Distributed octree data structures and local refinement method for the parallel solution of three-dimensional conservation laws. (English) Zbl 0937.65107
Bern, Marshall W. (ed.) et al., Grid generation and adaptive algorithms. Proceedings of a workshop, integral part of 1996-97 IMA program, Minnesota Univ., Minneapolis, MN, USA, April 28 - May 2, 1997. New York, NY: Springer. IMA Vol. Math. Appl. 113, 113-134 (1999).
Summary: Conservation laws are solved by a local Galerkin finite element procedure with adaptive space-time mesh refinement and explicit time integration. A distributed octree structure representing a spatial decomposition of the domain is used for mesh generation, and later may be used to correct for processor load imbalances introduced at adaptive enrichment steps. A Courant stability condition is used to select smaller time steps on smaller elements of the mesh, thereby greatly increasing efficiency relative to methods having a single global time step. To accommodate the variable time steps, octree partitioning is extended to use weights derived from element size. Computational results are presented for the three-dimensional Euler equations of compressible flow solved on an IBM SP2 computer. The problem examined is the flow inside a perforated shock tube.
For the entire collection see [Zbl 0932.00052].
For the entire collection see [Zbl 0932.00052].
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
| 76N10 | Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 35L25 | Higher-order hyperbolic equations |
