Numerical methods with particular solutions for nonhomogeneous Stokes and Brinkman systems

Carlos J. S. Alves, Nuno F. M. Martins, Ana L. Silvestre

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2 Citations (Scopus)

Abstract

This paper deals with the numerical approximation of solutions of Stokes and Brinkman systems using meshless methods. The aim is to solve a problem containing a nonzero body force, starting from the well known decomposition in terms of a particular solution and the solution of a homogeneous force problem. We propose two methods for the numerical construction of a particular solution. One method is based on the Neuber-Papkovich potentials, which we extend to nonhomogeneous Brinkman problems. A second method relies on a Helmholtz-type decomposition for the body force and enables the construction of divergence-free basis functions. Such basis functions are obtained from Hänkel functions and justified by new density results for the space H1(Ω). Several 2D numerical experiments are presented in order to discuss the feasibility and accuracy of both methods.

Original languageEnglish
Article number44
Number of pages23
JournalAdvances in Computational Mathematics
Volume48
Issue number4
DOIs
Publication statusPublished - Aug 2022

Keywords

  • Density theorems
  • Fundamental solutions
  • Meshfree method
  • Nonhomogeneous Brinkman equations
  • Nonhomogeneous Stokes equations
  • Particular solutions

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