A note on the conservative schemes for the Euler equations

Authors:
Huazhong Tang;Tiegang Liu
Affiliations:
LMAM, School of Mathematical Sciences, Peking University, Beijing, PR China;Institute of High Performance Computing, The Capricorn, Singapore Science Park II, Singapore, Singapore
Venue:
Journal of Computational Physics
Year:
2006

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Abstract

This note gives a numerical investigation for the popular high resolution conservative schemes when applied to inviscid, compressible, perfect gas flows with an initial high density ratio as well as a high pressure ratio. The results show that they work very inefficiently and may give inaccurate numerical results even over a very fine mesh when applied to such a problem. Numerical tests show that increasing the order of accuracy of the numerical schemes does not help much in improving the numerical results. How to cure this difficulty is still open.