A discontinuous Galerkin method for inviscid low Mach number flows
A discontinuous Galerkin method for inviscid low Mach number flows
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无粘性低马赫数流动的间断伽辽金法
DOI：
10.1016/j.jcp.2009.02.021
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
A. Nigro
中科院分区：
文献类型：
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作者：
F. Bassi;C. D. Bartolo;R. Hartmann;A. Nigro
本文将高阶不连续伽辽金（DG）有限元法推广到无粘低马赫数流动中。本文提出的方法旨在利用显式和隐式格式提高低马赫数下可压缩欧拉方程时间离散化的精度和效率。该算法基于经典的预处理技术，该技术通常需要修改控制方程的初始项和数值通量函数的耗散项（完全预处理方法）。本文证明了充分预处理有利于显式时间积分，而仅使用修正的数值通量函数的隐式格式是有效和准确的。因此隐式格式也可用于时间精确计算。通过求解NACA0012翼型在不同低马赫数下的无粘流动，利用不同程度的多项式近似证明了该方法的性能。在不同的网格拓扑上分别进行了预处理和不预处理的计算，分析了空间离散化对低马赫数下DG解精度的影响。
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.