Added the possibility to have sub-steps

Now per each Coulomb collision process there is the possibility to do
sub-steps. This helps in improving accuracy without reducing the time
step of the problem.

src/modules/init/moduleInput.f90

@@ -637,6 +637,7 @@ MODULE moduleInput
       CHARACTER(:), ALLOCATABLE:: electron
       INTEGER:: e
       CLASS(meshCell), POINTER:: cell
+      INTEGER:: subSteps
 
       !Firstly, check if the object 'interactions' exists
       CALL config%info('interactions', found)
@@ -770,8 +771,13 @@ MODULE moduleInput
               pt_i = speciesName2Index(species_i)
               CALL config%get(object // '.species_j', species_j, found)
               pt_j = speciesName2Index(species_j)
+              CALL config%get(object // '.subSteps', subSteps, found)
+              IF (.NOT. found) THEN
+                subSteps = 1
 
-              CALL coulombMatrix(i)%init(pt_i, pt_j)
+              END IF
+
+              CALL coulombMatrix(i)%init(pt_i, pt_j, subSteps)
 
             END DO
 

src/modules/mesh/moduleMesh.f90

@@ -961,10 +961,12 @@ MODULE moduleMesh
 
       CLASS(meshParticles), INTENT(in), TARGET:: self
       CLASS(meshCell), POINTER:: cell
+      TYPE(interactionsCoulomb):: pair
       INTEGER:: e
       INTEGER:: k
       INTEGER:: i, j
       INTEGER:: n
+      INTEGER:: t
       TYPE(lNode), POINTER:: partTemp
       INTEGER(8), ALLOCATABLE:: cellNodes(:)
       CLASS(meshNode), POINTER:: node
@@ -995,14 +997,15 @@ MODULE moduleMesh
                  temperatureNodes(1:cell%nNodes))
 
         DO k=1, nCoulombPairs
-          i = coulombMatrix(k)%sp_i%n
-          j = coulombMatrix(k)%sp_j%n
+          pair = coulombMatrix(k)
+          i = pair%sp_i%n
+          j = pair%sp_j%n
 
           !Do scattering of particles from species_i due to species j
           !Compute background properties of species_j
           DO n = 1, cell%nNodes
             node => self%nodes(cellNodes(n))%obj
-            CALL calculateOutput(node%output(j), output, node%v, coulombMatrix(k)%sp_j)
+            CALL calculateOutput(node%output(j), output, node%v, pair%sp_j)
             densityNodes(n)      = output%density/n_ref
             velocityNodes(n,1:3) = output%velocity(1:3)/v_ref
             temperatureNodes(n)  = output%temperature/T_ref
@@ -1018,7 +1021,7 @@ MODULE moduleMesh
 
             !If cell temperature is too low, skip particle to avoid division by zero
             IF (temperature>eps) THEN
-              l2 = coulombMatrix(k)%l2_j/temperature
+              l2 = pair%l2_j/temperature
               l  = SQRT(l2)
 
             ELSE
@@ -1028,17 +1031,13 @@ MODULE moduleMesh
 
             END IF
 
+            A  = pair%A_i*density
+
+            !Do the required substeps
+            DO t = 1, pair%nSubSteps
               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 (normC < eps) THEN
-              partTemp => partTemp%next
-
-              CYCLE
-
-            END IF
-
               !C_3 = z; C_1, C2 = x, y (per)
               C_per = NORM2(C(1:2))
               cosPhi = C(1)  / C_per
@@ -1056,13 +1055,12 @@ MODULE moduleMesh
               lW = l * normC
               GlW = G(lW)
               HlW = H(lW)
-            A  = coulombMatrix(k)%A_i*density
               AW = A / normC
 
               !Calculate changes in W due to collision process
-            deltaW_par = - A * coulombMatrix(k)%one_plus_massRatio_ij * l2 * GlW * tauMin
-            deltaW_par_square = SQRT(AW * GlW * tauMin)*randomMaxwellian()
-            deltaW_per_square = SQRT(AW * HlW * tauMin)*randomMaxwellian()
+              deltaW_par = - A * pair%one_plus_massRatio_ij * l2 * GlW * pair%tauSub
+              deltaW_par_square = SQRT(AW * GlW * pair%tauSub)*randomMaxwellian()
+              deltaW_per_square = SQRT(AW * HlW * pair%tauSub)*randomMaxwellian()
 
               !Random angle to distribute perpendicular change in velocity
               theta_per = PI2*random()
@@ -1075,6 +1073,8 @@ MODULE moduleMesh
               !Update particle velocity and return to laboratory frame
               partTemp%part%v = MATMUL(rotation, W) + velocity
 
+            END DO
+                                               
             !Move to the next particle in the list
             partTemp => partTemp%next
 

src/modules/moduleCoulomb.f90

@@ -12,6 +12,8 @@ MODULE moduleCoulomb
     REAL(8):: lnCoulomb !This can be done a function in the future
     REAL(8):: A_i
     REAL(8):: l2_j
+    REAL(8):: tauSub
+    INTEGER:: nSubSteps
     CONTAINS
       PROCEDURE, PASS:: init => initInteractionCoulomb
 
@@ -44,7 +46,7 @@ MODULE moduleCoulomb
 
     END FUNCTION H
 
-    SUBROUTINE initInteractionCoulomb(self, i, j)
+    SUBROUTINE initInteractionCoulomb(self, i, j, subSteps)
       USE moduleSpecies
       USE moduleErrors
       USE moduleConstParam
@@ -52,10 +54,14 @@ MODULE moduleCoulomb
       IMPLICIT NONE
 
       CLASS(interactionsCoulomb), INTENT(out):: self
+      INTEGER, INTENT(in):: subSteps
       INTEGER, INTENT(in):: i, j
       REAL(8):: Z_i, Z_j
       REAL(8):: scaleFactor
 
+      self%nSubSteps = subSteps
+      self%tauSub    = tauMin / REAL(self%nSubSteps)
+
       self%sp_i => species(i)%obj
       self%sp_j => species(j)%obj