Factorized Implicit Upwind Methods Applied to Inviscid Flows at High Mach Number
Factorized Implicit Upwind Methods Applied to Inviscid Flows at High Mach Number
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DOI：
10.2514/2.866
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发表时间：
2000
期刊：
影响因子：
2.5
通讯作者：
L. Mottura;L. Vigevano;M. Zaccanti
中科院分区：
文献类型：
--
作者：
L. Mottura;L. Vigevano;M. Zaccanti
本文通过对马赫数为5 ~ 20的二维定常无粘绕流的数值试验，比较了几种近似因式分解方法和用Roe近似Riemann解进行的有限体积空间离散方法的性能。比较进行评估，通过数值实验，每种方法的最佳Courant数。交替方向隐式和上下对称高斯-赛德尔方法在CPU时间方面产生最有效的因子分解。前者随马赫数的增加表现得很平滑，其性能不受网格尺寸的影响。后者可以实现更高的效率，但强烈依赖于所执行的松弛步骤的数量，需要在马赫数和网格尺寸方面进行优化。I.引言在时间推进、激波捕捉方法中，通常需要一个N隐式时间积分来改善向稳态的收敛。对于高马赫数的真实的气流，这种要求尤其正确，因为在这种情况下，显式方法的实际稳定性极限特别严格。将多步隐式方法应用于多维结构网格所产生的大块带状线性化算子，采用近似因子分解（AF）方法可以有效地求解。隐式算子可以沿网格方向沿着分裂，如Briley和McDonald 1和Beam和Warming 2的早期交替方向隐式（ADI）格式，或分裂成两个下-上（LU）因子，如Steger和Warming 3和Jameson和Turkel的原始LU格式。[4]然而，ADI格式如果不增加适当的数值阻尼，当以δ形式表示时，可能在三维中变得不稳定。因此，LU分解已经变得越来越流行，并且近年来已经提出了对该技术的许多改进。5 Yoon和Jameson，6，7结合LU分解a
The performance of several approximate factorization methods, coupled with a e nite volume spatial discretization using Roe’ s approximate Riemann solver, are compared by means of numerical tests on a two-dimensional steady inviscid e ow past a blunt body at Mach numbers ranging from 5 to 20. The comparisons are carried out evaluating, by numerical experiments, the optimal Courant number of each method. The alternating direction implicit and the lower ‐upper symmetric Gauss ‐Seidel methods result in the most efe cient factorizations, in terms of CPU time. The former behaves smoothly with increasing Mach number, and its performance is not affected by the grid size. The latter may achieve higher efe ciency but is strongly dependent on the number of relaxation steps performed, requiring optimization in terms of Mach number and grid size. I. Introduction A N IMPLICIT time integration is usually required to improve convergence toward steady state in time-marching, shockcapturing methods. This requirement is particularly true for high Mach number real gas e ows where the practical stability limit of explicit methods is particularly severe. The large block banded linearized operators, resulting from the application of multistep implicitmethodsto multidimensionalstructuredgrids,aresolvedmost efe ciently by resorting to approximate factorization (AF). The implicit operator may be split along the grid directions, as in the early alternating direction implicit (ADI) schemes of Briley and McDonald 1 andBeamand Warming, 2 orintotwolower ‐upper(LU) factors, as in the original LU schemes of Steger and Warming 3 and Jameson and Turkel. 4 The ADI scheme, without the addition of an appropriate amount of numerical damping, may, however, become unstable in three dimensions when formulated in delta form. Therefore, the LU factorization has become increasingly popular, and many improvements to this technique have been proposed in recent years. 5 Yoon and Jameson, 6,7 combined the LU factoriza