Abstract
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 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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Nadiga, B.T. An Euler solver based on locally adaptive discrete velocities. J Stat Phys 81, 129–146 (1995). https://doi.org/10.1007/BF02179972
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DOI: https://doi.org/10.1007/BF02179972