High-order semi-discrete central-upwind schemes for multi-dimensional Hamilton--Jacobi equations
Journal of Computational Physics
A central-constrained transport scheme for ideal magnetohydrodynamics
Journal of Computational Physics
Non-oscillatory central schemes for one- and two-dimensional MHD equations: I
Journal of Computational Physics
Central schemes on overlapping cells
Journal of Computational Physics
On the Total Variation of High-Order Semi-Discrete Central Schemes for Conservation Laws
Journal of Scientific Computing
Computations of steady and unsteady transport of pollutant in shallow water
Mathematics and Computers in Simulation
3D Adaptive central schemes: part I. Algorithms for assembling the dual mesh
Applied Numerical Mathematics
Applied Numerical Mathematics
MUSTA Fluxes for systems of conservation laws
Journal of Computational Physics
Fourth-order balanced source term treatment in central WENO schemes for shallow water equations
Journal of Computational Physics
Applied Numerical Mathematics
A characteristic-based shock-capturing scheme for hyperbolic problems
Journal of Computational Physics
A new fourth-order non-oscillatory central scheme for hyperbolic conservation laws
Applied Numerical Mathematics
FORCE schemes on unstructured meshes I: Conservative hyperbolic systems
Journal of Computational Physics
3D adaptive central schemes: Part I. Algorithms for assembling the dual mesh
Applied Numerical Mathematics
Journal of Computational Physics
Advances in Engineering Software
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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.