First Coulomb implementation that works

After fixing all possible divisions by zero I was able to find in the
Coulomb collision I think that this is a first working implementation of
a Coulomb operator based on moments.

Still to test a few things, modify the manual but I would say that I'm
satisfiyed right now. This operator won't be used that often but maybe
improving efficiency is still needed.

In the future a binary operator is required to be able to study cases
out of Maxwellian equilibrium.

src/modules/mesh/2DCyl/moduleMesh2DCyl.f90

@@ -163,7 +163,7 @@ MODULE moduleMesh2DCyl
       r2 = self%n2%getCoordinates()
       self%z  = (/r1(1), r2(1)/)
       self%r  = (/r1(2), r2(2)/)
-      self%weight = SUM(self%r)*5.D-1
+      self%weight = r2(2)**2 - r1(2)**2
       !Normal vector
       self%normal = (/ -(self%r(2)-self%r(1)), &
                          self%z(2)-self%z(1) , &

src/modules/mesh/moduleMesh.f90

@@ -977,6 +977,7 @@ MODULE moduleMesh
       REAL(8):: l2, l, lW, AW
       REAL(8):: deltaV(1:3), totalDeltaV_ij, normDeltaV
       REAL(8):: rnd
+      REAL(8):: eps = 1.D-10
 
 
       !$OMP DO SCHEDULE(DYNAMIC) PRIVATE(partTemp)
@@ -1011,13 +1012,22 @@ MODULE moduleMesh
             velocity    = cell%gatherF(partTemp%part%Xi, cell%nNodes, velocityNodes)
             temperature = cell%gatherF(partTemp%part%Xi, cell%nNodes, temperatureNodes)
 
-            l2 = coulombMatrix(k)%l2_j/temperature
-            l  = SQRT(l2)
+            !If cell temperature is too low, skip particle to avoid division by zero
+            IF (temperature>eps) THEN
+              l2 = coulombMatrix(k)%l2_j/temperature
+              l  = SQRT(l2)
+
+            ELSE
+              partTemp => partTemp%next
+
+              CYCLE
+
+            END IF
 
             W = partTemp%part%v - velocity
             normW = NORM2(W)
-            IF (normW < 1.D-12) THEN
-              !If relative velocity is too low, skip collision and move to next particle
+            !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
 
               CYCLE
@@ -1027,7 +1037,6 @@ MODULE moduleMesh
             lW = l * normW
             AW = coulombMatrix(k)%A_i/normW
 
-
             delta_par = -coulombMatrix(k)%A_i*coulombMatrix(k)%one_plus_massRatio_ij*density*l2*G(lW)
 
             delta_par_square = AW*density*G(lW)
@@ -1063,8 +1072,8 @@ MODULE moduleMesh
 
           END DO
 
+          !Do scattering of particles from species_j due to species i
           IF (i /= j) THEN
-            !Do scattering of particles from species_j due to species i
             !Compute background properties of species_i
             DO n = 1, cell%nNodes
               node => self%nodes(cellNodes(n))%obj
@@ -1076,6 +1085,7 @@ MODULE moduleMesh
             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)
@@ -1087,13 +1097,22 @@ MODULE moduleMesh
               velocity    = cell%gatherF(partTemp%part%Xi, cell%nNodes, velocityNodes)
               temperature = cell%gatherF(partTemp%part%Xi, cell%nNodes, temperatureNodes)
 
-              l2 = coulombMatrix(k)%l2_i/temperature
-              l  = SQRT(l2)
+              !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 (normW < 1.D-12) THEN
-                !If relative velocity is too low, skip collision and move to next particle
+              !If relative velocity is too low, skip collision and move to next particle
+              IF (normW < eps) THEN
                 partTemp => partTemp%next
 
                 CYCLE
@@ -1114,7 +1133,13 @@ MODULE moduleMesh
 
               !Normalize with average exchange per particle
               !TODO: This is a dirty trick to ensure conservation between species
-              dW = normDeltaV*dW/NORM2(dW)
+              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
@@ -1144,7 +1169,7 @@ MODULE moduleMesh
 
         END DO
 
-        DEALLOCATE(densityNodes, velocityNodes, temperatureNodes)
+        DEALLOCATE(densityNodes, velocityNodes, temperatureNodes, cellNodes)
 
       END DO
       !$OMP END DO

src/modules/moduleInject.f90

@@ -97,7 +97,7 @@ MODULE moduleInject
 
       self%id         =  i
       self%vMod       =  v / v_ref
-      self%n        =  n / NORM2(n)
+      self%n          =  n / NORM2(n)
       self%T          =  T / T_ref
       self%species    => species(sp)%obj
       tauInject = tau(self%species%n)