| タイトル | New Developments in the Method of Space-Time Conservation Element and Solution Element-Applications to Two-Dimensional Time-Marching Problems |
| 本文（外部サイト） | http://hdl.handle.net/2060/19950010470 |
| 著者（英） | Chang, Sin-Chung; Wang, Xiao-Yen; Chow, Chuen-Yen |
| 著者所属（英） | NASA Lewis Research Center |
| 発行日 | 1994-12-01 |
| 言語 | eng |
| 内容記述 | A new numerical discretization method for solving conservation laws is being developed. This new approach differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is motivated by several important physical/numerical considerations and designed to avoid several key limitations of the above traditional methods. As a result of the above considerations, a set of key principles for the design of numerical schemes was put forth in a previous report. These principles were used to construct several numerical schemes that model a 1-D time-dependent convection-diffusion equation. These schemes were then extended to solve the time-dependent Euler and Navier-Stokes equations of a perfect gas. It was shown that the above schemes compared favorably with the traditional schemes in simplicity, generality, and accuracy. In this report, the 2-D versions of the above schemes, except the Navier-Stokes solver, are constructed using the same set of design principles. Their constructions are simplified greatly by the use of a nontraditional space-time mesh. Its use results in the simplest stencil possible, i.e., a tetrahedron in a 3-D space-time with a vertex at the upper time level and other three at the lower time level. Because of the similarity in their design, each of the present 2-D solvers virtually shares with its 1-D counterpart the same fundamental characteristics. Moreover, it is shown that the present Euler solver is capable of generating highly accurate solutions for a famous 2-D shock reflection problem. Specifically, both the incident and the reflected shocks can be resolved by a single data point without the presence of numerical oscillations near the discontinuity. |
| NASA分類 | NUMERICAL ANALYSIS |
| レポートNO | 95N16885
NASA-TM-106758
E-9180
NAS 1.15:106758 |
| 権利 | Copyright, Distribution as joint owner in the copyright |
|
