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A finite-volume high-order ENO scheme for two-dimensional hyperbolic systems. (English) Zbl 0774.65066
From the authors’ summary: A finite-volume approach in developing a two- dimensional, high-order accurate, essentially non-oscillatory (ENO) shock-capturing scheme is considered. 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.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
35L70 Second-order nonlinear hyperbolic equations
76N15 Gas dynamics (general theory)
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