Summary
A new upwind method called Kinetic Flux Vector Splitting (KFVS) has been developed for the solution of the Euler equations of gas dynamics. This method is based on the fact that the Euler equations are the moments of the Boltzmann equation when the velocity distribution is a Maxwellian. It is shown that the KFVS is a suitable moment of the Courant-Isaacson-Rees (CIR) scheme applied to the Boltzmann equation and further that it is equivalent to the flux-difference splitting approach. It can also be regarded as a Kinetic Theory based Riemann solver. The KFVS has been combined with the TVD and UNO formalisms and its application to the test case of one-dimensional shock propagation has been shown to yield accurate wiggle-free solution with high resolution.
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References
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© 1989 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
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Mandal, J.C., Deshpande, S.M. (1989). Higher Order Accurate Kinetic Flux Vector Splitting Method for Euler Equations. In: Ballmann, J., Jeltsch, R. (eds) Nonlinear Hyperbolic Equations — Theory, Computation Methods, and Applications. Notes on Numerical Fluid Mechanics, vol 24. Vieweg+Teubner Verlag. https://doi.org/10.1007/978-3-322-87869-4_39
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DOI: https://doi.org/10.1007/978-3-322-87869-4_39
Publisher Name: Vieweg+Teubner Verlag
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