Coordinate System Control: Adaptive Meshes,
LOS ALAMOS NATIONAL LAB NM
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In the numerical solution of transient fluid flow problems, the flow variables are calculated at a finite number of aircraft. Typically, the points form ordered arrays which are joined together in some systematic way to form a computation mesh. On this mesh, the flow equations are approximated by finite differences, which are then marched in time. An algorithm which concentrates and disperses points automatically based on the numerical solution of the flow equations is described as adaptive. Here, an adaptive algorithm is derived from a minimum principle, and its application to transient flow problems in two dimensions is described. The major topics discussed are the variational formulation of a mesh generator with interior control, its use in adaptively rezoning a time-dependent problem, and the solution of the inverse problem to allow adaptive zoning of arbitrary initial meshes.