A non-homogeneous Riemann solver for shallow water equations in porous media

A Fast and Compact Solver for the Shallow Water Equations

This paper presents a fast and simple method for solving the shallow water equations. The water velocity and height variables are collocated on a uniform grid and a novel, unified scheme is used to advect all quantities together. Furthermore, we treat the fluid as weakly compressible to avoid solving a pressure Poisson equation. We sacrifice accuracy and unconditional stability for speed, but w...

An Fgmres Solver for the Shallow Water Equations 3512

The Shallow Water Equations (SWE) are a set of nonlinear hyperbolic equations, describing long waves relative to the water depth. Physical phenomena such as tidal waves in rivers and seas, breaking of waves on shallow beaches and even harbour oscillations can be modelled successfully with the SWE. The 3D SWE (1.1){(1.3) given below for Cartesian (;) coordinates are based on the hydrostatic assu...

An Efficient Fgmres Solver for the Shallow Water Equations

The Shallow Water Equations (SWE) are a set of nonlinear hyperbolic equations, describing long waves relative to the water depth. Physical phenomena such as tidal waves in rivers and seas, breaking of waves on shallow beaches and even harbour oscillations can be modelled successfully with the SWE. The 3D SWE (1.1){(1.3) given below for Cartesian (;) coordinates are based on the hydrostatic assu...

Non-Monotone Stochastic Generalized Porous Media Equations∗

By using the Nash inequality and a monotonicity approximation argument, existence and uniqueness of strong solutions are proved for a class of non-monotone stochastic generalized porous media equations. Moreover, we prove for a large class of stochastic PDE that the solutions stay in the smaller L2-space provided the initial value does, so that some recent results in the literature are consider...

Instability Analysis of Miscible Displacements in Homogeneous Porous Media