A projection method for locally refined grids. (English) Zbl 0859.76047

Minion, Michael L.

J. Comput. Phys. 127, No. 1, 158-178 (1996).

A numerical method for the solution of the two-dimensional Euler equations for incompressible flow on locally refined grids is presented. The method is a modified second-order Godunov-projection method. Second-order accuracy of the numerical method in time and space is established through numerical experiments. 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.

MSC:

76M20	Finite difference methods applied to problems in fluid mechanics
76B47	Vortex flows for incompressible inviscid fluids
65M50	Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs

Keywords:

gradient operator; divergence operator; two-dimensional Euler equations; second-order Godunov-projection method; refined grid MAC projection; multigrid method