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| A high order accurate MmB difference scheme for nonlinear hyperbolic conservation laws |
| Revised:February 24, 2004 |
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| DOI：10.7511/jslx20062040 |
| KeyWord:hyperbolic conservation laws,high order accuracy,MmB difference scheme,Euler equations |
| ZHENG Hua-sheng ZHAO Ning |
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| Abstract: |
| In this paper,a high-order accuracy,high resolution,generalized Godunov-type difference scheme is presented for 1D/2D nonlinear hyperbolic conservation laws.Firstly,the computational interval is divided into pieces of non-overlapping sub-intervals,and then each sub-interval is further subdivided into equal small-intervals according to required accuracy.Cell averaged-solutions from these small-intervals are used to reconstruct a high order polynomial approximation in small-interval boundaries. Furthermore the correction is introduced to prevent oscillations near discontinuities from the high-order approximation.Secondly,the approximate Riemann solver is used to compute numerical fluxs at small-intervals boundaries,and a high-order fully discretization method is obtained by applying high-order RungeKutta TVD time discretization.Moreover,we prove the MmB property of the scheme under a certain CFL condition,and extend to 1D/2D system of hyperbolic conservation laws.It does not necessitate the conventional field-by-field characteristic decomposition.Finally,several typical numerical experiments are given. The numerical results verify high resolution of the method. |
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