Gas-kinetic schemes for the compressible Euler equations: Positivity-preserving analysis

Zeitschrift fur Angewandte Mathematik und Physik

Volumn 50, Issue 2, 1999, Pages 258-281

  Tang, Tao ^a   Xu, Kun ^b  

^a SIMON FRASER UNIVERSITY   (Canada)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

BGK; Euler equations; Gas kinetic schemes; Maxwellian distribution; Positivity preserving

Indexed keywords

EID: 0033240198     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000330050150     Document Type: Article

References (19)

1. P.L. Bhatnagar, E.P. Gross, and M. Krook, A model for collision processes in gases I: small amplitude processes in charged and neutral one-component systems, Phys. Rev. 94 (1954), 511-525.
2. S. M. Deshpande, On the Maxwellian Distribution, Symetric Form and Entropy Conservation for the Euler Equations, Tech. Report 2583, NASA Langley, 1986.
3. S. M. Deshpande, Kinetic Theory Based New Upwind Methods for Inviscid Compressible Flows, AIAA Paper 86-0275, New York, 1986.
4. B. Enfield, C.D. Munz, P. L. Roe and B. Sjogreen, On Godunov type methods near low density, J. Comput. Phys. 92 (1991), 273-295.
5. J. L. Estivalezes and P. Villedieu, High-order positivity-preserving kinetic schemes for the compressible Euler equations, SIAM J. Numer. Anal. 33 (1996), 2050-2067.
6. A. Harten, P. D. Lax and B. Van Leer, On upstream differencing and Godunov-type schemes for hyperbolic conservation laws, SIAM Review 15 (1983), 35-61.
7. G.-S. Jiang and E. Tadmor, Non-oscillatory central schemes for multidimensional hyperbolic conservation laws, SIAM J. Sci. Comput.. 19 (1998), 1892-1917.
8. M.N. Kogan, Rarefied Gas Dynamics, Plenum Press, New York 1969.
9. X.-D. Liu and P. D. Lax, Positive schemes for solvi ig multi-dimensional hyperbolic sysytems of conservation laws, CFD J. 5 (1996), 1-24.
10. B. Perthame, Second-Order Boltzmann schemes for compressible Euler equation in one and two space dimensions, SIAM J. Numer. Anal. 29(1) (1992).
11. B. Perthame and C. W. Shu, On positivity preserving finite volume schemes for Euler equations, Numer. Math. 73 (1996), 119-130.
12. K.H. Prendergast and K. Xu, Numerical Hydrodynamics from Gas-Kinetic Theory, J. of Comput. Phys. 109 (1993), 53.
13. D. I. Pullin, Direct simulations methods for compressible inviscid ideal gas-flows, J. Comput. Phys. 34 (1980), 231-244.
14. P.L. Roe, Approximate Riemann solvers, parameter vectors and difference schemes, J. Comput. Phys. 43 (1981), 357.
15. R. Sanders and K. Prendergast, The possible relation of the three-kiloparsec arm to explosions in the galactic nucleus, in Astrophysical J. 188 (1974).
16. G. Toth and D. Odstrcil, Comparison of some flux corrected transport and total variation diminishing numerical schemes for hydrodynamic and magnetohydrodynamic problems, J. Comput. Phys. 128 (1996), 82-100.
17. K. Xu, Numerical Hydrodynamics from Gas-Kinetic Theory, Ph.D thesis, Columbia University, 1993.
18. K. Xu and K. Prendergast, Numerical Navier-Stokes solutions from gas-kinetic theory, J. Comput. Phys. 114 (1994), 9-17.
19. K. Xu, L. Martinelli and A. Jameson, Gas-kinetic finite volume methods, flux-vector splitting and artificial diffusion, J. Comput. Phys. 120 (1995), 48-65.