I hate Coulomb and his Scattering
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.
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2 changed files with 5 additions and 105 deletions
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@ -975,7 +975,7 @@ MODULE moduleMesh
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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):: W(3), dW(2), normW !Relative velocity between particle and species and its increment
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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):: l2, l, lW, AW
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REAL(8):: deltaV(1:3), totalDeltaV_ij, normDeltaV
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REAL(8):: deltaV(1:3)
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REAL(8):: rnd
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REAL(8):: rnd
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REAL(8):: eps = 1.D-10
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REAL(8):: eps = 1.D-10
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@ -1005,7 +1005,6 @@ MODULE moduleMesh
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END DO
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END DO
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!Loop over particles of species_i
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!Loop over particles of species_i
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totalDeltaV_ij = 0.D0
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partTemp => cell%listPart_in(i)%head
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partTemp => cell%listPart_in(i)%head
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DO WHILE(ASSOCIATED(partTemp))
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DO WHILE(ASSOCIATED(partTemp))
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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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@ -1026,6 +1025,7 @@ MODULE moduleMesh
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W = partTemp%part%v - velocity
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W = partTemp%part%v - velocity
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normW = NORM2(W)
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normW = NORM2(W)
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!If relative velocity is too low, skip collision to avoid division by zero and move to next particle
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!If relative velocity is too low, skip collision to avoid division by zero and move to next particle
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IF (normW < eps) THEN
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IF (normW < eps) THEN
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partTemp => partTemp%next
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partTemp => partTemp%next
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@ -1063,8 +1063,6 @@ MODULE moduleMesh
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deltaV = dW(1)*e1 + dW(2)*(COS(rnd)*e2 + SIN(rnd)*e3)
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deltaV = dW(1)*e1 + dW(2)*(COS(rnd)*e2 + SIN(rnd)*e3)
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totalDeltaV_ij = totalDeltaV_ij + NORM2(deltaV)
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!Change particle velocity
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!Change particle velocity
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partTemp%part%v = partTemp%part%v + deltaV
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partTemp%part%v = partTemp%part%v + deltaV
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@ -1072,101 +1070,6 @@ MODULE moduleMesh
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END DO
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END DO
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!Do scattering of particles from species_j due to species i
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IF (i /= j) THEN
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!Compute background properties of species_i
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DO n = 1, cell%nNodes
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node => self%nodes(cellNodes(n))%obj
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CALL calculateOutput(node%output(i), output, node%v, coulombMatrix(k)%sp_i)
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densityNodes(n) = output%density/n_ref
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velocityNodes(n,1:3) = output%velocity(1:3)/v_ref
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temperatureNodes(n) = output%temperature/T_ref
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END DO
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!Divide total momentum exchanged among all the particles of species j
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!TODO: This is a dirty trick to ensure conservation between species
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normDeltaV = totalDeltaV_ij / REAL(cell%listPart_in(j)%amount) * &
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(coulombMatrix(k)%sp_i%weight*coulombMatrix(k)%sp_i%m) / &
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(coulombMatrix(k)%sp_j%weight*coulombMatrix(k)%sp_j%m)
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!Loop over particles of species_j
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partTemp => cell%listPart_in(j)%head
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DO WHILE(ASSOCIATED(partTemp))
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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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temperature = cell%gatherF(partTemp%part%Xi, cell%nNodes, temperatureNodes)
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!If cell temperature is too low, skip particle to avoid division by zero
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IF (temperature>eps) THEN
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l2 = coulombMatrix(k)%l2_i/temperature
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l = SQRT(l2)
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ELSE
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partTemp => partTemp%next
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CYCLE
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END IF
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W = partTemp%part%v - velocity
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normW = NORM2(W)
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!If relative velocity is too low, skip collision and move to next particle
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IF (normW < eps) THEN
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partTemp => partTemp%next
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CYCLE
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END IF
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lW = l * normW
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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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!Normalize with average exchange per particle
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!TODO: This is a dirty trick to ensure conservation between species
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IF (NORM2(dW) > eps) THEN
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dW = normDeltaV*dW/NORM2(dW)
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ELSE
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dW = 0.D0
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END IF
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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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e1 = normalize(W)
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!Second one is perpendicular to it
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e2(1) = -e1(2)
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e2(2) = e1(1)
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e2(3) = 0.D0
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e2 = normalize(e2)
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!Third one is perpendicular to the other two
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e3 = crossProduct(e1, e2)
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e3 = normalize(e3)
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!Random number for direction
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rnd = PI2*random()
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deltaV = dW(1)*e1 + dW(2)*(COS(rnd)*e2 + SIN(rnd)*e3)
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!Change particle velocity
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partTemp%part%v = partTemp%part%v + deltaV
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partTemp => partTemp%next
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END DO
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END IF
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END DO
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END DO
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DEALLOCATE(densityNodes, velocityNodes, temperatureNodes, cellNodes)
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DEALLOCATE(densityNodes, velocityNodes, temperatureNodes, cellNodes)
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@ -8,10 +8,10 @@ MODULE moduleCoulomb
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TYPE:: interactionsCoulomb
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TYPE:: interactionsCoulomb
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CLASS(speciesGeneric), POINTER:: sp_i
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CLASS(speciesGeneric), POINTER:: sp_i
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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
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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_i, A_j
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REAL(8):: A_i
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REAL(8):: l2_j, l2_i
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REAL(8):: l2_j
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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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@ -60,7 +60,6 @@ MODULE moduleCoulomb
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self%sp_j => species(j)%obj
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self%sp_j => species(j)%obj
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self%one_plus_massRatio_ij = 1.D0 + (self%sp_i%weight*self%sp_i%m)/(self%sp_j%weight*self%sp_j%m)
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self%one_plus_massRatio_ij = 1.D0 + (self%sp_i%weight*self%sp_i%m)/(self%sp_j%weight*self%sp_j%m)
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self%one_plus_massRatio_ji = 1.D0 + (self%sp_j%weight*self%sp_j%m)/(self%sp_i%weight*self%sp_i%m)
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SELECT TYPE(sp => self%sp_i)
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SELECT TYPE(sp => self%sp_i)
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TYPE IS (speciesCharged)
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TYPE IS (speciesCharged)
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@ -85,10 +84,8 @@ MODULE moduleCoulomb
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scaleFactor = (n_ref * qe**4) / (eps_0**2 * m_ref**2 * v_ref**3) * ti_ref
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scaleFactor = (n_ref * qe**4) / (eps_0**2 * m_ref**2 * v_ref**3) * ti_ref
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self%A_i = 2.D0*Z_i**2*Z_j**2*self%lnCoulomb / self%sp_i%m**2 * scaleFactor
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self%A_i = 2.D0*Z_i**2*Z_j**2*self%lnCoulomb / self%sp_i%m**2 * scaleFactor
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self%A_j = 2.D0*Z_j**2*Z_i**2*self%lnCoulomb / self%sp_j%m**2 * scaleFactor
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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_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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