AN ADAPTIVE, HIGHER-ORDER GODUNOV METHOD FOR GAS DYNAMICS IN THREE-DIMENSIONAL ORTHOGONAL CURVILINEAR COORDINATES

We describe an adaptive higher-order Godunov method for the compressible Euler equations with an arbitrary convex equation of state in a three-dimensional system of orthogonal curvilin-ear coordinates. The single grid algorithm is a fractional-step method which uses a second-order Godunov method for gas dynamics in each fractional step. The single grid algorithm is coupled to a conservative local adaptive mesh reenement algorithm that selectively reenes regions of the computational grid to achieve a desired level of accuracy. Spherical and cylindrical coordinates are used to illustrate. Numerical results from a problem in spherical coordinates are shown.

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