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

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.

Benjamin Kadoch, Dmitry Kolomenskiy, Philippe Angot, Kai Schneider. A volume penalization method for incompressible flows and scalar advection-diffusion with moving obstacles. Journal of Computational Physics, Elsevier, 2012, 231 (12), pp.4365-4383. ⟨10.1016/j.jcp.2012.01.036⟩. ⟨hal-01032208⟩

Journal: Journal of Computational Physics

Date de publication: 01-01-2012

Auteurs:
  • Benjamin Kadoch
  • Dmitry Kolomenskiy
  • Philippe Angot
  • Kai Schneider

Digital object identifier (doi): http://dx.doi.org/10.1016/j.jcp.2012.01.036


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