Related papers: An adaptive central-upwind scheme on quadtree grid…
We present an adaptive well-balanced positivity preserving central-upwind scheme on quadtree grids for shallow water equations. The use of quadtree grids results in a robust, efficient and highly accurate numerical method. The quadtree…
In this paper, we construct a robust adaptive central-upwind scheme on unstructured triangular grids for two-dimensional shallow water equations with variable density. The method is well-balanced, positivity-preserving, and oscillation-free…
In this work, we develop a robust adaptive well-balanced and positivity-preserving central-upwind scheme on unstructured triangular grids for shallow water equations. The numerical method is an extension of the scheme from [{\sc Liu {\em et…
Our goal was to develop a robust algorithm for numerical simulation of one-dimensional shallow-water flow in a complex multiply-connected channel network with arbitrary geometry and variable topography. We apply a central-upwind scheme with…
This work introduces a novel adaptive central-upwind scheme designed for simulating compressible flows with discontinuities in the flow field. The proposed approach offers significant improvements in computational efficiency over the…
In this paper, we construct a well-balanced, positivity preserving finite volume scheme for the shallow water equations based on a continuous, piecewise linear discretization of the bottom topography. The main new technique is a special…
In order to improve the application maturity of high-order difference schemes, the free-stream preservation property, whose importance has been widely recognized in recent years, has been developed into a focus of study.. In past…
Applying high-order finite-difference schemes, like the extensively used linear-upwind or WENO schemes, to curvilinear grids can be problematic. The geometrically induced error from grid Jacobian and metrics evaluation can pollute the flow…
We present a new high-resolution, non-oscillatory semi-discrete central-upwind scheme for one-dimensional two-layer shallow-water flows with friction and entrainment along channels with arbitrary cross sections and bottom topography. These…
We develop a well-balanced central-upwind scheme for rotating shallow water model with horizontal temperature and/or density gradients---the thermal rotating shallow water (TRSW). The scheme is designed using the flux globalization…
We present a first order scheme based on a staggered grid for the shallow water equations with topography in two space dimensions, which enjoys several properties: positivity of the water height, preservation of constant states, and weak…
In this paper, we propose a new well-balanced fifth-order finite volume WENO method for solving one- and two-dimensional shallow water equations with bottom topography. The well-balanced property is crucial to the ability of a scheme to…
We propose novel less diffusive schemes for conservative one- and two-dimensional hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges in the development of accurate and robust numerical methods for the…
We develop well-balanced central schemes on overlapping cells for the Saint-Venant shallow water system and its variants. The main challenge in deriving the schemes is related to the fact that the Saint-Venant system contains a geometric…
For the first time, a general two-parameter family of entropy conservative numerical fluxes for the shallow water equations is developed and investigated. These are adapted to a varying bottom topography in a well-balanced way, i.e.…
A well-designed numerical method for the shallow water equations (SWE) should ensure well-balancedness, nonnegativity of water heights, and entropy stability. For a continuous finite element discretization of a nonlinear hyperbolic system…
In this work, we focus on the numerical approximation of the shallow water equations in two space dimensions. Our aim is to propose a well-balanced, all-regime and positive scheme. By well-balanced, it is meant that the scheme is able to…
We develop a new finite volume method using unstructured mesh-vertex grids for coupled systems modeling shallow water flows and solute transport over complex bottom topography. Novel well-balanced positivity preserving discretization…
We present a fully conservative, skew-symmetric finite difference scheme on transformed grids. The skew-symmetry preserves the kinetic energy by first principles, simultaneously avoiding a central instability mechanism and numerical…
We develop a new second-order unstaggered path-conservative central-upwind (PCCU) scheme for ideal and shallow water magnetohydrodynamics (MHD) equations. The new scheme possesses several important properties: it locally preserves the…