A FINITE-VOLUME HIGH-ORDER ENO SCHEME FOR 2-DIMENSIONAL HYPERBOLIC SYSTEMS

We consider here the finite-volume approach in developing a two-dimensional, high-order accurate, essentially non-oscillatory shock-capturing scheme. Such a scheme achieves high-order spatial accuracy by a piecewise polynomial approximation of the solution from its cell averages. High-order Runge-Kutta methods are employed for time integration, thus making such schemes best-suited for unsteady problems. The focal point in our development is a high-order spatial operator which will retain high-order accuracy in smooth regions, yet avoid the oscillatory behavior that is associated with interpolation across steep gradients. Such an operator is first presented within the context of a scalar function on a rectangular mesh and then extended to hyperbolic systems of equations and curvilinear meshes. Spatial and temporal accuracy are validated through grid refinement studies, involving the solutions of scalar hyperbolic equations and the Euler equations of gas dynamics. Through a control-volume approach, we find that this two-dimensional scheme is readily applied to inviscid flow problems involving solid walls and non-trivial geometries. Results of a physically relevant, numerical experiment are presented for qualitative and quantitative examination. © 1993 by Academic Press, Inc.