Natural continuous extensions of Runge-Kutta formulas
Mathematics of Computation
Genuinely multidimensional upwinding for the 2D shallow water equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
A Third-Order Semidiscrete Central Scheme for Conservation Laws and Convection-Diffusion Equations
SIAM Journal on Scientific Computing
A Fourth-Order Central WENO Scheme for Multidimensional Hyperbolic Systems of Conservation Laws
SIAM Journal on Scientific Computing
Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Journal of Computational Physics
Applied Numerical Mathematics
An efficient ghost fluid method for compressible multifluids in Lagrangian coordinate
Applied Numerical Mathematics
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Simple central-upwind schemes based on central weighted essentially non-oscillatory reconstructions are proposed in this paper for computing the approximate solutions of one- and two-dimensional Saint-Venant system of shallow water equations with high-resolution. Since the nonuniform width of the different local Riemann fans is calculated more accurately, the central-upwind schemes enjoy a much smaller numerical viscosity and the staggering between two neighboring sets of grids is avoided. Since the central-upwind schemes are combined with fourth-order central weighted essentially non-oscillatory reconstructions, the hereafter called CWENO-type central-upwind schemes have non-oscillatory behavior. The numerical results show the desired accuracy and high-resolution of our methods.