Time Dependent Boundary Conditions for Hyperbolic Systems
Abstract
Time dependent numerical models for hyperbolic systems, such as the fluid dynamics equations, require time dependent boundary conditions when the systems are solved in a finite domain. The "correct" boundary condition depends on the external solution, but for many problems the external solution is not known. In such cases nonreflecting boundary conditions often produce solutions with the desired behavior. This paper extends the concept of nonreflecting boundary conditions to the multidimensional case in non-rectangular coordinate systems. Results are given for several fluid dynamics test problems: the traveling shock wave, shock tube, spherical explosion, and homologous expansion problems in one dimension, and a traveling shock wave moving at a 45° angle with respect to the x axis in two dimensions.
- Publication:
-
Journal of Computational Physics
- Pub Date:
- January 1987
- DOI:
- 10.1016/0021-9991(87)90041-6
- Bibcode:
- 1987JCoPh..68....1T
- Keywords:
-
- Boundary Conditions;
- Boundary Value Problems;
- Computational Fluid Dynamics;
- Hyperbolic Differential Equations;
- Time Dependence;
- Cartesian Coordinates;
- Explosions;
- Shock Tubes;
- Shock Wave Propagation;
- Traveling Waves;
- Fluid Mechanics and Heat Transfer