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

  • Authors:

  • Benjamin Kadoch;Dmitry Kolomenskiy;Philippe Angot;Kai Schneider

  • Affiliations:

  • M2P2-UMR 6181 CNRS, Aix-Marseille Université, Ecole Centrale Marseille, Marseille, France and IUSTI-UMR 6595 CNRS, Aix-Marseille Université, Marseille, France;M2P2-UMR 6181 CNRS, Aix-Marseille Université, Ecole Centrale Marseille, Marseille, France and CERFACS, Toulouse, France;LATP-UMR 6632 CNRS, Aix-Marseille Université, Marseille, France and Centre de Mathématiques et d'Informatique, Aix-Marseille Université, Marseille, France;M2P2-UMR 6181 CNRS, Aix-Marseille Université, Ecole Centrale Marseille, Marseille, France and Centre de Mathématiques et d'Informatique, Aix-Marseille Université, Marseille, France

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2012

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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.