TY - JOUR

T1 - Schwarz alternating domain decomposition approach for the solution of two-dimensional Navier-Stokes flow problems by the method of approximate particular solutions

AU - Bustamante, Carlos Andres

AU - Power, Henry

AU - Florez, Whady Felipe

N1 - Publisher Copyright:
© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 777-797, 2015.

PY - 2015/5/1

Y1 - 2015/5/1

N2 - The method of approximate particular solutions (MAPS) is used to solve the two-dimensional Navier-Stokes equations. This method uses particular solutions of a nonhomogeneous Stokes problem, with the multiquadric radial basis function as a nonhomogeneous term, to approximate the velocity and pressure fields. The continuity equation is not explicitly imposed since the used particular solutions are mass conservative. To improve the computational efficiency of the global MAPS, the domain is split into overlapped subdomains where the Schwarz Alternating Algorithm is employed using velocity or traction values from neighboring subdomains as boundary conditions. When imposing only velocity boundary conditions, an extra step is required to find a reference value for the pressure at each subdomain to guarantee continuity of pressure across subdomains. The Stokes lid-driven cavity flow problem is solved to assess the performance of the Schwarz algorithm in comparison to a finite-difference-type localized MAPS. The Kovasznay flow problem is used to validate the proposed numerical scheme. Despite the use of relative coarse nodal distributions, numerical results show excellent agreement with respect to results reported in literature when solving the lid-driven cavity (up to Re = 10,000) and the backward facing step (at Re = 800) problems.

AB - The method of approximate particular solutions (MAPS) is used to solve the two-dimensional Navier-Stokes equations. This method uses particular solutions of a nonhomogeneous Stokes problem, with the multiquadric radial basis function as a nonhomogeneous term, to approximate the velocity and pressure fields. The continuity equation is not explicitly imposed since the used particular solutions are mass conservative. To improve the computational efficiency of the global MAPS, the domain is split into overlapped subdomains where the Schwarz Alternating Algorithm is employed using velocity or traction values from neighboring subdomains as boundary conditions. When imposing only velocity boundary conditions, an extra step is required to find a reference value for the pressure at each subdomain to guarantee continuity of pressure across subdomains. The Stokes lid-driven cavity flow problem is solved to assess the performance of the Schwarz algorithm in comparison to a finite-difference-type localized MAPS. The Kovasznay flow problem is used to validate the proposed numerical scheme. Despite the use of relative coarse nodal distributions, numerical results show excellent agreement with respect to results reported in literature when solving the lid-driven cavity (up to Re = 10,000) and the backward facing step (at Re = 800) problems.

KW - meshless methods

KW - Navier-Stokes

KW - particular solutions

UR - http://www.scopus.com/inward/record.url?scp=84988267049&partnerID=8YFLogxK

U2 - 10.1002/num.21917

DO - 10.1002/num.21917

M3 - Artículo

AN - SCOPUS:84988267049

VL - 31

SP - 777

EP - 797

JO - Numerical Methods for Partial Differential Equations

JF - Numerical Methods for Partial Differential Equations

SN - 0749-159X

IS - 3

ER -