Anisotropic mesh adaption: Towards user-independent, mesh-independent and solver-independent CFD. I: General principles. (English) Zbl 0981.76052

From the summary: The present paper is the lead article in a three-part series on anisotropic mesh adaptation and its applications to structured and unstructured meshes. A flexible approach is proposed and tested on two-dimensional, inviscid and viscous, finite volume and finite element flow solvers, over a wide range of speeds. The directional properties of an interpolation-based error estimate, extracted from the Hessian of the solution, are used to control the size and orientation of mesh edges. The approach is encapsulated into an edge-based anisotropic mesh optimization methodology (MOM), which uses a judicious sequence of four local operations: refinement, coarsening, edge swapping and point movement, to equi-distribute the error estimate along all edges, without any recourse to remeshing. The mesh adaptation convergence of the MOM loop is carefully studied for a wide variety of test cases.


76M10 Finite element methods applied to problems in fluid mechanics
76M12 Finite volume methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
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