A limiter based on kinetic theory. (English) Zbl 1127.82323
Summary: In the present paper the low Mach number limit of kinetic equations is used to develop a discretization for the incompressible Euler equation. The kinetic equation is discretized with a first and second order discretization in space. The discretized equation is then considered in the limit of low Mach and Knudsen number which gives rise to an interesting limiter for the convective part in the incompressible Euler equation. Numerical experiments are shown comparing different approaches.
MSC:
82C80 | Numerical methods of time-dependent statistical mechanics (MSC2010) |
76M28 | Particle methods and lattice-gas methods |
76P05 | Rarefied gas flows, Boltzmann equation in fluid mechanics |
82C40 | Kinetic theory of gases in time-dependent statistical mechanics |
Keywords:
Kinetic equations; Asymptotic analysis; Low Mach number limit; Second order upwind discretization; Slope limiter; Incompressible Euler equationReferences:
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