ADER-WENO finite volume schemes with space-time adaptive mesh refinement
ADER-WENO finite volume schemes with space-time adaptive mesh refinement
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DOI：
10.1016/j.jcp.2013.04.017
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发表时间：
2012-12
期刊：
影响因子：
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通讯作者：
M. Dumbser;O. Zanotti;Arturo Hidalgo;D. Balsara
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文献类型：
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作者：
M. Dumbser;O. Zanotti;Arturo Hidalgo;D. Balsara
提出了第一个在多维空间中采用自适应网格加密（AMR）的高阶一步ADER-WENO有限体积格式。通过韦诺重建获得高阶空间精度，而高阶一步时间离散使用局部时空间断Galerkin预测方法实现。由于基础方案的一步性质，所得到的算法特别适合于空时自适应网格上的AMR策略，即具有时间精确的本地时间步进。AMR属性已实现“细胞的细胞”，与标准的树型算法，而该计划已通过消息传递接口（MPI）的范例并行化。新的计划已被测试了广泛的例子的非线性系统的双曲守恒律，包括经典的可压缩气体动力学的欧拉方程和磁流体动力学（MHD）方程。高阶空间和时间已被确认通过数值收敛性研究和计算速度的详细分析，相对于高度精细的均匀网格。我们还展示了测试问题，提出的高阶AMR计划的行为明显优于传统的二阶AMR方法。该方案首次将高阶ADER方法与二维和三维空间的时空自适应网格相结合，有可能成为计算物理、应用数学和力学等领域的有用工具。
We present the first high order one-step ADER-WENO finite volume scheme with adaptive mesh refinement (AMR) in multiple space dimensions. High order spatial accuracy is obtained through a WENO reconstruction, while a high order one-step time discretization is achieved using a local space–time discontinuous Galerkin predictor method. Due to the one-step nature of the underlying scheme, the resulting algorithm is particularly well suited for an AMR strategy on space–time adaptive meshes, i.e. with time-accurate local time stepping. The AMR property has been implemented ‘cell-by-cell’, with a standard tree-type algorithm, while the scheme has been parallelized via the message passing interface (MPI) paradigm. The new scheme has been tested over a wide range of examples for nonlinear systems of hyperbolic conservation laws, including the classical Euler equations of compressible gas dynamics and the equations of magnetohydrodynamics (MHD). High order in space and time have been confirmed via a numerical convergence study and a detailed analysis of the computational speed-up with respect to highly refined uniform meshes is also presented. We also show test problems where the presented high order AMR scheme behaves clearly better than traditional second order AMR methods. The proposed scheme that combines for the first time high order ADER methods with space–time adaptive grids in two and three space dimensions is likely to become a useful tool in several fields of computational physics, applied mathematics and mechanics.