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

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 |