In computational fluid dynamics there have been many attempts to combine the advantages of having a fixed mesh, on which to carry out spatial calculations, with using particles moving according to the velocity field. These ideas in fact go back to particle-in-cell methods, proposed about 60 years ago. Of course, some procedure is needed to transfer field information between particles and mesh. There are many possible choices for this “assignment”, or “projection”. Several requirements may guide this choice. Two well-known ones are conservativity and stability, which apply to volume integrals of the fields. An additional one is here considered: preservation of information. This means that assignment from the particles onto the mesh and back should yield the same field values when the particles and the mesh coincide in position. The resulting method is termed “mass” assignment, due to its strong similarities with the finite element method. Several procedures are tested, including the well-known FLIP, on three scenarios: simple 1D convection, 2D convection of Zalesak’s disk, and a CFD simulation of the Taylor–Green periodic vortex sheet. Mass assignment is seen to be clearly superior to other methods.
The Finite Element Method for Fluid Dynamics
