Parallel computation of three-dimensional flows using overlapping grids with adaptive mesh refinement
- Centre for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States), E-mail: henshaw1@llnl.gov
- Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, NY 12180 (United States), E-mail: schwed@rpi.edu
This paper describes an approach for the numerical solution of time-dependent partial differential equations in complex three-dimensional domains. The domains are represented by overlapping structured grids, and block-structured adaptive mesh refinement (AMR) is employed to locally increase the grid resolution. In addition, the numerical method is implemented on parallel distributed-memory computers using a domain-decomposition approach. The implementation is flexible so that each base grid within the overlapping grid structure and its associated refinement grids can be independently partitioned over a chosen set of processors. A modified bin-packing algorithm is used to specify the partition for each grid so that the computational work is evenly distributed amongst the processors. All components of the AMR algorithm such as error estimation, regridding, and interpolation are performed in parallel. The parallel time-stepping algorithm is illustrated for initial-boundary-value problems involving a linear advection-diffusion equation and the (nonlinear) reactive Euler equations. Numerical results are presented for both equations to demonstrate the accuracy and correctness of the parallel approach. Exact solutions of the advection-diffusion equation are constructed, and these are used to check the corresponding numerical solutions for a variety of tests involving different overlapping grids, different numbers of refinement levels and refinement ratios, and different numbers of processors. The problem of planar shock diffraction by a sphere is considered as an illustration of the numerical approach for the Euler equations, and a problem involving the initiation of a detonation from a hot spot in a T-shaped pipe is considered to demonstrate the numerical approach for the reactive case. For both problems, the accuracy of the numerical solutions is assessed quantitatively through an estimation of the errors from a grid convergence study. The parallel performance of the approach is examined for the shock diffraction problem.
- OSTI ID:
- 21159407
- Journal Information:
- Journal of Computational Physics, Vol. 227, Issue 16; Other Information: DOI: 10.1016/j.jcp.2008.04.033; PII: S0021-9991(08)00243-X; Copyright (c) 2008 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
Similar Records
Moving Overlapping Grids with Adaptive Mesh Refinement for High-Speed Reactive and Non-reactive Flow
A coupled discontinuous Galerkin-Finite Volume framework for solving gas dynamics over embedded geometries
Related Subjects
GENERAL PHYSICS
ACCURACY
ADVECTION
ALGORITHMS
BOUNDARY-VALUE PROBLEMS
CALCULATION METHODS
CONVERGENCE
DECOMPOSITION
DIFFRACTION
DIFFUSION EQUATIONS
ERRORS
EXACT SOLUTIONS
EXPLOSIONS
HOT SPOTS
INTERPOLATION
NONLINEAR PROBLEMS
PERFORMANCE
THREE-DIMENSIONAL CALCULATIONS
TIME DEPENDENCE