Composite overlapping meshes for the solution of partial differential equations
Journal of Computational Physics
A manual for the multiblock PARTI runtime primitives
A manual for the multiblock PARTI runtime primitives
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 family of low dispersive and low dissipative explicit schemes for flow and noise computations
Journal of Computational Physics
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
On sub-linear convergence for linearly degenerate waves in capturing schemes
Journal of Computational Physics
Journal of Computational Physics
A composite grid solver for conjugate heat transfer in fluid-structure systems
Journal of Computational Physics
Journal of Computational Physics
Deforming composite grids for solving fluid structure problems
Journal of Computational Physics
Deforming composite grids for solving fluid structure problems
Journal of Computational Physics
Upwind schemes for the wave equation in second-order form
Journal of Computational Physics
Richardson Extrapolation for Linearly Degenerate Discontinuities
Journal of Scientific Computing
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This paper presents a new computational framework for the simulation of solid mechanics on general overlapping grids with adaptive mesh refinement (AMR). The approach, described here for time-dependent linear elasticity in two and three space dimensions, is motivated by considerations of accuracy, efficiency and flexibility. We consider two approaches for the numerical solution of the equations of linear elasticity on overlapping grids. In the first approach we solve the governing equations numerically as a second-order system (SOS) using a conservative finite-difference approximation. The second approach considers the equations written as a first-order system (FOS) and approximates them using a second-order characteristic-based (Godunov) finite-volume method. A principal aim of the paper is to present the first careful assessment of the accuracy and stability of these two representative schemes for the equations of linear elasticity on overlapping grids. This is done by first performing a stability analysis of analogous schemes for the first-order and second-order scalar wave equations on an overlapping grid. The analysis shows that non-dissipative approximations can have unstable modes with growth rates proportional to the inverse of the mesh spacing. This new result, which is relevant for the numerical solution of any type of wave propagation problem on overlapping grids, dictates the form of dissipation that is needed to stabilize the scheme. Numerical experiments show that the addition of the indicated form of dissipation and/or a separate filter step can be used to stabilize the SOS scheme. They also demonstrate that the upwinding inherent in the Godunov scheme, which provides dissipation of the appropriate form, stabilizes the FOS scheme. We then verify and compare the accuracy of the two schemes using the method of analytic solutions and using problems with known solutions. These latter problems provide useful benchmark solutions for time dependent elasticity. We also consider two problems in which exact solutions are not available, and use a posterior error estimates to assess the accuracy of the schemes. One of these two problems is additionally employed to demonstrate the use of dynamic AMR and its effectiveness for resolving elastic ''shock'' waves. Finally, results are presented that compare the computational performance of the two schemes. These demonstrate the speed and memory efficiency achieved by the use of structured overlapping grids and optimizations for Cartesian grids.