Natural continuous extensions of Runge-Kutta formulas
Mathematics of Computation
Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
Nonoscillatory Central Schemes for Multidimensional Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Flux difference splitting and the balancing of source terms and flux gradients
Journal of Computational Physics
The surface gradient method for the treatment of source terms in the shallow-water equations
Journal of Computational Physics
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
Journal of Computational Physics
Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws
WENO schemes for balance laws with spatially varying flux
Journal of Computational Physics
Journal of Computational Physics
Central Runge--Kutta Schemes for Conservation Laws
SIAM Journal on Scientific Computing
Journal of Computational Physics
Balanced Central Schemes for the Shallow Water Equations on Unstructured Grids
SIAM Journal on Scientific Computing
3D Adaptive central schemes: part I. Algorithms for assembling the dual mesh
Applied Numerical Mathematics
Finite volume and WENO scheme in one-dimensional vascular system modelling
Computers & Mathematics with Applications
Advances in Engineering Software
Journal of Computational Physics
A kinetic flux-vector splitting method for single-phase and two-phase shallow flows
Computers & Mathematics with Applications
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The aim of this work is to develop a well-balanced central weighted essentially non-oscillatory (CWENO) method, fourth-order accurate in space and time, for shallow water system of balance laws with bed slope source term. Time accuracy is obtained applying a Runge-Kutta scheme (RK), coupled with the natural continuous extension (NCE) approach. Space accuracy is obtained using WENO reconstructions of the conservative variables and of the water-surface elevation. Extension of the applicability of the standard CWENO scheme to very irregular bottoms, preserving high-order accuracy, is obtained introducing two original procedures. The former involves the evaluation of the point-values of the flux derivative, coupled with the bed slope source term. The latter involves the spatial integration of the source term, analytically manipulated to take advantage from the regularity of the free-surface elevation, usually smoother than the bottom elevation. Both these procedures satisfy the C-property, the property of exactly preserving the quiescent flow. Several standard one-dimensional test cases are used to verify high-order accuracy, exact C-property, and good resolution properties for smooth and discontinuous solutions.