The use of dual reciprocity method for 2D laminar viscous flow

S Kmeť,E Kormaníková,K Kotrasová,Juraj Mužík

doi:10.1051/matecconf/202031000044

Abstract

The paper presents the use of the dual reciprocity multidomain singular boundary method (SBMDR) for the solution of the laminar viscous flow problem described by Navier-Stokes equations. A homogeneous part of the solution is solved using a singular boundary method with the 2D Stokes fundamental solution - Stokeslet. The dual reciprocity approach has been chosen because it is ideal for the treatment of the nonhomogeneous and nonlinear terms of Navier-Stokes equations. The presented SBMDR 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) [4] and the singular boundary method (SBM) [5]
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 complex-shaped domains

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 a number of 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 complex-shaped domains. To bypass the fictitious boundary construction, the SBM formulation adopts a concept of the origin intensity factors (OIFs). The SBM with dual reciprocity (DR) technique is used to handle the nonlinear convection terms of NS equations

Governing equations

LLmm nn LLkk

Dual reciprocity method - Particular solution

Simulation of the lid-driven cavity problem

Conclusions