High order well-balanced asymptotic preserving finite difference WENO schemes for the shallow water equations in all Froude numbers

by   Guanlan Huang, et al.

In this paper, high order semi-implicit well-balanced and asymptotic preserving finite difference WENO schemes are proposed for the shallow water equations with a non-flat bottom topography. We consider the Froude number ranging from O(1) to 0, which in the zero Froude limit becomes the "lake equations" for balanced flow without gravity waves. We apply a well-balanced finite difference WENO reconstruction, coupled with a stiffly accurate implicit-explicit (IMEX) Runge-Kutta time discretization. The resulting semi-implicit scheme can be shown to be well-balanced, asymptotic preserving (AP) and asymptotically accurate (AA) at the same time. Both one- and two-dimensional numerical results are provided to demonstrate the high order accuracy, AP property and good performance of the proposed methods in capturing small perturbations of steady state solutions.



There are no comments yet.


page 1

page 2

page 3

page 4


High-order accurate entropy stable finite difference schemes for the shallow water magnetohydrodynamics

This paper develops the high-order accurate entropy stable (ES) finite d...

An Arbitrary High Order and Positivity Preserving Method for the Shallow Water Equations

In this paper, we develop and present an arbitrary high order well-balan...

High Order Semi-implicit WENO Schemes for All Mach Full Euler System of Gas Dynamics

In this paper, we propose high order semi-implicit schemes for the all M...

An asymptotic preserving semi-implicit multiderivative solver

In this work we construct a multiderivative implicit-explicit (IMEX) sch...

A two-dimensional high-order well-balanced scheme for the shallow water equations with topography and Manning friction

We develop a two-dimensional high-order numerical scheme that exactly pr...

A well-balanced positivity-preserving quasi-Lagrange moving mesh DG method for the shallow water equations

A high-order, well-balanced, positivity-preserving quasi-Lagrange moving...

A high-order well-balanced positivity-preserving moving mesh DG method for the shallow water equations with non-flat bottom topography

A rezoning-type adaptive moving mesh discontinuous Galerkin method is pr...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.