Abstract
A system of elliptic partial differential equations and boundary conditions has been developed for generating boundary-fitted element discretizations of two-dimensional free and moving boundary problems. Terms in the differential equations are scaled for dimensional homogeneity and adjustable weighting of orthogonality, smoothness, and concentration of the coordinate mesh they govern. Grid points become finite element nodes mapped isoparametrically or subparametrically from a simple or patched computational domain. Concentration terms contain control functions and parameters that influence node spacing along each coordinate independently; overall control is by patchwise parameters and functions. Successful selection of these to follow deforming flow regions is straightforward and is illustrated by analysis of steady and transient slide coating flows.
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