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Dear various gods, finally...

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I had to go back to sherlock2008montecarlo to properly understand the
change in frame of reference and how to translate that into the code.
The language there is clear and understandable for a dumb person like
me.

Now I have a Coulomb linear operator that at least works.

However, still not fully 100% conservative, need to fix this with a
correction for intra-species collisions.

I skip gym today because I was unable to focus on other things than
this.
This commit is contained in:
Jorge Gonzalez 2023-07-11 09:58:50 +02:00
commit c45ffa5380
2 changed files with 39 additions and 28 deletions
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63
src/modules/mesh/moduleMesh.f90
View file

@ -971,15 +971,16 @@ MODULE moduleMesh
TYPE(outputFormat):: output
REAL(8), ALLOCATABLE:: densityNodes(:), velocityNodes(:,:), temperatureNodes(:) !values in node
REAL(8):: density, velocity(1:3), temperature!values at particle position
REAL(8), DIMENSION(1:3):: e1, e2, e3
REAL(8):: delta_par, delta_par_square, delta_per, delta_per_square
REAL(8):: normW
REAL(8):: l2, l, lW, AW, AW2, AW3
REAL(8):: deltaW, deltaThe, deltaPhi
REAL(8):: cosDeltaPhi, sinDeltaPhi
REAL(8):: cosDeltaThe, sinDeltaThe
REAL(8):: deltaV(1:3) !Relative particle velocity increment
REAL(8):: rnd
REAL(8):: C(1:3), W(1:3) !relative velocity and velocity in the relative frame of reference
REAL(8):: l, lW, l2
REAL(8):: normC, normW
REAL(8):: theta, phi !angles between w and c
REAL(8):: cosThe, sinThe
REAL(8):: cosPhi, sinPhi
REAL(8):: rotation(1:3,1:3) !Rotation matrix to go back to laboratory frame
REAL(8):: A, AW
REAL(8):: deltaW_par, deltaW_par_square, deltaW_per_square !Increments of W
REAL(8):: theta_per !Random angle for perpendicular direction
REAL(8):: eps = 1.D-10
@ -1026,36 +1027,46 @@ MODULE moduleMesh
END IF
normW = NORM2(partTemp%part%v - velocity)
C = partTemp%part%v - velocity
normC = NORM2(C)
!If relative velocity is too low, skip collision to avoid division by zero and move to next particle
IF (normW < eps) THEN
IF (normC < eps) THEN
partTemp => partTemp%next
CYCLE
END IF
lW = l * normW
AW = coulombMatrix(k)%A_i/normW
AW2 = coulombMatrix(k)%A_i/normW**2 / 2.D0
AW3 = coulombMatrix(k)%A_i/normW**3 / 2.D0
deltaW = (-coulombMatrix(k)%A_i*coulombMatrix(k)%one_plus_massRatio_ij*l2*G(lW) - AW2*G(lW) + AW2*ERF(lw)) * tauMin + &
SQRT(AW * G(lW) * tauMin) * ABS(randomMaxwellian())
deltaThe = SQRT(2.D0 * AW3 * H(lW) * tauMin)*ABS(randomMaxwellian())
deltaPhi = PI2 * random()
theta = ACOS(C(3) / normC)
cosThe = COS(theta)
sinThe = SIN(theta)
phi = SIGN(1.D0, C(1)) * ACOS(C(1) / SQRT(C(1)**2 + C(2)**2))
cosPhi = COS(phi)
sinPhi = SIN(phi)
cosDeltaThe = COS(deltaThe)
sinDeltaThe = SIN(deltaThe)
cosDeltaPhi = COS(deltaPhi)
sinDeltaPhi = SIN(deltaPhi)
rotation(1, 1:3) = (/ cosThe*cosPhi, -sinPhi, sinThe*cosPhi /)
rotation(2, 1:3) = (/ cosThe*sinPhi, cosPhi, sinThe*sinPhi /)
rotation(3, 1:3) = (/-sinThe, 0.D0, cosThe /)
!Rotate velocity frame assuming theta = phi = 0
deltaV = (normW + deltaW) * (/ sinDeltaThe * cosDeltaPhi, sinDeltaThe * sinDeltaPhi, cosDeltaPhi /)
!W at start is = (0, 0, normC), so normW = normC
lW = l * normC
A = coulombMatrix(k)%A_i*density
AW = A / normC
deltaW_par = - A * coulombMatrix(k)%one_plus_massRatio_ij * l2 * G(lW) * tauMin
deltaW_par_square = SQRT(AW * G(lW) * tauMin)*randomMaxwellian()
deltaW_per_square = SQRT(AW * H(lW) * tauMin)*randomMaxwellian()
theta_per = PI2*random()
!Change W
W(1) = deltaW_per_square * COS(theta_per)
W(2) = deltaW_per_square * SIN(theta_per)
W(3) = normC + deltaW_par + deltaW_par_square
!Change particle velocity
partTemp%part%v = partTemp%part%v + deltaV
partTemp%part%v = velocity + MATMUL(rotation, W)
partTemp => partTemp%next

2
src/modules/moduleCoulomb.f90
View file

@ -83,7 +83,7 @@ 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_i = Z_i**2*Z_j**2*self%lnCoulomb / (2.D0 * PI**2 * self%sp_i%m**2) * scaleFactor
self%l2_j = self%sp_j%m / 2.D0 !Missing temperature because it's cell dependent