A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
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DOI：
10.1006/jcph.1996.5572
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发表时间：
1997-03-01
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;Rebay, S
本文研究了可压缩纳维-斯托克斯方程数值求解的高阶精确间断有限元方法。我们通过使用混合公式处理粘性项，将最初考虑用于双曲系统（例如欧拉方程）的不连续有限元离散扩展到纳维-斯托克斯方程的情况。该方法结合了基于有限体积和有限元方法的两个关键思想，通过黎曼问题来解释波传播的物理原理，并通过单元内的高阶多项式近似来获得精度。因此，该方法非常适合计算非结构化网格上纳维-斯托克斯方程的高阶精确解。通过使用常数、线性、二次和三次元素计算平板上和 NACA0012 翼型周围的可压缩粘性流，说明了该方法的性能。 (C) 1997 年学术出版社。
This paper deals with a high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations. We extend a discontinuous finite element discretization originally considered for hyperbolic systems such as the Euler equations to the case of the Navier-Stokes equations by treating the viscous terms with a mixed formulation. The method combines two key ideas which are at the basis of the finite volume and of the finite element method, the physics of wave propagation being accounted for by means of Riemann problems and accuracy being obtained by means of high-order polynomial approximations within elements. As a consequence the method is ideally suited to compute high-order accurate solution of the Navier-Stokes equations on unstructured grids, The performance of the proposed method is illustrated by computing the compressible viscous flow on a flat plate and around a NACA0012 airfoil for several flow regimes using constant, linear, quadratic, and cubic elements. (C) 1997 Academic Press.