A numerical method for the solution of the two-dimensional Euler equatons for incompressible flow on locally refined grids is presented. The method is a second-order Godunov-projection method adapted from Bell, Colella, and Glaz. Second-order accuracy of the numerical method in time and space is established through numerical experiments. The main contributions of this work concern the formulation and implementation of a projection for refined grids. A discussion of the adjointness relation between gradient and divergence operators for a refined grid MAC projection is presented, and a refined grid approximate projection is developed. An efficient multigrid method which exactly solves the projection is developed, and a method for casting certain approximate projections as MAC projections on refined grids is presented.
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Michael L. Minion (1996) studied this question.
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