相关论文: Kinetic entropy inequality and hydrostatic reconst…
We propose an efficient numerical scheme for the resolution of a non-hydrostatic Saint-Venant type model. The model is a shallow water type approximation of the incompressbile Euler system with free surface and slightly differs from the…
In this work, we develop a new hydrostatic reconstruction procedure to construct well-balanced schemes for one and multilayer shallow water flows, including wetting and drying. Initially, we derive the method for a path-conservative finite…
We are interested in the numerical approximation of the hydrostatic free surface incompressible Navier-Stokes equations. By using a layer-averaged version of the equations, we are able to extend previous results obtained for shallow water…
The present work focuses on the numerical approximation of the weak solutions of the shallow water model over a non-flat topography. In particular, we pay close attention to steady solutions with nonzero velocity. The goal of this work is…
We propose a variational framework for the resolution of a non-hydrostatic Saint-Venant type model with bottom topography. This model is a shallow water type approximation of the incompressible Euler system with free surface and slightly…
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…
First-order hydrostatic reconstruction (HR) schemes for shallow water equations are highly diffusive whereas high-order schemes can produce entropy-violating solutions. Our goal is to develop a flux correction with maximum antidiffusive…
In this contribution we derive and analyze a new numerical method for kinetic equations based on a variable transformation of the moment approximation. Classical minimum-entropy moment closures are a class of reduced models for kinetic…
The hydrostatic equilibrium state is the consequence of the exact hydrostatic balance between hydrostatic pressure and external force. Standard finite volume or finite difference schemes cannot keep this balance exactly due to their…
The moment of entropy equation for vector-BGK model results in the entropy equation for macroscopic model. However, this is usually not the case in numerical methods because the current literature consists only of entropy conserving/stable…
We present a novel discrete velocity kinetic framework to consistently recover the viscous shallow water equations. The proposed model has the following fundamental advantages and novelties: (a) A novel interpretation and general framework…
We study nonlinear hyperbolic conservation laws with non-convex flux in one space dimension and, for a broad class of numerical methods based on summation by parts operators, we compute numerically the kinetic functions associated with each…
In this work we consider entropy stable discontinuous Galerkin methods applied to nonconservative hyperbolic systems. We introduce a new class of entropy conservative fluctuations that allow us to construct entropy conservative schemes…
This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted…
The following work concerns the construction of an entropy dissipative finite volume solver based on the convex combination of an entropy conservative and an entropy dissipative flux. We aim to construct a semidiscrete scheme that is…
Entropy stable methods have become increasingly popular in the field of computational fluid dynamics. They often work by satisfying some form of a discrete entropy inequality: a discrete form of the 2nd law of thermodynamics. Schemes which…
Many numerical schemes for hyperbolic systems require a piecewise polynomial reconstruction of the cell averaged values, and to simulate perturbed steady states accurately we require a so called 'well balanced' reconstruction scheme. For…
We present in this paper a pressure correction scheme for the drift-flux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is…
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant…
In this paper, C1-conforming element methods are analyzed for the stream function formulation of a single layer non-stationary quasi-geostrophic equation in the ocean circulation model. In its first part, some new regularity results are…