Meshfree finite differences for vector Poisson and pressure Poisson equations with electric boundary conditions

Dong Zhou, Benjamin Seibold, David Shirokoff, Prince Chidyagwai, Rodolfo Ruben Rosales

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

We demonstrate how meshfree finite difference methods can be applied to solve vector Poisson problems with electric boundary conditions. In these, the tangential velocity and the incompressibility of the vector field are prescribed at the boundary. Even on irregular domains with only convex corners, canonical nodalbased finite elements may converge to the wrong solution due to a version of the Babuška paradox. In turn, straightforward meshfree finite differences converge to the true solution, and even high-order accuracy can be achieved in a simple fashion. The methodology is then extended to a specific pressure Poisson equation reformulation of the Navier-Stokes equations that possesses the same type of boundary conditions. The resulting numerical approach is second order accurate and allows for a simple switching between an explicit and implicit treatment of the viscosity terms.

Original languageEnglish (US)
Title of host publicationMeshfree Methods for Partial Differential Equations VII
EditorsMichael Griebel, Marc Alexander Schweitzer
PublisherSpringer Verlag
Pages223-246
Number of pages24
ISBN (Electronic)9783319068978
DOIs
StatePublished - 2015
Externally publishedYes
Event7th International Workshop on Meshfree Methods for Partial Differential Equations, 2013 - Bonn, Germany
Duration: Sep 9 2013Sep 11 2013

Publication series

NameLecture Notes in Computational Science and Engineering
Volume100
ISSN (Print)1439-7358

Other

Other7th International Workshop on Meshfree Methods for Partial Differential Equations, 2013
CountryGermany
CityBonn
Period9/9/139/11/13

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Engineering(all)
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Mathematics

Keywords

  • Finite-differences
  • High-orde
  • Incompressible
  • Manufactured solution
  • Meshfree
  • Navier-Stokes
  • Pressure Poisson equation
  • Reformulation
  • Vector Poisson equation

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