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I hate Coulomb and his Scattering

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I found no way to ensure conservation in the linear Coulomb operator.
Thus, now two collisions have to be declared if sp_i /= sp_j: collision
ij and collision ji.

This does not conserve energy so please use under your own risk, like
everything else.

Still, I think something is wrong with this implementation and I'm
really tired.
This commit is contained in:
Jorge Gonzalez 2023-07-07 16:36:31 +02:00
commit a26dc04051
2 changed files with 5 additions and 105 deletions
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101
src/modules/mesh/moduleMesh.f90
View file

@ -975,7 +975,7 @@ MODULE moduleMesh
REAL(8):: delta_par, delta_par_square, delta_per, delta_per_square
REAL(8):: W(3), dW(2), normW !Relative velocity between particle and species and its increment
REAL(8):: l2, l, lW, AW
REAL(8):: deltaV(1:3), totalDeltaV_ij, normDeltaV
REAL(8):: deltaV(1:3)
REAL(8):: rnd
REAL(8):: eps = 1.D-10
@ -1005,7 +1005,6 @@ MODULE moduleMesh
END DO
!Loop over particles of species_i
totalDeltaV_ij = 0.D0
partTemp => cell%listPart_in(i)%head
DO WHILE(ASSOCIATED(partTemp))
density = cell%gatherF(partTemp%part%Xi, cell%nNodes, densityNodes)
@ -1026,6 +1025,7 @@ MODULE moduleMesh
W = partTemp%part%v - velocity
normW = NORM2(W)
!If relative velocity is too low, skip collision to avoid division by zero and move to next particle
IF (normW < eps) THEN
partTemp => partTemp%next
@ -1063,8 +1063,6 @@ MODULE moduleMesh
deltaV = dW(1)*e1 + dW(2)*(COS(rnd)*e2 + SIN(rnd)*e3)
totalDeltaV_ij = totalDeltaV_ij + NORM2(deltaV)
!Change particle velocity
partTemp%part%v = partTemp%part%v + deltaV
@ -1072,101 +1070,6 @@ MODULE moduleMesh
END DO
!Do scattering of particles from species_j due to species i
IF (i /= j) THEN
!Compute background properties of species_i
DO n = 1, cell%nNodes
node => self%nodes(cellNodes(n))%obj
CALL calculateOutput(node%output(i), output, node%v, coulombMatrix(k)%sp_i)
densityNodes(n) = output%density/n_ref
velocityNodes(n,1:3) = output%velocity(1:3)/v_ref
temperatureNodes(n) = output%temperature/T_ref
END DO
!Divide total momentum exchanged among all the particles of species j
!TODO: This is a dirty trick to ensure conservation between species
normDeltaV = totalDeltaV_ij / REAL(cell%listPart_in(j)%amount) * &
(coulombMatrix(k)%sp_i%weight*coulombMatrix(k)%sp_i%m) / &
(coulombMatrix(k)%sp_j%weight*coulombMatrix(k)%sp_j%m)
!Loop over particles of species_j
partTemp => cell%listPart_in(j)%head
DO WHILE(ASSOCIATED(partTemp))
density = cell%gatherF(partTemp%part%Xi, cell%nNodes, densityNodes)
velocity = cell%gatherF(partTemp%part%Xi, cell%nNodes, velocityNodes)
temperature = cell%gatherF(partTemp%part%Xi, cell%nNodes, temperatureNodes)
!If cell temperature is too low, skip particle to avoid division by zero
IF (temperature>eps) THEN
l2 = coulombMatrix(k)%l2_i/temperature
l = SQRT(l2)
ELSE
partTemp => partTemp%next
CYCLE
END IF
W = partTemp%part%v - velocity
normW = NORM2(W)
!If relative velocity is too low, skip collision and move to next particle
IF (normW < eps) THEN
partTemp => partTemp%next
CYCLE
END IF
lW = l * normW
AW = coulombMatrix(k)%A_j/normW
delta_par = -coulombMatrix(k)%A_j*coulombMatrix(k)%one_plus_massRatio_ji*density*l2*G(lW)
delta_par_square = AW*density*G(lW)
delta_per_square = AW*density*H(lW)
dW(1) = delta_par*tauMin + randomMaxwellian()*SQRT(delta_par_square*tauMin)
dW(2) = ABS(randomMaxwellian()*SQRT(delta_per_square*tauMin))
!Normalize with average exchange per particle
!TODO: This is a dirty trick to ensure conservation between species
IF (NORM2(dW) > eps) THEN
dW = normDeltaV*dW/NORM2(dW)
ELSE
dW = 0.D0
END IF
!System of reference for the velocity change
!First one is parallel to the relative velocity
e1 = normalize(W)
!Second one is perpendicular to it
e2(1) = -e1(2)
e2(2) = e1(1)
e2(3) = 0.D0
e2 = normalize(e2)
!Third one is perpendicular to the other two
e3 = crossProduct(e1, e2)
e3 = normalize(e3)
!Random number for direction
rnd = PI2*random()
deltaV = dW(1)*e1 + dW(2)*(COS(rnd)*e2 + SIN(rnd)*e3)
!Change particle velocity
partTemp%part%v = partTemp%part%v + deltaV
partTemp => partTemp%next
END DO
END IF
END DO
DEALLOCATE(densityNodes, velocityNodes, temperatureNodes, cellNodes)

9
src/modules/moduleCoulomb.f90
View file

@ -8,10 +8,10 @@ MODULE moduleCoulomb
TYPE:: interactionsCoulomb
CLASS(speciesGeneric), POINTER:: sp_i
CLASS(speciesGeneric), POINTER:: sp_j
REAL(8):: one_plus_massRatio_ij, one_plus_massRatio_ji
REAL(8):: one_plus_massRatio_ij
REAL(8):: lnCoulomb !This can be done a function in the future
REAL(8):: A_i, A_j
REAL(8):: l2_j, l2_i
REAL(8):: A_i
REAL(8):: l2_j
CONTAINS
PROCEDURE, PASS:: init => initInteractionCoulomb
@ -60,7 +60,6 @@ MODULE moduleCoulomb
self%sp_j => species(j)%obj
self%one_plus_massRatio_ij = 1.D0 + (self%sp_i%weight*self%sp_i%m)/(self%sp_j%weight*self%sp_j%m)
self%one_plus_massRatio_ji = 1.D0 + (self%sp_j%weight*self%sp_j%m)/(self%sp_i%weight*self%sp_i%m)
SELECT TYPE(sp => self%sp_i)
TYPE IS (speciesCharged)
@ -85,10 +84,8 @@ MODULE moduleCoulomb
scaleFactor = (n_ref * qe**4) / (eps_0**2 * m_ref**2 * v_ref**3) * ti_ref
self%A_i = 2.D0*Z_i**2*Z_j**2*self%lnCoulomb / self%sp_i%m**2 * scaleFactor
self%A_j = 2.D0*Z_j**2*Z_i**2*self%lnCoulomb / self%sp_j%m**2 * scaleFactor
self%l2_j = self%sp_j%m / 2.D0 !Missing temperature because it's cell dependent
self%l2_i = self%sp_i%m / 2.D0 !Missing temperature because it's cell dependent
END SUBROUTINE initInteractionCoulomb