Solving Two-dimensional Euler Equations
On Hexagonal Mesh By A Novel
Macro Particle Method
Author(s)
K.-K. Chan & P.-A. Heng
Abstract
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.
Keywords
particle-in-cell methods, macro particle methods, hexagonal mesh.
Related Book
Other papers in this volume
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