Abstract
A second-order Godunov method is proposed for the solution of general systems of conservation laws on arbitrary grids. Some applications are discussed: moving and deforming grids, local grid refinement, Lagrangian grids that make contact discontinuities perfectly sharp, and a new way to solve the time dependent small disturbance transonic flow equations of gas dynamics. As part of the algorithm, a way is presented to solve generalized Riemann problems with second-order accuracy.
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