A MOVING FINITE DIFFERENCE METHOD FOR PARTIAL DIFFERENTIAL EQUATIONS

A moving grid method which has its origin from dierential geometry is studied. The method deforms an intial grid according to a vector field calculated by a Poisson equation. The forcing term of the Poisson equation is determined by the time derivative of a positive moni- tor function. It adapts the grid at each time step by keeping the volume of each cell proportional to the (normalized) time-dependent monitor func- tion. A moving finite dierence method is formulated which transforms a time dependent partial dierential equation by the grid mapping and then simulates the transformed equation on a fixed orthogonal grid in the computational domain. The method is demonstrated by solving model problems and an incompressible flow problem.

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