Well-balanced finite volume evolution Galerkin methods for the shallow water equations
arXiv:1501.03618 · doi:10.1016/j.jcp.2006.06.015
Abstract
We present a new well-balanced finite volume method within the framework of the finite volume evolution Galerkin (FVEG) schemes. The methodology will be illustrated for the shallow water equations with source terms modelling the bottom topography and Coriolis forces. Results can be generalized to more complex systems of balance laws. The FVEG methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are taken into account explicitly. We derive a well- balanced approximation of the integral equations and prove that the FVEG scheme is well-balanced for the stationary steady states as well as for the steady jets in the rotational frame. Several numerical experiments for stationary and quasi-stationary states as well as for steady jets confirm the reliability of the well-balanced FVEG scheme.
Cited by in corpus (10)
- Collocation Methods for High-Order Well-Balanced Methods for Systems of Balance Laws
- High-order well-balanced methods for systems of balance laws: a control-based approach
- Well-balanced high-order finite difference methods for systems of balance laws
- An Arbitrary High Order and Positivity Preserving Method for the Shallow Water Equations
- Well-Balanced Central Schemes on Overlapping Cells with Constant Subtraction Techniques for the Saint-Venant Shallow Water System
- High-order well-balanced finite-volume schemes for barotropic flows. Development and numerical comparisons
- Well balanced finite volume schemes for shallow water equations on manifolds
- Runge-Kutta discontinuous local evolution Galerkin methods for the shallow water equations on the cubed-sphere
- Structure-Preserving Numerical Methods for Two Nonlinear Systems of Dispersive Wave Equations
- A least-squares based nodal scheme for cell-centered Lagrangian hydrodynamics