New option for initial distribution of species

The number of particles per cell can be defined when giving an initial
distribution fora species. If not, the typical method of using the
species weight is used. This is particularly useful for cylindrical
coordinates in which very little particles might end up in the axis if a
constant weight is used.

doc/user-manual/bibliography.bib.sav

@@ -0,0 +1,77 @@
+% Encoding: UTF-8
+
+@InProceedings{boris1970relativistic,
+  author    = {Boris, Jay P},
+  booktitle = {Proc. Fourth Conf. Num. Sim. Plasmas},
+  title     = {Relativistic plasma simulation-optimization of a hybrid code},
+  year      = {1970},
+  pages     = {3--67},
+}
+
+@article{higginson2020corrected,
+  title={A corrected method for Coulomb scattering in arbitrarily weighted particle-in-cell plasma simulations},
+  author={Higginson, Drew Pitney and Holod, Ihor and Link, Anthony},
+  journal={Journal of Computational Physics},
+  volume={413},
+  pages={109450},
+  year={2020},
+  publisher={Elsevier}
+}
+
+@Misc{gfortranURL,
+  author       = {GNU Project},
+  title        = {gfortran - the GNU Fortran compiler},
+  howpublished = {\url{https://gcc.gnu.org/wiki/GFortran}},
+}
+
+@Misc{ifortURL,
+  author       = {Intel\textsuperscript{\textregistered}},
+  title        = {Intel\textsuperscript{\textregistered} Fortran Compiler},
+  howpublished = {\url{https://software.intel.com/content/www/us/en/develop/tools/oneapi/components/fortran-compiler.html}},
+}
+
+@Misc{openblasURL,
+  title        = {OpenBLAS, an optimized BLAS library},
+  howpublished = {\url{https://www.openblas.net/}},
+}
+
+@Misc{jsonfortranURL,
+  title        = {JSON-Fortran},
+  howpublished = {\url{https://github.com/jacobwilliams/json-fortran}},
+}
+
+@Misc{jsonURL,
+  title        = {JSON, JavaScript Object Notation},
+  howpublished = {\url{https://www.json.org/json-en.html}},
+}
+
+@Misc{gmshURL,
+  author       = {Christophe Geuzaine and Jean-François Remacle},
+  title        = {Gmsh},
+  howpublished = {\url{https://gmsh.info/}},
+}
+
+@Article{welford1962note,
+  author    = {Welford, BP},
+  journal   = {Technometrics},
+  title     = {Note on a method for calculating corrected sums of squares and products},
+  year      = {1962},
+  number    = {3},
+  pages     = {419--420},
+  volume    = {4},
+  publisher = {Taylor \& Francis},
+}
+
+@Article{sherlock2008monte,
+  author    = {Sherlock, Mark},
+  journal   = {Journal of Computational Physics},
+  title     = {A Monte-Carlo method for Coulomb collisions in hybrid plasma models},
+  year      = {2008},
+  number    = {4},
+  pages     = {2286--2292},
+  volume    = {227},
+  groups    = {Particle-in-cell},
+  publisher = {Elsevier},
+}
+
+@Comment{jabref-meta: databaseType:bibtex;}

doc/user-manual/fpakc_UserManual.tex

@@ -708,11 +708,15 @@ make
                                   \begin{itemize}
                                     \item \textbf{species}: Character.
                                                             Name of species as defined in the object \textbf{species}.
-                                    \item \textbf{file}:    Character.
+                                    \item \textbf{file}: Character.
-                                                            Output file from previous run used as an initial state for the species.
+                                                         Output file from previous run used as an initial state for the species.
-                                                            The file format must be the same as in \textbf{geometry.meshType}
+                                                         The file format must be the same as in \textbf{geometry.meshType}
-                                                            Initial particles are assumed to have a Maxwellian distribution.
+                                                         Initial particles are assumed to have a Maxwellian distribution.
-                                                            File must be located at \textbf{output.path}.
+                                                         File must be located at \textbf{output.path}.
+                                    \item \textbf{particlesPerCell}: Integer.
+                                                                     Optional.
+                                                                     Initial number of particles per cell.
+                                                                     If not, the number of particles per cell will be assigned based on the species weight and the cell volume.
                                   \end{itemize}
         \end{itemize}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

src/modules/init/moduleInput.f90

@@ -324,7 +324,8 @@ MODULE moduleInput
       REAL(8):: densityCen
       !Mean velocity and temperature at particle position
       REAL(8):: velocityXi(1:3), temperatureXi
-      INTEGER:: nNewPart = 0.D0
+      INTEGER:: nNewPart = 0
+      REAL(8):: weight = 0.D0
       CLASS(meshCell), POINTER:: cell
       TYPE(particle), POINTER:: partNew
       REAL(8):: vTh
@@ -343,6 +344,9 @@ MODULE moduleInput
           !Reads node values at the nodes
           filename = path // spFile
           CALL mesh%readInitial(filename, density, velocity, temperature)
+          !Check if initial number of particles is given
+          CALL config%get(object // '.particlesPerCell', nNewPart, found)
+
           !For each volume in the node, create corresponding particles
           DO e = 1, mesh%numCells
             !Scale variables
@@ -355,7 +359,11 @@ MODULE moduleInput
             densityCen = mesh%cells(e)%obj%gatherF((/ 0.D0, 0.D0, 0.D0 /), nNodes, sourceScalar)
 
             !Calculate number of particles
-            nNewPart = INT(densityCen * (mesh%cells(e)%obj%volume*Vol_ref) / species(sp)%obj%weight)
+            IF (.NOT. found) THEN
+              nNewPart = FLOOR(densityCen * (mesh%cells(e)%obj%volume*Vol_ref) / species(sp)%obj%weight)
+
+            END IF
+            weight = densityCen * (mesh%cells(e)%obj%volume*Vol_ref) / REAL(nNewPart)
 
             !Allocate new particles
             DO p = 1, nNewPart
@@ -392,7 +400,7 @@ MODULE moduleInput
 
               partNew%n_in   = .TRUE.
 
-              partNew%weight = species(sp)%obj%weight
+              partNew%weight = weight
 
               !Assign particle to temporal list of particles
               CALL partInitial%add(partNew)