Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Journal of Computational Physics
The surface gradient method for the treatment of source terms in the shallow-water equations
Journal of Computational Physics
ADER: A High-Order Approach for Linear Hyperbolic Systems in 2D
Journal of Scientific Computing
ADER: Arbitrary High Order Godunov Approach
Journal of Scientific Computing
Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws
Fast high order ADER schemes for linear hyperbolic equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
ADER schemes for three-dimensional non-linear hyperbolic systems
Journal of Computational Physics
ADER schemes on adaptive triangular meshes for scalar conservation laws
Journal of Computational Physics
Derivative Riemann solvers for systems of conservation laws and ADER methods
Journal of Computational Physics
Extension of WAF Type Methods to Non-Homogeneous Shallow Water Equations with Pollutant
Journal of Scientific Computing
A multi-moment finite volume formulation for shallow water equations on unstructured mesh
Journal of Computational Physics
Hi-index | 31.45 |
This paper deals with the construction of high-order ADER numerical schemes for solving the one-dimensional shallow water equations with variable bed elevation. The non-linear version of the schemes is based on ENO reconstructions. The governing equations are expressed in terms of total water height, instead of total water depth, and discharge. The ENO polynomial interpolation procedure is also applied to represent the variable bottom elevation. ADER schemes of up to fifth order of accuracy in space and time for the advection and source terms are implemented and systematically assessed, with particular attention to their convergence rates. Non-oscillatory results are obtained for discontinuous solutions both for the steady and unsteady cases. The resulting schemes can be applied to solve realistic problems characterized by non-uniform bottom geometries.