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首页> 外文期刊>Journal of Computational Physics >Discontinuous Galerkin method for Navier-Stokes equations using kinetic flux vector splitting
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Discontinuous Galerkin method for Navier-Stokes equations using kinetic flux vector splitting

机译：动态通量矢量分裂的Navier-Stokes方程的间断Galerkin方法

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摘要

Kinetic schemes for compressible flow of gases are constructed by exploiting the connection between Boltzmann equation and the Navier-Stokes equations. This connection allows us to construct a flux splitting for the Navier-Stokes equations based on the direction of molecular motion from which a numerical flux can be obtained. The naive use of such a numerical flux function in a discontinuous Galerkin (DG) discretization leads to an unstable scheme in the viscous dominated case. Stable schemes are constructed by adding additional terms either in a symmetric or non-symmetric manner which are motivated by the DG schemes for elliptic equations. The novelty of the present scheme is the use of kinetic fluxes to construct the stabilization terms. In the symmetric case, interior penalty terms have to be added for stability and the resulting schemes give optimal convergence rates in numerical experiments. The non-symmetric schemes lead to a cell energy/entropy inequality but exhibit sub-optimal convergence rates. These properties are studied by applying the schemes to a scalar convection-diffusion equation and the 1-D compressible Navier-Stokes equations. In the case of Navier-Stokes equations, entropy variables are used to construct stable schemes.
机译：利用Boltzmann方程和Navier-Stokes方程之间的联系，构造了可压缩气体流动的动力学方案。这种联系使我们能够根据分子运动的方向构造Navier-Stokes方程的通量分裂，从中可以获得数值通量。在不连续的Galerkin（DG）离散化中如此简单地使用这种数值通量函数会导致在粘性占主导的情况下产生不稳定的方案。通过以椭圆方程的DG方案为动力，以对称或不对称的方式添加其他项来构造稳定的方案。本方案的新颖性是利用动通量来构造稳定项。在对称情况下，必须添加内部罚分项以保持稳定性，并且所得方案在数值实验中可提供最佳收敛速度。非对称方案导致单元能量/熵不等式，但表现出次优的收敛速度。通过将这些方案应用于标量对流扩散方程和一维可压缩Navier-Stokes方程，研究了这些性质。在Navier-Stokes方程的情况下，熵变量用于构造稳定方案。

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