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Higher order finite volume central schemes for multi-dimensional hyperbolic problems. (English) Zbl 1393.65044

Summary: Different ways of implementing dimension-by-dimension CWENO reconstruction are discussed and the most efficient method is applied to develop a fourth order accurate finite volume central scheme for multi-dimensional hyperbolic problems. Fourth order accuracy and shock capturing nature of the scheme are demonstrated in various nonlinear multi-dimensional problems. In order to show the overall performance of the present central scheme numerical errors and non-oscillatory behavior are compared with existing multi-dimensional CWENO based central schemes for various multi-dimensional problems. Moreover, the benefits of the present fourth order central scheme over third order implementation are shown by comparing the numerical dissipation and computational cost between the two.

MSC:

65N08 Finite volume methods for boundary value problems involving PDEs
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
35L65 Hyperbolic conservation laws
35Q31 Euler equations
76N15 Gas dynamics (general theory)
76L05 Shock waves and blast waves in fluid mechanics
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