An Euler Solver Based on Locally Adaptive Discrete Velocities

Details An Euler Solver Based on Locally Adaptive Discrete Velocities An Euler Solver Based on Locally Adaptive Discrete Velocities

1995-01-23

arxiv.org/abs/comp-gas/9501010v1

Journal of Statistical Physics 81 (1995) 129-146

Nonlinear Sciences

Cellular Automata and Lattice Gases

17 pages including 2 figures and CMFortran code listing. All in one postscript file (adv.ps) compressed and uuencoded (adv.uu)

Scientific paper

10.1007/BF02179972

A new discrete-velocity model is presented to solve the three-dimensional Euler equations. The velocities in the model are of an adaptive nature---both the origin of the discrete-velocity space and the magnitudes of the discrete-velocities are dependent on the local flow--- and are used in a finite volume context. The numerical implementation of the model follows the near-equilibrium flow method of Nadiga and Pullin [1] and results in a scheme which is second order in space (in the smooth regions and between first and second order at discontinuities) and second order in time. (The three-dimensional code is included.) For one choice of the scaling between the magnitude of the discrete-velocities and the local internal energy of the flow, the method reduces to a flux-splitting scheme based on characteristics. As a preliminary exercise, the result of the Sod shock-tube simulation is compared to the exact solution.

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