一类三维时空二阶精度高分辨率MmB差分格式

A class of space-time second order accurate high resolution MmB difference schemes in 3D

直接把Nessyahu和Tadmor[1,2]的思想推广到三维非线性双曲型守恒律情形,以交错形式Lax-Friedrichs格式为基本模块,使用二阶分片线性逼近代替一阶分片常数逼近,减少了Lax-Friedrichs格式的过多数值粘性.通过对混合导数离散形式的适当处理,构造了一类不须解Riemann问题、具有时空二阶精度高分辨率的MmB差分格式。这些差分格式很容易推广到向量系统中去。最后,一些数值模拟计算结果也证明了这些差分格式的有效性。

From the 3D nonlinear hyperbolic conservation laws, the H.Ne ssyahu and E.Tadmor's methods^() are developed directly to the 3D cases. The interlace types Lax-Friedrichs are used as a basic building block and the first order ones is substituted by the second-order piecewise-linear constant degree approximate. That reduce the excessive numerical viscosity typical to the Lax-Friedrichs forms. By treating the co-derivative separated form properly, a new Riemann-solver-free class of difference schemes is constructed to scalar nonlinear hyperbolic conservation laws for three dimensional flows. It can be proved that, these schemes have second order accurate in space and time domains and satisfy MmB properties under the appropriate CFL limitation . In addition, these schemes can also be extended to the vector systems conservation laws. Finally, several numerical experiments show that the performances of these schemes are quite satisfactory.