A volume penalization method for incompressible flows and scalar advection-diffusion with moving obstacles

Benjamin Kadoch, Dmitry Kolomenskiy, Philippe Angot, Kai Schneider

Research output: Contribution to journalArticlepeer-review

63 Citations (Scopus)

Abstract

A volume penalization method for imposing homogeneous Neumann boundary conditions in advection-diffusion equations is presented. Thus complex geometries which even may vary in time can be treated efficiently using discretizations on a Cartesian grid. A mathematical analysis of the method is conducted first for the one-dimensional heat equation which yields estimates of the penalization error. The results are then confirmed numerically in one and two space dimensions. Simulations of two-dimensional incompressible flows with passive scalars using a classical Fourier pseudo-spectral method validate the approach for moving obstacles. The potential of the method for real world applications is illustrated by simulating a simplified dynamical mixer where for the fluid flow and the scalar transport no-slip and no-flux boundary conditions are imposed, respectively.

Original languageEnglish
Pages (from-to)4365-4383
Number of pages19
JournalJournal of Computational Physics
Volume231
Issue number12
DOIs
Publication statusPublished - 20 Jun 2012
Externally publishedYes

Keywords

  • Moving obstacles
  • Neumann boundary conditions
  • Spectral methods
  • Volume penalization

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