Simulation of a viscous fluid spreading by a bidimensional shallow water model

TL;DR

This paper introduces a numerical method for simulating viscous fluid spreading in a moving domain using a bidimensional shallow water model, applicable to flooding and tsunami intrusion scenarios.

Contribution

It develops a novel numerical approach based on the Arbitrary Lagrangian Eulerian formulation for viscous shallow water equations in a moving domain.

Findings

Effective simulation of flooding and tsunami intrusion scenarios.

Accurate modeling of viscous fluid spreading in dynamic domains.

Validation of the numerical method against benchmark problems.

Abstract

In this paper we propose a numerical method to solve the Cauchy problem based on the viscous shallow water equations in an horizontally moving domain. More precisely, we are interested in a flooding and drying model, used to modelize the overflow of a river or the intrusion of a tsunami on ground. We use a non conservative form of the two-dimensional shallow water equations, in eight velocity formulation and we build a numerical approximation, based on the Arbitrary Lagrangian Eulerian formulation, in order to compute the solution in the moving domain.