Well-balanced Finite Volume Evolution Galerkin Methods for the 2d Shallow Water Equations on Adaptive Grids
نویسندگان
چکیده
Abstract. We extend a well-balanced finite volume evolution Galerkin (FVEG) method to nonuniform grids. As a model problem, we consider the two-dimensional shallow water equations with a source term modelling the bottom topography. Our work is based on the well-balanced scheme proposed in (Lukáčová, Noelle, Kraft, J.Comp.Physics, 221, 2007). We present selected test cases to demonstrate the capabilities of the scheme.
منابع مشابه
Well-balanced finite volume evolution Galerkin methods for the shallow water equations
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 appr...
متن کاملFinite Volume Evolution Galerkin Methods for the Shallow Water Equations with Dry Beds
We present a new Finite Volume Evolution Galerkin (FVEG) scheme for the solution of the shallow water equations (SWE) with the bottom topography as a source term. Our new scheme will be based on the FVEG methods presented in (Lukáčová, Noelle and Kraft, J. Comp. Phys. 221, 2007), but adds the possibility to handle dry boundaries. The most important aspect is to preserve the positivity of the wa...
متن کاملWell-balanced r-adaptive and moving mesh space-time discontinuous Galerkin method for the shallow water equations
In this article we introduce a well-balanced discontinuous Galerkin method for the shallow water equations on moving meshes. Particular emphasis will be given on r-adaptation in which mesh points of an initially uniform mesh move to concentrate in regions where interesting behaviour of the solution is observed. Obtaining well-balanced numerical schemes for the shallow water equations on fixed m...
متن کاملWell-balanced bicharacteristic-based scheme for multilayer shallow water flows including wet/dry fronts
The aim of this paper is to present a new well-balanced finite volume scheme for two-dimensional multilayer shallow water flows including wet/dry fronts. The ideas, presented here for the two-layer model, can be generalized to a multilayer case in a straightforward way. The method developed here is constructed in the framework of the Finite Volume Evolution Galerkin (FVEG) schemes. The FVEG met...
متن کاملCoupling superposed 1D and 2D shallow-water models: source terms and finite volume schemes
We study the superposition of 1D and 2D shallow-water equations with non-flat topographies, in the context of river flood modeling. Since we superpose both models in the bidimensional areas, we focus on the definition of the coupling term required in the 1D equations. Using explicit finite volume schemes, we propose a definition of the discrete coupling term leading to schemes globally well-bal...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009