Lid-driven cavity flow using dual reciprocity

Juraj Mužík,Roman Bulko,J Melcer,K Kotrasová,A.V Benin,I Major

doi:10.1051/matecconf/202031300043

Abstract

The paper presents the use of the multi-domain dual reciprocity method of fundamental solutions (MD-MFSDR) for the analysis of the laminar viscous flow problem described by Navier-Stokes equations. A homogeneous part of the solution is solved using the method of fundamental solutions with the 2D Stokes fundamental solution Stokeslet. The dual reciprocity approach has been chosen because it is ideal for the treatment of the non-homogeneous and nonlinear terms of Navier-Stokes equations. The presented DR-MFS approach to the solution of the 2D flow problem is demonstrated on a standard benchmark problem - lid-driven cavity.

Highlights

The solution of Navier–Stokes (NS) equations is one of the basic tasks of computational fluid mechanics
The methods based on boundary integral theory are represented by the local boundary integral element method (LBIEM) [1], the boundary element method (BEM) [2, 3]
The method of fundamental solutions (MFS) presented in this article belongs to the class of so-called Trefftz methods

Summary

Introduction

The solution of Navier–Stokes (NS) equations is one of the basic tasks of computational fluid mechanics This nonlinear system of differential equations has already been solved by several numerical methods, starting with the finite difference method through the finite element method to meshless and boundary type methods. In the case of BEM the singularities of the fundamental solution are handled by proper integration method, the MFS overcomes the singularity using a fictitious boundary, but the optimum location of this boundary remains the open problem especially for complexshaped domains. To handle the non-linear and non-homogeneous part of the NS equation solution, which is not captured by the fundamental solution, the Dual Reciprocity Method (DRM) approach is adopted. The DRM global nature has been altered by partitioning the computational domain into smaller sub-domains or domain elements and on each of them, the dual reciprocity method was applied to obtain an expression for nonlinear terms. The agreement between the results of the proposed technique and the results of other authors is excellent

Method of fundamental solutions – MFS

Dual reciprocity method

Simulation of the lid-driven cavity problem

Conclusions