Issue with random position in volumes

Fixed an issue in which  the position in triangular an thetrahedron
elements were not correctly being computed.

Other minor issues fixed:
  - Units in input file now do not use '/'.
  - Collisions accuratly conserve momentum.
  - Minor improvements in mass calculation in collisions.

runs/0D_Argon/curve_Temperature.gp

@@ -0,0 +1,64 @@
+reset
+set macros
+term = 'postscript eps color enhanced'
+font = 'font "CMUSerif-Roman,20"'
+linew = 'lw 2.0'
+times='"{/Symbol \264}"'
+size_x=8.5
+size_y=5.2
+
+tmar=0.998
+bmar=0.145
+
+lmarLabel = 0.070
+
+lmar=lmarLabel+0.085
+rmar=0.97
+
+space_x=(rmar-lmar)
+
+xt_off_0=0.5
+yt_off_0=0.6
+
+set xtics nomirror offset 0.0,xt_off_0
+set mxtics 2
+
+set ytics nomirror offset yt_off_0,0.0
+set mytics 2
+
+set pointsize 1.5
+
+set style line 1  pt 4              lc rgb "#B50427" #Squares   red
+set style line 2  pt 6              lc rgb "#3B4CC1" #Circles   blue
+set style line 3  pt 1              lc rgb "#2CA02C" #Crosses   green
+set style line 4  pt 2              lc rgb "#FE7F0E" #Exes      orange
+set style line 5  pt 8              lc rgb "#D6696B" #Triangles light red
+set style line 10       lt 1 lw 2.0 lc rgb "black"   #Black solid line
+
+set terminal @term size size_x cm, size_y cm @linew @font
+
+set output "comp_temp.eps"
+
+#files
+filename1 = "OUTPUT_Argon.dat"
+filename2 = "OUTPUT_Argon+.dat"
+
+set lmargin at screen lmar 
+set rmargin at screen rmar
+
+set xrange [-0.01:1.01]
+set xtics 0.2
+set xlabel "Time (s)" offset 0.0,1.2
+
+set yrange [250:3550]
+set format y "%3.0f"
+set ytics 500
+set ylabel "Temperature (K)" offset 1.4,0.0
+
+set key width 0.5 height 0.1 spacing 1.3 samplen 0.2 box opaque font ",16"
+set key at graph 0.95, graph 0.9 right top
+
+plot filename1 u ($1):($7)                                          t "Ar"     ls 1 with lines, \
+     filename2 u ($1):($7)                                          t "Ar^{+}" ls 2 with lines, \
+     '< paste OUTPUT_Argon.dat OUTPUT_Argon+.dat' u ($1):($7 + $14) t "Sum"    ls 3 with lines
+

src/modules/mesh/2DCart/moduleMesh2DCart.f90

@@ -622,7 +622,7 @@ MODULE moduleMesh2DCart
       REAL(8), ALLOCATABLE:: fPsi(:)
 
       xii(1) = random( 0.D0, 1.D0)
-      xii(2) = random( 0.D0, 1.D0)
+      xii(2) = random( 0.D0, 1.D0 - xii(1))
       xii(3) = 0.D0
 
       fPsi = self%fPsi(xii)

src/modules/mesh/2DCyl/moduleMesh2DCyl.f90

@@ -643,10 +643,9 @@ MODULE moduleMesh2DCyl
       REAL(8), ALLOCATABLE:: fPsi(:)
 
       xii(1) = random( 0.D0, 1.D0)
-      xii(2) = random( 0.D0, 1.D0)
+      xii(2) = random( 0.D0, 1.D0 - xii(1))
       xii(3) = 0.D0
 
-      ALLOCATE(fPsi(1:3))
       fPsi = self%fPsi(xii)
 
       r(1) = DOT_PRODUCT(fPsi, self%z)

src/modules/mesh/3DCart/moduleMesh3DCart.f90

@@ -215,7 +215,9 @@ MODULE moduleMesh3DCart
       REAL(8):: xii(1:3)
       REAL(8):: fPsi(1:3)
 
-      xii = (/random(), random(), 0.D0 /)
+      xii(1) = random( 0.D0, 1.D0)
+      xii(2) = random( 0.D0, 1.D0 - xii(1))
+      xii(3) = 0.D0
 
       fPsi = self%fPsi(xii)
       r = (/DOT_PRODUCT(fPsi, self%x), &
@@ -294,9 +296,9 @@ MODULE moduleMesh3DCart
       REAL(8):: xii(1:3)
       REAL(8), ALLOCATABLE:: fPsi(:)
 
-      xii(1) = random(0.D0, 1.D0)
+      xii(1) = random( 0.D0, 1.D0)
-      xii(2) = random(0.D0, 1.D0)
+      xii(2) = random( 0.D0, 1.D0 - xii(1))
-      xii(3) = random(0.D0, 1.D0)
+      xii(3) = random( 0.D0, 1.D0 - xii(1) - xii(2))
 
       ALLOCATE(fPsi(1:4))
       fPsi = self%fPsi(xii)

src/modules/mesh/inout/gmsh2/moduleMeshOutputGmsh2.f90

@@ -43,7 +43,7 @@ MODULE moduleMeshOutputGmsh2
         WRITE(60, "(A)") '$EndNodeData'
         WRITE(60, "(A)") '$NodeData'
         WRITE(60, "(A)") '1'
-        WRITE(60, "(A)") '"' // species(i)%obj%name // ' velocity (m/s)"'
+        WRITE(60, "(A)") '"' // species(i)%obj%name // ' velocity (m s^-1)"'
         WRITE(60, *) 1
         WRITE(60, *) time
         WRITE(60, *) 3
@@ -189,7 +189,7 @@ MODULE moduleMeshOutputGmsh2
         
         WRITE(20, "(A)") '$ElementData'
         WRITE(20, "(A)") '1'
-        WRITE(20, "(A)") '"Electric Field (V/m)"'
+        WRITE(20, "(A)") '"Electric Field (V m^-1)"'
         WRITE(20, *) 1
         WRITE(20, *) time
         WRITE(20, *) 3

src/modules/mesh/moduleMesh.f90

@@ -186,15 +186,6 @@ MODULE moduleMesh
 
     END SUBROUTINE initVol_interface
 
-    SUBROUTINE scatter_interface(self, part)
-      USE moduleSpecies
-      
-      IMPORT:: meshVol
-      CLASS(meshVol), INTENT(in):: self
-      CLASS(particle), INTENT(in):: part
-
-    END SUBROUTINE scatter_interface
-
     PURE FUNCTION gatherEF_interface(self, xi) RESULT(EF)
       IMPORT:: meshVol
       CLASS(meshVol), INTENT(in):: self
@@ -574,6 +565,7 @@ MODULE moduleMesh
 
     !TODO: try to combine this with the findCell for a regular mesh
     !Find the volume in which particle reside in the mesh for collisions
+    !No boundary interaction taken into account
     SUBROUTINE findCellCollMesh(part)
       USE moduleSpecies
       IMPLICIT NONE
@@ -669,7 +661,7 @@ MODULE moduleMesh
       DO e=1, self%numVols
         vol => self%vols(e)%obj
         nPart = vol%listPart_in%amount
-        !Computes iterations if there is more than one particle in the cell
+        !Calculates number of collisions if there is more than one particle in the cell
         IF (nPart > 1) THEN
           !Probability of collision
           pMax = vol%totalWeight*vol%sigmaVrelMax*tauMin/vol%volume

src/modules/moduleCollisions.f90

@@ -5,7 +5,7 @@ MODULE moduleCollisions
   !Abstract type for collision between two particles
   TYPE, ABSTRACT:: collisionBinary
     REAL(8):: rMass !Reduced mass
-    REAL(8):: sMass !Summed mass
+    REAL(8):: sMassInv !Summed mass
     TYPE(table1D):: crossSec !cross section of collision
     CONTAINS
       PROCEDURE(collideBinary_interface), PASS, DEFERRED:: collide
@@ -169,8 +169,8 @@ MODULE moduleCollisions
       CALL collision%crossSec%convert(eV2J/(m_ref*v_ref**2), 1.D0/L_ref**2)
 
       !Calculates reduced mass
-      collision%sMass =  mass_i+mass_j
+      collision%sMassInv =  1.D0/(mass_i+mass_j)
-      collision%rMass = (mass_i*mass_j)/collision%sMass
+      collision%rMass    = (mass_i*mass_j)*collision%sMassInv
 
     END SUBROUTINE initBinaryElastic
 
@@ -180,6 +180,7 @@ MODULE moduleCollisions
       USE moduleSpecies
       USE moduleConstParam
       USE moduleRandom
+      USE moduleMath
       IMPLICIT NONE
 
       CLASS(collisionBinaryElastic), INTENT(in):: self
@@ -193,7 +194,7 @@ MODULE moduleCollisions
       REAL(8), DIMENSION(1:3):: vCM
       REAL(8):: vp(1:3)
 
-      vRel = SUM(DABS(part_i%v-part_j%v)) !TODO make function of norm1
+      vRel = NORM2(part_i%v-part_j%v)
       eRel = self%rMass*vRel**2
       sigmaVrel = self%crossSec%get(eRel)*vRel
       sigmaVrelMaxNew = sigmaVrelMaxNew + sigmaVrel
@@ -205,8 +206,8 @@ MODULE moduleCollisions
         vp  = vRel*randomDirectionVHS()
 
         !Assign velocities to particles
-        part_i%v = vCM + m_j*vp/self%sMass
+        part_i%v = vCM + m_j*vp*self%sMassInv
-        part_j%v = vCM - m_i*vp/self%sMass
+        part_j%v = vCM - m_i*vp*self%sMassInv
 
       END IF
 
@@ -238,8 +239,8 @@ MODULE moduleCollisions
       CALL collision%crossSec%convert(eV2J/(m_ref*v_ref**2), 1.D0/L_ref**2)
 
       !Calculates reduced mass
-      collision%sMass =  mass_i+mass_j
+      collision%sMassInv =  1.D0/(mass_i+mass_j)
-      collision%rMass = (mass_i*mass_j)/collision%sMass
+      collision%rMass    = (mass_i*mass_j)*collision%sMassInv
 
       !Specific parameters for ionization collision
       SELECT TYPE(collision)
@@ -269,6 +270,7 @@ MODULE moduleCollisions
       USE moduleErrors
       USE moduleList
       USE moduleRandom
+      USE moduleMath
       USE OMP_LIB
       IMPLICIT NONE
 
@@ -283,7 +285,7 @@ MODULE moduleCollisions
       REAL(8), DIMENSION(1:3):: vp_e, vp_n
 
       !eRel (in units of [m][L]^2[t]^-2
-      vRel = SUM(DABS(part_i%v-part_j%v)) !TODO make function of norm1
+      vRel = NORM2(part_i%v-part_j%v)
       eRel = self%rMass*vRel**2
       !Relative energy must be higher than threshold
       IF (eRel > self%eThreshold) THEN
@@ -370,8 +372,8 @@ MODULE moduleCollisions
       CALL collision%crossSec%convert(eV2J/(m_ref*v_ref**2), 1.D0/L_ref**2)
 
       !Calculates reduced mass
-      collision%sMass =  mass_i+mass_j
+      collision%sMassInv =  1.D0/(mass_i+mass_j)
-      collision%rMass = (mass_i*mass_j)/collision%sMass
+      collision%rMass    = (mass_i*mass_j)*collision%sMassInv
 
       !Specific parameters for ionization collision
       SELECT TYPE(collision)
@@ -401,7 +403,7 @@ MODULE moduleCollisions
       USE moduleErrors
       USE moduleList
       USE moduleRandom
-      USE OMP_LIB
+      USE moduleMath
       IMPLICIT NONE
 
       CLASS(collisionBinaryRecombination), INTENT(in):: self
@@ -414,7 +416,7 @@ MODULE moduleCollisions
       REAL(8), DIMENSION(1:3):: vp_i
 
       !eRel (in units of [m][L]^2[t]^-2
-      vRel = SUM(DABS(part_i%v-part_j%v)) !TODO make function of norm1
+      vRel = NORM2(part_i%v-part_j%v)
       eRel = self%rMass*vRel**2
       !Relative energy must be higher than threshold
       sigmaVrel = self%crossSec%get(eRel)*vRel
@@ -476,8 +478,8 @@ MODULE moduleCollisions
       CALL collision%crossSec%convert(eV2J/(m_ref*v_ref**2), 1.D0/L_ref**2)
 
       !Calculates reduced mass
-      collision%sMass =  mass_i+mass_j
+      collision%sMassInv =  1.D0/(mass_i+mass_j)
-      collision%rMass = (mass_i*mass_j)/collision%sMass
+      collision%rMass    = (mass_i*mass_j)/collision%sMassInv
 
     END SUBROUTINE initBinaryChargeExchange
 
@@ -485,6 +487,7 @@ MODULE moduleCollisions
                                            part_i, part_j)
       USE moduleSpecies
       USE moduleRandom
+      USE moduleMath
       IMPLICIT NONE
 
       CLASS(collisionBinaryChargeExchange), INTENT(in):: self
@@ -496,7 +499,7 @@ MODULE moduleCollisions
       REAL(8):: eRel !relative energy
 
       !eRel (in units of [m][L]^2[t]^-2
-      vRel = SUM(DABS(part_i%v-part_j%v)) !TODO make function of norm1
+      vRel = NORM2(part_i%v-part_j%v)
       eRel = self%rMass*vRel**2
       sigmaVrel = self%crossSec%get(eRel)*vRel
       sigmaVrelMaxNew = sigmaVrelMaxNew + sigmaVrel