On the use of composite grid schemes in computational aerodynamics
Computer Methods in Applied Mechanics and Engineering
Composite overlapping meshes for the solution of partial differential equations
Journal of Computational Physics
A numerical method to calculate the two-dimensional flow around an underwater obstacle
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Using MPI-2: Advanced Features of the Message Passing Interface
Using MPI-2: Advanced Features of the Message Passing Interface
An adaptive numerical scheme for high-speed reactive flow on overlapping grids
Journal of Computational Physics
A moving overset grid method for interface dynamics applied to non-Newtonian Hele-Shaw flow
Journal of Computational Physics
Moving overlapping grids with adaptive mesh refinement for high-speed reactive and non-reactive flow
Journal of Computational Physics
Parallel clustering algorithms for structured AMR
Journal of Parallel and Distributed Computing
A high-resolution Godunov method for compressible multi-material flow on overlapping grids
Journal of Computational Physics
A High-Order Accurate Parallel Solver for Maxwell’s Equations on Overlapping Grids
SIAM Journal on Scientific Computing
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
A composite grid solver for conjugate heat transfer in fluid-structure systems
Journal of Computational Physics
An evaluation of the FCT method for high-speed flows on structured overlapping grids
Journal of Computational Physics
Adaptive mesh refinement for stochastic reaction-diffusion processes
Journal of Computational Physics
Journal of Computational Physics
Deforming composite grids for solving fluid structure problems
Journal of Computational Physics
Numerical methods for solid mechanics on overlapping grids: Linear elasticity
Journal of Computational Physics
A multithreaded solver for the 2D Poisson equation
Proceedings of the 2012 Symposium on High Performance Computing
Automatic off-body overset adaptive Cartesian mesh method based on an octree approach
Journal of Computational Physics
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
Journal of Computational Physics
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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.