Meshless simulation of dam break using MLPG-RBF and shallow water equations

Juraj Mužík,Martina Holičková,S Jemioło,A Zbiciak,M Gajewski,M Mitew-Czajewska,M Krzemiński

doi:10.1051/matecconf/201711700127

Juraj Mužík, Martina Holičková + Show 5 more

Open Access

https://doi.org/10.1051/matecconf/201711700127

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Journal: MATEC Web of Conferences	Publication Date: Jan 1, 2017
License type: cc-by

Affiliation: University of Žilina

Abstract

This article focuses on the application of the meshless local Petrov-Galerkin (MLPG) method to solve the shallow water equations (SWE). This localized approach is based on the meshless weak formulation with the use of radial-basis functions (RBF) as the trial functions. Comparing with mesh-based methods, the present method is more efficient for large-scale problems with complex geometries. In this work, the numerical model is applied to simulate a dam-break problem as one of most descriptive benchmark problems for SWE. As a result, the adopted meshless method not only shows its algorithm applicability for class of problems described by SWE, but also brings more efficiency than several conventional mesh-based methods.

Highlights

The numerical models based on the shallow water equations (SWE) are commonly applied in hydraulic problems such as dam break analysis, open channel flows and sloshing wave problem
The numerical approximations of these methods are mainly based on the radial-basis functions (RBFs)
We examine the applications of the meshless local Petrov-Galerkin (MLPG)-RBF to solve the SWE

Summary

Introduction

The numerical models based on the shallow water equations (SWE) are commonly applied in hydraulic problems such as dam break analysis, open channel flows and sloshing wave problem. The numerical approximations of these methods are mainly based on the radial-basis functions (RBFs). The conventional MLPG method has advantages of the high accurate solution, the use of moving least-squares approximation (lack of delta property), brings some problems to the implementation of the boundary conditions. To overcome these difficulties the RBF interpolation method is adopted. The governing equations are discretized by the MLPG-RBF method in spatial domain and by Euler scheme in temporal direction. Conclusions and suggestions will be given based on the numerical model results

Two-dimensional shallow water equations

The meshless local Petrov-Galerkin method with radial basis functions

Methodology

The discrete form

Numerical results - 2D dam-break problem by non-linear SWE model

Conclusions