Numerical Study of Three-Dimensional Flows Using Unfactored Upwind-Relaxation Sweeping Algorithm

✍ Scribed by G.-C. Zha; E. Bilgen

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 313 KB
• Volume: 125
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1006/jcph.1996.0104

✦ Synopsis

putation which is offset to some extent by larger time step sizes. Edwards and McRae [7] developed their nonlinear

The linear stability analysis of the unfactored upwind relaxationsweeping (URS) algorithm for 3D flow field calculations has been relaxation solver for 3D viscous flows with the mixture of carried out and it is shown that the URS algorithm is unconditionally upwind and central differencing. The method is shown to stable. The algorithm is independent of the global sweeping direcbe efficient, but still related to the LU factorization. tion selection. However, choosing the direction with relatively low Employing the upwind schemes in 2D cases, implicit variable gradient as the global sweeping direction results in a higher unfactored relaxation algorithms demonstrate their strikdegree of stability. Three-dimensional compressible Euler equations are solved by using the implicit URS algorithm to study internal ing convergency rate due to large time steps allowed [8flows of a non-axisymmetric nozzle with a circular-to-rectangular 11]. For 3D cases, the achievements, however, are not transition duct and complex shock wave structures for a 3D channel so impressive. Candler and MacCormack [12] extended flow. The efficiency and robustness of the URS algorithm has been MacCormack's 1984 implicit unfactored algorithm to 3D demonstrated.