×
Banda, Mapundi K.; Junk, Michael; Klar, Axel

A limiter based on kinetic theory. (English) Zbl 1127.82323

Transp. Theory Stat. Phys. 31, No. 4-6, 491-512 (2002).
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.

Cited in 1 Document

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 equation
Cite Review PDF
Full Text: DOI

References:

[1] Almgren A.S., SIAM Sci. Comp. 17 pp 358– (1996) · Zbl 0845.76055 · doi:10.1137/S1064827593244213
[2] Bardos C., J. Stat. Phys. 63 pp 323– (1991) · doi:10.1007/BF01026608
[3] Bell J.B., J. Comp. Phys. 85 pp 257– (1989) · Zbl 0681.76030 · doi:10.1016/0021-9991(89)90151-4
[4] Brown D., J. Comp. Phys. 122 pp 165– (1995) · Zbl 0849.76043 · doi:10.1006/jcph.1995.1205
[5] Chen S., Ann. Rev. Fluid Mech. 30 pp 329– (1998) · Zbl 1398.76180 · doi:10.1146/annurev.fluid.30.1.329
[6] De Masi A., CPAM 42 pp 1189– (1989)
[7] Deshpande S.M., A State-of-the-Art Reference to the Latest Developments In CFD (1995)
[8] Elton B., SIAM J. Numer. Anal. 32 pp 1327– (1995) · Zbl 0845.35018 · doi:10.1137/0732062
[9] Frisch U., Complex Systems 1 pp 649– (1987)
[10] Gaskell P.H., Int. J. Num. Meth. in Fluids 8 pp 617– (1988) · Zbl 0668.76118 · doi:10.1002/fld.1650080602
[11] Inamuro T., Phys. Fluids 9 pp 3535– (1997) · Zbl 1185.76869 · doi:10.1063/1.869426
[12] Jin S., SIAM J. Num. Anal. 35 pp 2405– (1998) · Zbl 0938.35097 · doi:10.1137/S0036142997315962
[13] Junk M., J. Comp. Phys. 151 pp 947– (1999) · Zbl 0944.76056 · doi:10.1006/jcph.1999.6228
[14] Klar A., J. Comp. Phys. 148 pp 1– (1999) · Zbl 0931.76074 · doi:10.1006/jcph.1998.6123
[15] Kurganov A., J. Comp. Phys. 160 pp 241– (2000) · Zbl 0987.65085 · doi:10.1006/jcph.2000.6459
[16] Martin D., J. Comp. Phys. 163 pp 271– (2000) · Zbl 0991.76052 · doi:10.1006/jcph.2000.6575
[17] Naldi G., SIAM J. Numer. Anal. 37 pp 1246– (2000) · Zbl 0954.35109 · doi:10.1137/S0036142997328810
[18] Sone Y., Advances in Kinetic Theory and Continuum Mechanics, Proceedings of a Symposium Held in Honour of Henri Cabannes (Paris) pp 19– (1990)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.