Solving Two-dimensional Euler Equations On Hexagonal Mesh By A Novel Macro Particle Method
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K.-K. Chan & P.-A. Heng
In this paper a novel numerical solver for two-dimensional compressible and inviscid flow problems is presented. This method can be considered as a Lagrangian particle method similar to particle-in-cell (PIC) methods. But, instead of using bundle of point particles, our method employs only one macro particle to model the fluid element in a cell. At the beginning of each time step, the volumes of the macro particles are the same as the cell’s volume and the macro particles are regularly distributed on the grid point so that each particle is coincident with its cell. The 2D Euler equations are reformulated so that the force interactions among the macro particles are well understood and easier for the macro particle implementation. The macro particles move across the grid cells during the Lagrangian phase and then they are remapped to the grid points again in the remapping phase. The remapping phase is implemented by splitting the macro particles into smaller pieces (sub-particles) according to the particles’ boundaries displacements and the sub-particles in each cell are combined to obtain a single macro particle before the end of the remapping phase. One of the advantages of our method is that the physical quantities including mass, total energy and momentum are all conserved. A benchmark test known as the double Mach reflection is simulated on a hexagonal mesh with a CFL number equal to 1.5 and very good results are obtained. Furthermore, the computational time per time-step is very short. Keywords: particle-in-cell methods, macro particle methods, hexagonal mesh.
particle-in-cell methods, macro particle methods, hexagonal mesh.