| Abstract: | ![]()
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. The mesh optimization generic coupling of MOM with finite volume and finite element flow solvers is shown to yield the same final mesh no matter what the starting point is. It is also shown that on such optimized meshes, the need for computational fluid dynamics (CFD) stabilization artifices, such as upwinding or artificial viscosity, are drastically reduced, if not altogether eliminated, in most well‐posed formulations. These two conclusions can be considered significant steps towards mesh‐independent and solver‐independent CFD. The structure of the three‐part series is thus, 1, general principles; 2, methodology and applications to structured and unstructured grids; 3, applications to three‐dimensional flows. Copyright © 2000 John Wiley & Sons, Ltd. |
