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首页> 外文期刊>Journal of Computational Physics >A discontinuous Galerkin method for inviscid low Mach number flows
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A discontinuous Galerkin method for inviscid low Mach number flows

机译：不连续的低马赫数流的不连续Galerkin方法

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In this work we extend the high-order discontinuous Galerkin (DG) finite element method to inviscid low Mach number flows. The method here presented is designed to improve the accuracy and efficiency of the solution at low Mach numbers using both explicit and implicit schemes for the temporal discretization of the compressible Euler equations. The algorithm is based on a classical preconditioning technique that in general entails modifying both the instationary term of the governing equations and the dissipative term of the numerical flux function (full preconditioning approach). In the paper we show that full preconditioning is beneficial for explicit time integration while the implicit scheme turns out to be efficient and accurate using just the modified numerical flux function. Thus the implicit scheme could also be used for time accurate computations. The performance of the method is demonstrated by solving an inviscid flow past a NACA0012 airfoil at different low Mach numbers using various degrees of polynomial approximations. Computations with and without preconditioning are performed on different grid topologies to analyze the influence of the spatial discretization on the accuracy of the DG solutions at low Mach numbers.
机译：在这项工作中，我们将高阶不连续Galerkin（DG）有限元方法扩展为无粘性的低马赫数流。本文介绍的方法旨在使用可压缩的Euler方程的时间离散化的显式和隐式方案，在低马赫数下提高解的准确性和效率。该算法基于经典的预处理技术，通常需要修改控制方程的固定项和数值通量函数的耗散项（完全预处理方法）。在本文中，我们表明完全预处理对于显式时间积分是有好处的，而隐式方案仅使用修改后的数值通量函数就变得高效，准确。因此，隐式方案也可以用于时间精确的计算。通过使用不同程度的多项式逼近来求解通过低马赫数的，穿过NACA0012机翼的无粘性流，证明了该方法的性能。在不同的网格拓扑上执行带或不带预处理的计算，以分析空间离散化对低马赫数下DG解的准确性的影响。

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