An artificial compressibility flux for the discontinuous Galerkin solution of the incompressible Navier-Stokes equations
An artificial compressibility flux for the discontinuous Galerkin solution of the incompressible Navier-Stokes equations
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DOI：
10.1016/j.jcp.2006.03.006
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发表时间：
2006-11-01
影响因子：
4.1
通讯作者：
Rebay, S.
中科院分区：
文献类型：
--
作者：
Bassi, F.;Crivellini, A.;Rebay, S.
间断Galerkin（DG）方法已被证明是非常适合于构造鲁棒的高阶数值格式的非结构化和可能的非结构化网格的各种问题。它们在不可压缩Navier-Stokes（INS）方程中的应用最近也得到了考虑，尽管这个问题还远没有得到充分的探讨。在这项工作中，我们提出了一种新的方法来求解以守恒形式写成的惯性导航系统方程的DG数值解。在连续性和动量方程中的无粘数值通量的计算使用的黎曼问题的（精确）解决方案与当地的人工压缩性扰动的方程提供的速度和压力的值。与大多数现有的方法不同，人工可压缩性在这里仅在界面通量水平引入，因此导致INS方程的一致离散化，而与引入的人工可压缩性的量无关。粘性项的离散化遵循成熟的DG格式BR 2。通过计算Kovasznay流和二维盖驱动空腔流在很宽的雷诺数范围内和各种程度的多项式近似的性能和精度的方法证明。(c)2006年爱思唯尔公司All rights reserved.
Discontinuous Galerkin (DG) methods have proved to be well suited for the construction of robust high-order numerical schemes on unstructured and possibly nonconforming grids for a variety of problems. Their application to the incompressible Navier-Stokes (INS) equations has also been recently considered, although the subject is far from being fully explored. In this work, we propose a new approach for the DG numerical solution of the INS equations written in conservation form. The inviscid numerical fluxes both in the continuity and in the momentum equation are computed using the values of velocity and pressure provided by the (exact) solution of the Riemann problem associated with a local artificial compressibility perturbation of the equations. Unlike in most of the existing methods, artificial compressibility is here introduced only at the interface flux level, therefore resulting in a consistent discretization of the INS equations irrespectively of the amount of artificial compressibility introduced. The discretization of the viscous term follows the well-established DG scheme named BR2. The performance and the accuracy of the method are demonstrated by computing the Kovasznay flow and the two-dimensional lid-driven cavity flow for a wide range of Reynolds numbers and for various degrees of polynomial approximation. (c) 2006 Elsevier Inc. All rights reserved.