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A general topology Godunov method. (English) Zbl 0665.76032
We describe a numerical technique for solving 2-dimensional compressible multimaterial problems using a general topology mesh. Multimaterial problems are characterized by the presence of interfaces whose shapes may become arbitrarily complex in the course of dynamic evolution. Computational methods based on more conventional fixed-connectivity quadrilateral meshes do not have adequate flexibility to follow convoluted interface shapes and frequently fail due to excessive mesh distortion. The present method is based on a mesh of arbitrary polygonal cells. Because this mesh is dual to a triangulation, its topology is unrestricted and it is able to accommodate arbitrary boundary shapes. Additionally, this mesh is able to quickly and smoothly change local mesh resolution, thus economizing on the number of mesh cells, and it is able to improve mesh isotropy because in a region of uniform mesh the cells tend to become regular hexagons. The underlying algorithms are based on those of the CAVEAT code. These consist of an explicit, finite-volume, cell-centered, arbitrary Lagrangian-Eulerian technique, coupled with the Godunov method, which together are readily adaptable to a general topology mesh.
Several special techniques have been developed for this extension to a more general mesh. They include an interface propagation scheme based on Huygens’ construction, a “near-Lagrangian” mesh rezoning algorithm that minimizes advection while enhancing mesh regularity, an efficient global remapping algorithm that is capable of conservatively transferring quantities from one general mesh to another and various mesh restructering algorithms, such as mesh reconnection, smoothing, and point addition and deletion.

MSC:
76D05 Navier-Stokes equations for incompressible viscous fluids
65N99 Numerical methods for partial differential equations, boundary value problems
76M99 Basic methods in fluid mechanics
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