High order space–time adaptive ADER-WENO finite volume schemes for non-conservative hyperbolic systems
High order space–time adaptive ADER-WENO finite volume schemes for non-conservative hyperbolic systems
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DOI：
10.1016/j.cma.2013.09.022
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发表时间：
2013-04
影响因子：
7.2
通讯作者：
M. Dumbser;Arturo Hidalgo;O. Zanotti
中科院分区：
文献类型：
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作者：
M. Dumbser;Arturo Hidalgo;O. Zanotti
本文提出了一类高阶有限体积格式，该格式将一步ADER-WENO有限体积法与时空自适应网格加密（AMR）相结合，求解非保守双曲型方程组。由此产生的算法，这是特别适合于在可压缩多相流的材料界面的治疗，是基于：（i）在空间中通过韦诺重建获得的高精度的顺序，（ii）通过局部时空不连续Galerkin预测方法的高阶一步时间离散化，和（iii）使用的路径保守计划处理非保守项的方程。具有时间精确的局部时间步长的AMR特性，已经根据逐单元策略处理，强烈依赖于高阶一步时间离散化，这自然允许使用不同的时间步长在元素之间的界面处的跳跃项的高阶精确和一致的计算。新格式已成功地验证了一些测试问题的Baer-Nunziato模型的可压缩多相流。
We present a class of high order finite volume schemes for the solution of non-conservative hyperbolic systems that combines the one-step ADER-WENO finite volume approach with space–time adaptive mesh refinement (AMR). The resulting algorithm, which is particularly well suited for the treatment of material interfaces in compressible multi-phase flows, is based on: (i) high order of accuracy in space obtained through WENO reconstruction, (ii) a high order one-step time discretization via a local space–time discontinuous Galerkin predictor method, and (iii) the use of a path conservative scheme for handling the non-conservative terms of the equations. The AMR property withtime accurate local time stepping, which has been treated according to acell-by-cellstrategy, strongly relies on the high order one-step time discretization, which naturally allows a high order accurate and consistent computation of the jump terms at interfaces between elements using different time steps. The new scheme has been successfully validated on some test problems for the Baer–Nunziato model of compressible multiphase flows.