INFLUENCE OF PENALIZATION AND BOUNDARY TREATMENT ON THE STABILITY AND ACCURACY OF HIGH-ORDER DISCONTINUOUS GALERKIN SCHEMES FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS
INFLUENCE OF PENALIZATION AND BOUNDARY TREATMENT ON THE STABILITY AND ACCURACY OF HIGH-ORDER DISCONTINUOUS GALERKIN SCHEMES FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS
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DOI：
10.1142/s0218396x12500191
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发表时间：
2013-01
影响因子：
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通讯作者：
A. Richter;E. Brußies;J. Stiller
中科院分区：
文献类型：
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作者：
A. Richter;E. Brußies;J. Stiller
引入了一种用于可压缩Navier-Stokes方程的高阶内罚间断Galerkin方法，该方法是对Hartmann和Houston给出的格式的修改。在本文中，我们研究了惩罚和边界处理对准确性的影响。通过观察特征值和条件数，找到了惩罚项 μ 的下限，而收敛研究则描述了合理的上限以及对临界时间步长的线性依赖性。通过研究守恒特性，我们证明了不同的边界处理对精度的影响有几个数量级，并提出了合理的策略来提高守恒特性。
A high-order interior penalty discontinuous Galerkin method for the compressible Navier–Stokes equations is introduced, which is a modification of the scheme given by Hartmann and Houston. In this paper we investigate the influence of penalization and boundary treatment on accuracy. By observing eigenvalues and condition numbers, a lower bound for the penalization term μ was found, whereas convergence studies depict reasonable upper bounds and a linear dependence on the critical time step size. By investigating conservation properties we demonstrate that different boundary treatments influence the accuracy by several orders of magnitude, and propose reasonable strategies to improve conservation properties.