Solving the Euler Equations Using Adaptive Mesh Motion and Refinement
ARMY ARMAMENT RESEARCH DEVELOPMENT AND ENGINEERING CENTER WATERVLIET NY BENET LABS
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We use an adaptive mesh moving and refinement finite volume method to solve the transient Euler equations of compressible flow in one and two space dimensions. Numerical solutions are generated by a MacCormack scheme with Daviss artificial viscosity model. Richardsons extrapolation is used to calculate estimates of the local discretization error which can be used to control mesh motion and refinement. Questions regarding the optimal combination of adaptive strategies and the characterization of the initial mesh are investigated. Results indicate that local mesh refinement with and without mesh moving provide dramatic improvements in accuracy over uniform mesh solutions that mesh motion provides good results on relatively fine initial meshes that each problem has an optimal initial mesh and that it is more efficient to begin with a coarser than optimal mesh and refine rather than starting with too fine a mesh and that a combination of both the adaptive strategies produced the most accurate solutions.
- Numerical Mathematics
- Fluid Mechanics