|A volume penalization method for incompressible flows and scalar advection-diffusion with moving obstacles |
Auteur(s): Kadoch Benjamin, Kolomenskiy Dmitry, Angot P., Schneider Kai
(Article) Publié: Journal Of Computational Physics, vol. 231 p.4365-4383 (2012)
Ref HAL: hal-01032208_v1
Exporter : BibTex | endNote
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.