Correction with conservation
Now the method is much better in conserving total energy. However, still there is an issue with collisions between species of dispaprate mass.
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2 changed files with 59 additions and 47 deletions
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@ -966,7 +966,6 @@ MODULE moduleMesh
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INTEGER:: i, j
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INTEGER:: i, j
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INTEGER:: n
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INTEGER:: n
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TYPE(lNode), POINTER:: partTemp
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TYPE(lNode), POINTER:: partTemp
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REAL(8):: W(3), dW(2) !Relative velocity between particle and species and its increment
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INTEGER(8), ALLOCATABLE:: cellNodes(:)
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INTEGER(8), ALLOCATABLE:: cellNodes(:)
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CLASS(meshNode), POINTER:: node
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CLASS(meshNode), POINTER:: node
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TYPE(outputFormat):: output
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TYPE(outputFormat):: output
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@ -974,7 +973,8 @@ MODULE moduleMesh
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REAL(8):: density, velocity(1:3), temperature!values at particle position
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REAL(8):: density, velocity(1:3), temperature!values at particle position
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REAL(8), DIMENSION(1:3):: e1, e2, e3
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REAL(8), DIMENSION(1:3):: e1, e2, e3
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REAL(8):: delta_par, delta_par_square, delta_per, delta_per_square
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REAL(8):: delta_par, delta_par_square, delta_per, delta_per_square
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REAL(8):: l, lW, AW
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REAL(8):: W(3), dW(2), normW !Relative velocity between particle and species and its increment
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REAL(8):: l2, l, lW, AW
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REAL(8):: rnd
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REAL(8):: rnd
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@ -1007,12 +1007,25 @@ MODULE moduleMesh
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density = cell%gatherF(partTemp%part%Xi, cell%nNodes, densityNodes)
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density = cell%gatherF(partTemp%part%Xi, cell%nNodes, densityNodes)
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velocity = cell%gatherF(partTemp%part%Xi, cell%nNodes, velocityNodes)
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velocity = cell%gatherF(partTemp%part%Xi, cell%nNodes, velocityNodes)
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temperature = cell%gatherF(partTemp%part%Xi, cell%nNodes, temperatureNodes)
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temperature = cell%gatherF(partTemp%part%Xi, cell%nNodes, temperatureNodes)
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l = coulombMatrix(k)%l_j/SQRT(temperature)
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l2 = coulombMatrix(k)%l2_j/temperature
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l = SQRT(l2)
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W = partTemp%part%v - velocity
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W = partTemp%part%v - velocity
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lW = l * NORM2(W)
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normW = NORM2(W)
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AW = coulombMatrix(k)%A_ij/NORM2(W)
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lW = l * normW
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!Axis of the relative velocity
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AW = coulombMatrix(k)%A_i/normW
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delta_par = -coulombMatrix(k)%A_i*coulombMatrix(k)%one_plus_massRatio_ij*density*l2*G(lW)
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delta_par_square = AW*density*G(lW)
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delta_per_square = AW*density*H(lW)
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dW(1) = delta_par*tauMin + randomMaxwellian()*SQRT(delta_par_square*tauMin)
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dW(2) = ABS(randomMaxwellian()*SQRT(delta_per_square*tauMin))
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!System of reference for the velocity change
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!First one is parallel to the relative velocity
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!First one is parallel to the relative velocity
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e1 = normalize(W)
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e1 = normalize(W)
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!Second one is perpendicular to it
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!Second one is perpendicular to it
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@ -1024,18 +1037,12 @@ MODULE moduleMesh
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e3 = crossProduct(e2, e1)
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e3 = crossProduct(e2, e1)
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e3 = normalize(e3)
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e3 = normalize(e3)
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delta_par = -coulombMatrix(k)%A_ij*coulombMatrix(k)%one_plus_massRatio_ij*density*l**2*G(lW)
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!Random number for direction
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rnd = PI2*random()
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delta_par_square = AW*density*G(lW)
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!Change particle velocity
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partTemp%part%v = partTemp%part%v + dW(1)*e1 + dW(2)*(COS(rnd)*e2 + &
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delta_per_square = AW*density*H(lW)
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SIN(rnd)*e3)
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dW(1) = delta_par*tauMin + randomMaxwellian()*SQRT(delta_par_square*tauMin)
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dW(2) = DABS(randomMaxwellian()*SQRT(delta_per_square*tauMin))
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rnd = random()
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partTemp%part%v = partTemp%part%v + dW(1)*e1 + dW(2)*(COS(PI2*rnd)*e2 + &
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SIN(PI2*rnd)*e3)
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partTemp => partTemp%next
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partTemp => partTemp%next
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@ -1057,12 +1064,25 @@ MODULE moduleMesh
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density = cell%gatherF(partTemp%part%Xi, cell%nNodes, densityNodes)
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density = cell%gatherF(partTemp%part%Xi, cell%nNodes, densityNodes)
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velocity = cell%gatherF(partTemp%part%Xi, cell%nNodes, velocityNodes)
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velocity = cell%gatherF(partTemp%part%Xi, cell%nNodes, velocityNodes)
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temperature = cell%gatherF(partTemp%part%Xi, cell%nNodes, temperatureNodes)
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temperature = cell%gatherF(partTemp%part%Xi, cell%nNodes, temperatureNodes)
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l = coulombMatrix(k)%l_i/SQRT(temperature)
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l2 = coulombMatrix(k)%l2_i/temperature
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l = SQRT(l2)
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W = partTemp%part%v - velocity
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W = partTemp%part%v - velocity
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lW = l * NORM2(W)
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normW = NORM2(W)
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AW = coulombMatrix(k)%A_ji/NORM2(W)
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lW = l * normW
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!Axis of the relative velocity
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AW = coulombMatrix(k)%A_j/normW
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delta_par = -coulombMatrix(k)%A_j*coulombMatrix(k)%one_plus_massRatio_ji*density*l2*G(lW)
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delta_par_square = AW*density*G(lW)
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delta_per_square = AW*density*H(lW)
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dW(1) = delta_par*tauMin + randomMaxwellian()*SQRT(delta_par_square*tauMin)
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dW(2) = ABS(randomMaxwellian()*SQRT(delta_per_square*tauMin))
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!System of reference for the velocity change
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!First one is parallel to the relative velocity
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!First one is parallel to the relative velocity
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e1 = normalize(W)
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e1 = normalize(W)
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!Second one is perpendicular to it
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!Second one is perpendicular to it
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@ -1074,18 +1094,9 @@ MODULE moduleMesh
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e3 = crossProduct(e2, e1)
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e3 = crossProduct(e2, e1)
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e3 = normalize(e3)
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e3 = normalize(e3)
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delta_par = -coulombMatrix(k)%A_ji*coulombMatrix(k)%one_plus_massRatio_ji*density*l**2*G(lW)
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rnd = PI2*random()
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partTemp%part%v = partTemp%part%v + dW(1)*e1 + dW(2)*(COS(rnd)*e2 + &
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delta_par_square = AW*density*G(lW)
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SIN(rnd)*e3)
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delta_per_square = AW*density*H(lW)
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dW(1) = delta_par*tauMin + randomMaxwellian()*SQRT(delta_par_square*tauMin)
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dW(2) = DABS(randomMaxwellian()*SQRT(delta_per_square*tauMin))
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rnd = random()
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partTemp%part%v = partTemp%part%v + dW(1)*e1 + dW(2)*(COS(PI2*rnd)*e2 + &
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SIN(PI2*rnd)*e3)
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partTemp => partTemp%next
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partTemp => partTemp%next
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@ -10,8 +10,8 @@ MODULE moduleCoulomb
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CLASS(speciesGeneric), POINTER:: sp_j
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CLASS(speciesGeneric), POINTER:: sp_j
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REAL(8):: one_plus_massRatio_ij, one_plus_massRatio_ji
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REAL(8):: one_plus_massRatio_ij, one_plus_massRatio_ji
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REAL(8):: lnCoulomb !This can be done a function in the future
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REAL(8):: lnCoulomb !This can be done a function in the future
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REAL(8):: A_ij, A_ji
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REAL(8):: A_i, A_j
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REAL(8):: l_j, l_i
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REAL(8):: l2_j, l2_i
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CONTAINS
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CONTAINS
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PROCEDURE, PASS:: init => initInteractionCoulomb
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PROCEDURE, PASS:: init => initInteractionCoulomb
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@ -79,12 +79,13 @@ MODULE moduleCoulomb
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END SELECT
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END SELECT
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self%lnCoulomb = 12.0
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self%lnCoulomb = 12.0 !Make this function dependent
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self%A_ij = 8.D0*PI*Z_i**2*Z_j**2*e_ref**4*self%lnCoulomb / self%sp_i%m
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self%A_ji = 8.D0*PI*Z_j**2*Z_i**2*e_ref**4*self%lnCoulomb / self%sp_j%m
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self%l_j = SQRT(self%sp_j%m / 2.D0) !Missing temperature because it's cell dependent
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self%A_i = 8.D0*PI*Z_i**2*Z_j**2*self%lnCoulomb / self%sp_i%m**2
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self%l_i = SQRT(self%sp_i%m / 2.D0) !Missing temperature because it's cell dependent
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self%A_j = 8.D0*PI*Z_j**2*Z_i**2*self%lnCoulomb / self%sp_j%m**2
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self%l2_j = self%sp_j%m / 2.D0 !Missing temperature because it's cell dependent
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self%l2_i = self%sp_i%m / 2.D0 !Missing temperature because it's cell dependent
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END SUBROUTINE initInteractionCoulomb
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END SUBROUTINE initInteractionCoulomb
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