Flooding and Drying in Discontinuous Galerkin Discretizations of Shallow Water Equations
نویسنده
چکیده
Abstract. Accurate modeling of flooding and drying is important in forecasting river floods and near-shore hydrodynamics. We consider the space-time discontinuous Galerkin finite element discretization for shallow water equations with linear approximations of flow field. In which, the means (zeroth order approximation) is used to conserve the mass and momentum, and the slopes (first order approximation) are used to capture the front movement accurately in contrast to the finite volume schemes, where the slopes have to be reconstructed. As a preliminary step, we specify the front movement from some available exact solutions and show that the numerical results are second order accurate for linear polynomials. To resolve the front movement accurately in the context of discontinuous Galerkin discretizations, the front tracking and the front capturing methods are currently under investigation.
منابع مشابه
A well-balanced Runge–Kutta Discontinuous Galerkin method for the Shallow-Water Equations with flooding and drying
متن کامل
A wetting and drying treatment for the Runge–Kutta discontinuous Galerkin solution to the shallow water equations
This paper proposes a wetting and drying treatment for the piecewise linear Runge–Kutta discontinuous Galerkin approximation to the shallow water equations. The method takes a fixed mesh approach as opposed to mesh adaptation techniques and applies a post-processing operator to ensure the positivity of the mean water depth within each finite element. In addition, special treatments are applied ...
متن کاملSpace-time Discontinuous Galerkin Method for Rotating Shallow Water Flows
In the present work, we analyze the rotating shallow water equations including bottom topography using a space-time discontinuous Galerkin finite element method. The method results in non-linear equations per element, which are solved locally by establishing the element communication with a numerical HLLC flux. To deal with spurious oscillations around discontinuities, we employ a stabilization...
متن کاملiHDG: An Iterative HDG Framework for Partial Differential Equations
We present a scalable iterative solver for high-order hybridized discontinuous Galerkin (HDG) discretizations of linear partial differential equations. It is an interplay between domain decomposition methods and HDG discretizations, and hence inheriting advances from both sides. In particular, the method can be viewed as a Gauss-Seidel approach that requires only independent element-by-element ...
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 کامل