Implicit time-marching methods for the transonic Euler equations
| Autor: | Daiguji, Hisaaki |
|---|---|
| Jazyk: | japonština |
| Rok vydání: | 1985 |
| Zdroj: | 航空宇宙技術研究所特別資料 = Special Publication of National Aerospace Laboratory SP-5. 5:51-60 |
| ISSN: | 0289-260X |
| Popis: | In this paper implicit time-marching methods for solving the compressible Euler equations in general curvilinear coordinates are presented, laying stress on treatments of the solid wall boundary. In one of the present methods, the momentum equations of contravariant velocity components are used instead of the momentum equations of physical velocity components in the existing theories. The numerical methods are based on the well-known Beam-Warming delta-form approximate-factorization scheme (1978), and make use of the diagonal form by Pulliam-Chaussee (198l) and the flux splitting by Steger-Warming (1981). Use of these two techniques requires less computational work and is capable of taking a sufficiently large Courant number. The finite-difference equations obtained finally can be easily solved by dividing them into five steps. The first, third and fifth steps are product of matrix by vector, and the second and fourth steps are the calculation of a system of linear equations with a tri-diagonal matrix by Gaussian elimination. The solid wall boundary condition is only one condition where the contravariant velocity component transverse to the boundary is zero, provided that the fundamental equations can be applied on this boundary. This boundary condition must be considered first immediately after the explicit calculation, and next in the system of linear equations in the implicit calculation. These treatments of the boundary condition can be realized by using the momentum equations of contravariant velocity components. The values of the residual, i. e. right hand side, including at and near the boundary points, can be completely reduced to zero by these treatments. 資料番号: NALSP0005008 レポート番号: NAL SP-5 |
| Databáze: | OpenAIRE |
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