We present the first fourth-order central scheme for two-dimensional hyperbolic systems of conservation laws. Our new method is based on a central weighted nonoscillatory approach. The heart of our method is the reconstruction step, in which a genuinely two-dimensional interpolant is reconstructed from cell averages by taking a convex combination of building blocks in the form of biquadratic polynomials. Similarly to other central schemes, our new method enjoys the simplicity of the black-box approach. All that is required in order to solve a problem is to supply the flux function and an estimate on the speed of propagation. The high-resolution properties of the scheme as well as its resistance to mesh orientation, and the effectiveness of the componentwise approach, are demonstrated in a variety of numerical examples.

A Fourth Order Central WENO Scheme for Multi-Dimensional Hyperbolic Systems of Conservation Laws

PUPPO, GABRIELLA ANNA;
2002-01-01

Abstract

We present the first fourth-order central scheme for two-dimensional hyperbolic systems of conservation laws. Our new method is based on a central weighted nonoscillatory approach. The heart of our method is the reconstruction step, in which a genuinely two-dimensional interpolant is reconstructed from cell averages by taking a convex combination of building blocks in the form of biquadratic polynomials. Similarly to other central schemes, our new method enjoys the simplicity of the black-box approach. All that is required in order to solve a problem is to supply the flux function and an estimate on the speed of propagation. The high-resolution properties of the scheme as well as its resistance to mesh orientation, and the effectiveness of the componentwise approach, are demonstrated in a variety of numerical examples.
2002
hyperbolic systems, central difference schemes, high-order accuracy, nonoscillatory schemes, weighted essentially nonoscillatory reconstruction, central weighted essentially nonoscilla- tory reconstruction
Levy, D.; Puppo, GABRIELLA ANNA; Russo, G.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/1789587
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