Parallel heterogeneous mesh refinement for multidimensional convection-diffusion equations using an Euler-Lagrange method
We develop an efficient finite differences numerical solution for the two-space dimension Burgers' equation, and the viscous gas dynamics equations. Our numerical solution efficiently includes the real viscous terms that model the behavior of shock, internal and boundary layers. First the equations are advanced on a coarse mesh subject to a hyperbolic stability condition. Regions of significant parabolic activity are identified using a new parabolic threshold criterion which requires no special boundary treatment. The coarse mesh is dynamically decomposed and the mesh is refined in these regions. A new biased clustering algorithm is introduced which allows tailoring the geometry of the refined meshes to the underlying machine architecture or enhancing the convergence speed of iterative methods across overlapping meshes. The decomposition is heterogeneous in the sense that the problem formulation of the equations as well as the solution methods may vary from mesh to mesh. In particular, a mixed Euler-Lagrange explicit-implicit method is developed that explicitly advances the coarse mesh relative to an Eulerian reference frame, and implicitly advances the refined meshes relative to moving Lagrangian reference frames. On the refined meshes that surround regions of significant parabolic activity, the method is second order accurate in space. A second order interpolation step from the moving refined Lagrange mesh to a corresponding Lagrange mesh, whose image in the Eulerian reference frame coincides with the original mesh refinement, preserves this spatial accuracy in the Eulerian reference frame. Schwarz iterations are used between overlapping refined meshes to communicate the interdependence of the implicit solution method that has been artificially separated into independent overlapping refined meshes to allow parallel processing. 176 refs., 61 figs., 8 tabs.
- Research Organization:
- Lawrence Livermore National Lab., CA (USA)
- DOE Contract Number:
- W-7405-ENG-48
- OSTI ID:
- 5811778
- Report Number(s):
- UCRL-53950; ON: DE89016702
- Resource Relation:
- Other Information: Thesis (Ph.D.). Portions of this document are illegible in microfiche products. Thesis. Submitted to University of California, Davis, CA
- Country of Publication:
- United States
- Language:
- English
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