A characteristic/finite element algorithm for the 3-D Navier-Stokes equations using unstructured grids
A characteristic/finite element algorithm for the 3-D Navier-Stokes equations using unstructured grids
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DOI：
10.1016/s0045-7825(99)00003-1
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发表时间：
1999-07-27
影响因子：
7.2
通讯作者：
Ethier, CR
中科院分区：
文献类型：
--
作者：
Minev, PD;Ethier, CR
本文讨论了一种基于特征法求解三维Navier-Stokes方程的有限元算法。该算法基于对广义Stokes问题的对流项进行时间分割，包括对流项的逐点特征积分和广义Stokes问题的Uzawa积分。特征积分方案中代价最大的部分是查找包含给定特征脚的元素。本研究使用了一种非常有效的元素搜索算法，该算法对复杂几何图形特别有用。本文讨论了该算法的实现，并将所得代码的性能与基于更传统的四阶龙格-库塔对流积分的代码进行了比较。测试了各种流动问题，包括纳维-斯托克斯方程的解析解，盖子驱动腔中的流动，如何通过向后的台阶，以及端侧吻合的流动。在所有情况下，所提出的算法表现出优于传统的对流项显式处理的性能。(C) 1999 Elsevier Science S.A.版权所有
This paper discusses a finite element algorithm for solution of the 3-D Navier-Stokes equations that is based on the method of characteristics. The algorithm which is based on a time-slitting of the convective terms from the generalized Stokes problem, comprises a point-wise characteristic integration of the convective terms and Uzawa integration of the generalized Stokes problem. The most costly part of the characteristic integration scheme is the search for an element containing the foot of a given characteristic. The present study uses a very efficient algorithm for element searching which is particularly useful fbr complex geometries. The implementation of the algorithm is discussed in the paper and the resulting code's performance is compared to that of a code based on a more conventional, fourth-order Runge-Kutta convection integration. A variety of flow problems are tested, including an analytical solution of the Navier-Stokes equations, flow in a lid-driven cavity, how over a backward-facing step, and flow in an end-to-side anastomoses. In all cases, the proposed algorithm demonstrated performance superior to that of a conventional explicit treatment of the convective terms. (C) 1999 Elsevier Science S.A. All rights reserved.