| 郑华盛,赵宁.非线性双曲型守恒律的高精度MmB差分格式[J].计算力学学报,2006,23(2):218~222 |
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| 非线性双曲型守恒律的高精度MmB差分格式 |
| A high order accurate MmB difference scheme for nonlinear hyperbolic conservation laws |
| 修订日期：2004-02-24 |
| DOI：10.7511/jslx20062040 |
| 中文关键词: 双曲型守恒律 高阶精度 MmB差分格式 Euler方程组 |
| 英文关键词:hyperbolic conservation laws,high order accuracy,MmB difference scheme,Euler equations |
| 基金项目:航空基金;国防预研基金 |
| 郑华盛 赵宁 |
| [1]南京航空航天大学空气动力学系,南京210016 [2]南昌航空工业学院信息与计算科学系,南昌330034 |
| 摘要点击次数: 1430 |
| 全文下载次数: 13 |
| 中文摘要: |
| 构造了一维非线性双曲型守恒律方程的一个高精度、高分辨率的广义Godunov型差分格式。其构造思想是：首先将计算区间划分为若干个互不相交的小区间，再根据精度要求等分小区间，通过各细小区间上的单元平均状态变量，重构各等分小区间交界面上的状态变量，并加以校正；其次，利用近似Riemann解算子求解细小区间交界面上的数值通量，并结合高阶Runge—Kutta TVD方法进行时间离散，得到了高精度的全离散方法。证明了该格式的MmB特性。然后，将格式推广到一、二维双曲型守恒方程组情形。最后给出了一、二维Euler方程组的几个典型的数值算例，验证了格式的高效性。 |
| 英文摘要: |
| 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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