
!Gathers the electric field at position xi
|
|
PURE FUNCTION gatherEFQuad(self,xi) RESULT(EF)
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylQuad), INTENT(in):: self
|
|
REAL(8), INTENT(in):: xi(1:3)
|
|
REAL(8):: dPsi(1:2,1:4)
|
|
REAL(8):: dPsiR(1:2,1:4)!Derivative of shpae functions in global coordinates
|
|
REAL(8):: invJ(1:2,1:2), detJ
|
|
REAL(8):: phi(1:4)
|
|
REAL(8):: EF(1:3)
|
|
|
|
phi = (/self%n1%emData%phi, &
|
|
self%n2%emData%phi, &
|
|
self%n3%emData%phi, &
|
|
self%n4%emData%phi /)
|
|
|
|
dPsi = self%dPsi(xi)
|
|
detJ = self%detJac(xi,dPsi)
|
|
invJ = self%invJac(xi,dPsi)
|
|
dPsiR = MATMUL(invJ, dPsi)/detJ
|
|
EF(1) = -DOT_PRODUCT(dPsiR(1,:), phi)
|
|
EF(2) = -DOT_PRODUCT(dPsiR(2,:), phi)
|
|
EF(3) = 0.D0
|
|
|
|
END FUNCTION gatherEFQuad
|
|
|
|
!Gets nodes from quadrilateral element
|
|
PURE FUNCTION getNodesQuad(self) RESULT(n)
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylQuad), INTENT(in):: self
|
|
INTEGER, ALLOCATABLE:: n(:)
|
|
|
|
ALLOCATE(n(1:4))
|
|
n = (/self%n1%n, self%n2%n, self%n3%n, self%n4%n /)
|
|
|
|
END FUNCTION getNodesQuad
|
|
|
|
!Transforms physical coordinates to element coordinates
|
|
PURE FUNCTION phy2logQuad(self,r) RESULT(xN)
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylQuad), INTENT(in):: self
|
|
REAL(8), INTENT(in):: r(1:3)
|
|
REAL(8):: xN(1:3)
|
|
REAL(8):: xO(1:3), detJ, invJ(1:2,1:2), f(1:2)
|
|
REAL(8):: dPsi(1:2,1:4), fPsi(1:4)
|
|
REAL(8):: conv
|
|
|
|
!Iterative newton method to transform coordinates
|
|
conv=1.D0
|
|
xO=0.D0
|
|
|
|
DO WHILE(conv>1.D-4)
|
|
dPsi = self%dPsi(xO)
|
|
invJ = self%invJac(xO, dPsi)
|
|
fPsi = self%fPsi(xO)
|
|
f(1) = DOT_PRODUCT(fPsi,self%z)-r(1)
|
|
f(2) = DOT_PRODUCT(fPsi,self%r)-r(2)
|
|
detJ = self%detJac(xO,dPsi)
|
|
xN(1:2)=xO(1:2) - MATMUL(invJ, f)/detJ
|
|
conv=MAXVAL(DABS(xN-xO),1)
|
|
xO=xN
|
|
|
|
END DO
|
|
|
|
END FUNCTION phy2logQuad
|
|
|
|
!Gets the next element for a logical position xi
|
|
SUBROUTINE nextElementQuad(self, xi, nextElement)
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylQuad), INTENT(in):: self
|
|
REAL(8), INTENT(in):: xi(1:3)
|
|
CLASS(*), POINTER, INTENT(out):: nextElement
|
|
REAL(8):: xiArray(1:4)
|
|
INTEGER:: nextInt
|
|
|
|
xiArray = (/ -xi(2), xi(1), xi(2), -xi(1) /)
|
|
nextInt = MAXLOC(xiArray,1)
|
|
!Selects the higher value of directions and searches in that direction
|
|
NULLIFY(nextElement)
|
|
SELECT CASE (nextInt)
|
|
CASE (1)
|
|
nextElement => self%e1
|
|
CASE (2)
|
|
nextElement => self%e2
|
|
CASE (3)
|
|
nextElement => self%e3
|
|
CASE (4)
|
|
nextElement => self%e4
|
|
END SELECT
|
|
|
|
END SUBROUTINE nextElementQuad
|
|
|
|
!TRIA ELEMENT
|
|
!Init tria element
|
|
SUBROUTINE initVolTria2DCyl(self, n, p)
|
|
USE moduleRefParam
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylTria), INTENT(out):: self
|
|
INTEGER, INTENT(in):: n
|
|
INTEGER, INTENT(in):: p(:)
|
|
REAL(8), DIMENSION(1:3):: r1, r2, r3
|
|
|
|
!Assign node index
|
|
self%n = n
|
|
|
|
!Assign nodes to element
|
|
self%n1 => mesh%nodes(p(1))%obj
|
|
self%n2 => mesh%nodes(p(2))%obj
|
|
self%n3 => mesh%nodes(p(3))%obj
|
|
!Get element coordinates
|
|
r1 = self%n1%getCoordinates()
|
|
r2 = self%n2%getCoordinates()
|
|
r3 = self%n3%getCoordinates()
|
|
self%z = (/r1(1), r2(1), r3(1)/)
|
|
self%r = (/r1(2), r2(2), r3(2)/)
|
|
!Assign node volume
|
|
CALL self%area()
|
|
self%n1%v = self%n1%v + self%arNodes(1)
|
|
self%n2%v = self%n2%v + self%arNodes(2)
|
|
self%n3%v = self%n3%v + self%arNodes(3)
|
|
|
|
self%sigmaVrelMax = sigma_ref/L_ref**2
|
|
|
|
CALL OMP_INIT_LOCK(self%lock)
|
|
|
|
END SUBROUTINE initVolTria2DCyl
|
|
|
|
!Random position in quadrilateral volume
|
|
FUNCTION randPosVolTria(self) RESULT(r)
|
|
USE moduleRandom
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylTria), INTENT(in):: self
|
|
REAL(8):: r(1:3)
|
|
REAL(8):: xii(1:3)
|
|
REAL(8), ALLOCATABLE:: fPsi(:)
|
|
|
|
xii(1) = random( 0.D0, 1.D0)
|
|
xii(2) = random( 0.D0, 1.D0)
|
|
xii(3) = 0.D0
|
|
|
|
ALLOCATE(fPsi(1:3))
|
|
fPsi = self%fPsi(xii)
|
|
|
|
r(1) = DOT_PRODUCT(fPsi, self%z)
|
|
r(2) = DOT_PRODUCT(fPsi, self%r)
|
|
r(3) = 0.D0
|
|
|
|
END FUNCTION randposVolTria
|
|
|
|
!Calculates area for triangular element
|
|
PURE SUBROUTINE areaTria(self)
|
|
USE moduleConstParam, ONLY: PI
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylTria), INTENT(inout):: self
|
|
REAL(8):: r, xi(1:3)
|
|
REAL(8):: detJ
|
|
REAL(8):: fPsi(1:3)
|
|
|
|
self%volume = 0.D0
|
|
self%arNodes = 0.D0
|
|
!2D 1 point Gauss Quad Integral
|
|
xi = (/1.D0/3.D0, 1.D0/3.D0, 0.D0 /)
|
|
detJ = self%detJac(xi)*PI !2PI*1/2
|
|
fPsi = self%fPsi(xi)
|
|
r = DOT_PRODUCT(fPsi,self%r)
|
|
self%volume = r*detJ
|
|
self%arNodes = fPsi*r*detJ
|
|
|
|
END SUBROUTINE areaTria
|
|
|
|
!Shape functions for triangular element
|
|
PURE FUNCTION fPsiTria(xi) RESULT(fPsi)
|
|
IMPLICIT NONE
|
|
|
|
REAL(8), INTENT(in):: xi(1:3)
|
|
REAL(8), ALLOCATABLE:: fPsi(:)
|
|
|
|
ALLOCATE(fPsi(1:3))
|
|
|
|
fPsi(1) = 1.D0 - xi(1) - xi(2)
|
|
fPsi(2) = xi(1)
|
|
fPsi(3) = xi(2)
|
|
|
|
END FUNCTION fPsiTria
|
|
|
|
!Derivative element function at coordinates xi
|
|
PURE FUNCTION dPsiTria(xi) RESULT(dPsi)
|
|
IMPLICIT NONE
|
|
|
|
REAL(8), INTENT(in):: xi(1:3)
|
|
REAL(8), ALLOCATABLE:: dPsi(:,:)
|
|
|
|
ALLOCATE(dPsi(1:2,1:3))
|
|
|
|
dPsi(1,:) = dPsiTriaXi1(xi(2))
|
|
dPsi(2,:) = dPsiTriaXi2(xi(1))
|
|
|
|
END FUNCTION dPsiTria
|
|
|
|
!Derivative element function (xi1)
|
|
PURE FUNCTION dPsiTriaXi1(xi2) RESULT(dPsiXi1)
|
|
IMPLICIT NONE
|
|
|
|
REAL(8), INTENT(in):: xi2
|
|
REAL(8):: dPsiXi1(1:3)
|
|
|
|
dPsiXi1(1) = -1.D0
|
|
dPsiXi1(2) = 1.D0
|
|
dPsiXi1(3) = 0.D0
|
|
|
|
END FUNCTION dPsiTriaXi1
|
|
|
|
!Derivative element function (xi1)
|
|
PURE FUNCTION dPsiTriaXi2(xi1) RESULT(dPsiXi2)
|
|
IMPLICIT NONE
|
|
|
|
REAL(8), INTENT(in):: xi1
|
|
REAL(8):: dPsiXi2(1:3)
|
|
|
|
dPsiXi2(1) = -1.D0
|
|
dPsiXi2(2) = 0.D0
|
|
dPsiXi2(3) = 1.D0
|
|
|
|
END FUNCTION dPsiTriaXi2
|
|
|
|
PURE SUBROUTINE partialDerTria(self, dPsi, dz, dr)
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylTria), INTENT(in):: self
|
|
REAL(8), INTENT(in):: dPsi(1:,1:)
|
|
REAL(8), INTENT(out), DIMENSION(1:2):: dz, dr
|
|
|
|
dz(1) = DOT_PRODUCT(dPsi(1,:),self%z)
|
|
dz(2) = DOT_PRODUCT(dPsi(2,:),self%z)
|
|
dr(1) = DOT_PRODUCT(dPsi(1,:),self%r)
|
|
dr(2) = DOT_PRODUCT(dPsi(2,:),self%r)
|
|
|
|
END SUBROUTINE partialDerTria
|
|
|
|
!Computes element local stiffness matrix
|
|
PURE FUNCTION elemKTria(self) RESULT(ke)
|
|
USE moduleConstParam, ONLY: PI2
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylTria), INTENT(in):: self
|
|
REAL(8):: r, xi(1:3)
|
|
REAL(8):: fPsi(1:3), dPsi(1:2,1:3)
|
|
REAL(8):: ke(1:3,1:3)
|
|
REAL(8):: invJ(1:2,1:2), detJ
|
|
INTEGER:: l
|
|
|
|
ke=0.D0
|
|
xi=0.D0
|
|
!Start 2D Gauss Quad Integral
|
|
DO l=1, 4
|
|
xi(1) = xi1Tria(l)
|
|
xi(2) = xi2Tria(l)
|
|
dPsi = self%dPsi(xi)
|
|
detJ = self%detJac(xi,dPsi)
|
|
invJ = self%invJac(xi,dPsi)
|
|
fPsi = self%fPsi(xi)
|
|
r = DOT_PRODUCT(fPsi,self%r)
|
|
ke = ke + MATMUL(TRANSPOSE(MATMUL(invJ,dPsi)),MATMUL(invJ,dPsi))*r*wTria(l)/detJ
|
|
|
|
END DO
|
|
ke = ke*PI2
|
|
|
|
END FUNCTION elemKTria
|
|
|
|
!Computes element local source vector
|
|
PURE FUNCTION elemFTria(self, source) RESULT(localF)
|
|
USE moduleConstParam, ONLY: PI2
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylTria), INTENT(in):: self
|
|
REAL(8), INTENT(in):: source(1:)
|
|
REAL(8), ALLOCATABLE:: localF(:)
|
|
REAL(8):: fPsi(1:3)
|
|
REAL(8):: r, xi(1:3)
|
|
REAL(8):: detJ, f
|
|
INTEGER:: l
|
|
|
|
ALLOCATE(localF(1:3))
|
|
localF = 0.D0
|
|
xi = 0.D0
|
|
!Start 2D Gauss Quad Integral
|
|
DO l=1, 4
|
|
xi(1) = xi1Tria(l)
|
|
xi(2) = xi2Tria(l)
|
|
detJ = self%detJac(xi)
|
|
fPsi = self%fPsi(xi)
|
|
r = DOT_PRODUCT(fPsi,self%r)
|
|
f = DOT_PRODUCT(fPsi,source)
|
|
localF = localF + r*f*fPsi*wTria(l)*detJ
|
|
|
|
END DO
|
|
localF = localF*PI2
|
|
|
|
END FUNCTION elemFTria
|
|
|
|
!Computes weights in the element nodes
|
|
PURE FUNCTION weightTria(xi) RESULT(w)
|
|
IMPLICIT NONE
|
|
|
|
REAL(8), INTENT(in):: xi(1:3)
|
|
REAL(8), ALLOCATABLE:: w(:)
|
|
|
|
w = fPsiTria(xi)
|
|
|
|
END FUNCTION weightTria
|
|
|
|
PURE FUNCTION insideTria(xi) RESULT(ins)
|
|
IMPLICIT NONE
|
|
|
|
REAL(8), INTENT(in):: xi(1:3)
|
|
LOGICAL:: ins
|
|
|
|
ins = xi(1) >= 0.D0 .AND. &
|
|
xi(2) >= 0.D0 .AND. &
|
|
1.D0 - xi(1) - xi(2) >= 0.D0
|
|
|
|
END FUNCTION insideTria
|
|
|
|
!Scatter properties of particles into element
|
|
SUBROUTINE scatterTria(self, part)
|
|
USE moduleOutput
|
|
USE moduleSpecies
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylTria), INTENT(in):: self
|
|
CLASS(particle), INTENT(in):: part
|
|
TYPE(outputNode), POINTER:: vertex
|
|
REAL(8):: w_p(1:3)
|
|
REAL(8):: tensorS(1:3,1:3)
|
|
|
|
w_p = self%weight(part%xi)
|
|
tensorS = outerProduct(part%v, part%v)
|
|
|
|
vertex => self%n1%output(part%sp)
|
|
vertex%den = vertex%den + part%weight*w_p(1)
|
|
vertex%mom(:) = vertex%mom(:) + part%weight*w_p(1)*part%v(:)
|
|
vertex%tensorS(:,:) = vertex%tensorS(:,:) + part%weight*w_p(1)*tensorS
|
|
|
|
vertex => self%n2%output(part%sp)
|
|
vertex%den = vertex%den + part%weight*w_p(2)
|
|
vertex%mom(:) = vertex%mom(:) + part%weight*w_p(2)*part%v(:)
|
|
vertex%tensorS(:,:) = vertex%tensorS(:,:) + part%weight*w_p(2)*tensorS
|
|
|
|
vertex => self%n3%output(part%sp)
|
|
vertex%den = vertex%den + part%weight*w_p(3)
|
|
vertex%mom(:) = vertex%mom(:) + part%weight*w_p(3)*part%v(:)
|
|
vertex%tensorS(:,:) = vertex%tensorS(:,:) + part%weight*w_p(3)*tensorS
|
|
|
|
END SUBROUTINE scatterTria
|
|
|
|
!Gathers the electric field at position xi
|
|
PURE FUNCTION gatherEFTria(self,xi) RESULT(EF)
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylTria), INTENT(in):: self
|
|
REAL(8), INTENT(in):: xi(1:3)
|
|
REAL(8):: dPsi(1:2,1:3)
|
|
REAL(8):: dPsiR(1:2,1:3)!Derivative of shpae functions in global coordinates
|
|
REAL(8):: invJ(1:2,1:2), detJ
|
|
REAL(8):: phi(1:3)
|
|
REAL(8):: EF(1:3)
|
|
|
|
phi = (/self%n1%emData%phi, &
|
|
self%n2%emData%phi, &
|
|
self%n3%emData%phi /)
|
|
|
|
dPsi = self%dPsi(xi)
|
|
detJ = self%detJac(xi,dPsi)
|
|
invJ = self%invJac(xi,dPsi)
|
|
dPsiR = MATMUL(invJ, dPsi)/detJ
|
|
EF(1) = -DOT_PRODUCT(dPsiR(1,:), phi)
|
|
EF(2) = -DOT_PRODUCT(dPsiR(2,:), phi)
|
|
EF(3) = 0.D0
|
|
|
|
END FUNCTION gatherEFTria
|
|
|
|
!Gets node indexes from triangular element
|
|
PURE FUNCTION getNodesTria(self) RESULT(n)
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylTria), INTENT(in):: self
|
|
INTEGER, ALLOCATABLE:: n(:)
|
|
|
|
ALLOCATE(n(1:3))
|
|
n = (/self%n1%n, self%n2%n, self%n3%n /)
|
|
|
|
END FUNCTION getNodesTria
|
|
|
|
!Transforms physical coordinates to element coordinates
|
|
PURE FUNCTION phy2logTria(self,r) RESULT(xi)
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylTria), INTENT(in):: self
|
|
REAL(8), INTENT(in):: r(1:3)
|
|
REAL(8):: xi(1:3)
|
|
REAL(8):: invJ(1:2,1:2), detJ
|
|
REAL(8):: deltaR(1:2)
|
|
REAL(8):: dPsi(1:2,1:3)
|
|
|
|
!Direct method to convert coordinates
|
|
xi = 0.D0 !Irrelevant, required for input
|
|
deltaR = (/ r(1) - self%z(1), r(2) - self%r(1) /)
|
|
dPsi = self%dPsi(xi)
|
|
invJ = self%invJac(xi, dPsi)
|
|
detJ = self%detJac(xi, dPsi)
|
|
xi(1:2) = MATMUL(invJ,deltaR)/detJ
|
|
|
|
END FUNCTION phy2logTria
|
|
|
|
SUBROUTINE nextElementTria(self, xi, nextElement)
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCylTria), INTENT(in):: self
|
|
REAL(8), INTENT(in):: xi(1:3)
|
|
CLASS(*), POINTER, INTENT(out):: nextElement
|
|
REAL(8):: xiArray(1:3)
|
|
INTEGER:: nextInt
|
|
|
|
xiArray = (/ xi(2), 1.D0-xi(1)-xi(2), xi(1) /)
|
|
nextInt = MINLOC(xiArray,1)
|
|
NULLIFY(nextElement)
|
|
SELECT CASE (nextInt)
|
|
CASE (1)
|
|
nextElement => self%e1
|
|
CASE (2)
|
|
nextElement => self%e2
|
|
CASE (3)
|
|
nextElement => self%e3
|
|
END SELECT
|
|
|
|
END SUBROUTINE nextElementTria
|
|
|
|
!COMMON FUNCTIONS FOR CYLINDRICAL VOLUME ELEMENTS
|
|
!Computes element Jacobian determinant
|
|
PURE FUNCTION detJ2DCyl(self, xi, dPsi_in) RESULT(dJ)
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCyl), INTENT(in):: self
|
|
REAL(8), INTENT(in):: xi(1:3)
|
|
REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:,1:)
|
|
REAL(8), ALLOCATABLE:: dPsi(:,:)
|
|
REAL(8):: dJ
|
|
REAL(8):: dz(1:2), dr(1:2)
|
|
|
|
IF(PRESENT(dPsi_in)) THEN
|
|
dPsi = dPsi_in
|
|
|
|
ELSE
|
|
dPsi = self%dPsi(xi)
|
|
|
|
END IF
|
|
|
|
CALL self%partialDer(dPsi, dz, dr)
|
|
dJ = dz(1)*dr(2)-dz(2)*dr(1)
|
|
|
|
END FUNCTION detJ2DCyl
|
|
|
|
!Computes element Jacobian inverse matrix (without determinant)
|
|
PURE FUNCTION invJ2DCyl(self,xi,dPsi_in) RESULT(invJ)
|
|
IMPLICIT NONE
|
|
|
|
CLASS(meshVol2DCyl), INTENT(in):: self
|
|
REAL(8), INTENT(in):: xi(1:3)
|
|
REAL(8), INTENT(in), OPTIONAL:: dPsi_in(1:,1:)
|
|
REAL(8), ALLOCATABLE:: dPsi(:,:)
|
|
REAL(8):: dz(1:2), dr(1:2)
|
|
REAL(8):: invJ(1:2,1:2)
|
|
|
|
IF(PRESENT(dPsi_in)) THEN
|
|
dPsi=dPsi_in
|
|
|
|
ELSE
|
|
dPsi = self%dPsi(xi)
|
|
|
|
END IF
|
|
|
|
CALL self%partialDer(dPsi, dz, dr)
|
|
invJ(1,:) = (/ dr(2), -dz(2) /)
|
|
invJ(2,:) = (/ -dr(1), dz(1) /)
|
|
|
|
END FUNCTION invJ2DCyl
|
|
|
|
END MODULE moduleMesh2DCyl
|