Implicit discontinuous Galerkin method on agglomerated high-order grids for 3D simulations
Implicit discontinuous Galerkin method on agglomerated high-order grids for 3D simulations
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用于 3D 模拟的聚集高阶网格的隐式不连续 Galerkin 方法
DOI：
10.1016/j.cja.2016.10.004
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发表时间：
2016-10
影响因子：
5.7
通讯作者：
Chen Zhenwu
中科院分区：
文献类型：
--
作者：
Lu Hongqiang;Wu Yizhao;Zhou Shijie;Chen Zhenwu
高质量的几何表示对于高阶方法保持其高阶精度至关重要。研究了一种与间断伽辽金（DG）方法相结合的聚集高阶网格生成方法，用于求解3D可压缩欧拉和纳维-斯托克斯方程。在此方法中，首先通过标准商业网格生成工具生成精细的线性网格。利用团聚方法，可以快速获得二次高阶网格，该网格虽然粗糙，但提供了高质量的几何表示，因此非常适合高阶计算。利用DG方法对得到的网格进行高阶离散化，并对离散化后的系统进行全隐式处理，得到稳态解。对多个流动问题的数值实验表明，凝聚高阶网格与DG方法在处理弯曲几何流动问题时效果良好。研究还发现，利用完全隐式离散系统和 p 排序方法，DG 方法可以在几个时间步内达到收敛状态，与显式方法相比，效率显着提高。
High quality of geometry representation is regarded essential for high-order methods to maintain their high-order accuracy. An agglomerated high-order mesh generating method is investigated in combination with discontinuous Galerkin (DG) method for solving the 3D compressible Euler and Navier-Stokes equations. In this method, a fine linear mesh is first generated by standard commercial mesh generation tools. By taking advantage of an agglomeration method, a quadratic high-order mesh is quickly obtained, which is coarse but provides a high-quality geometry representation, thus very suitable for high-order computations. High-order discretizations are performed on the obtained grids with DG method and the discretized system is treated fully implicitly to obtain steady state solutions. Numerical experiments on several flow problems indicate that the agglomerated high-order mesh works well with DG method in dealing with flow problems of curved geometries. It is also found that with a fully implicit discretized system and a p-sequencing method, the DG method can achieve convergence state within several time steps which shows significant efficiency improvements compared to its explicit counterparts.
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