Numerical validation of the volume penalization method in three-dimensional pseudo-spectral simulations

摘要

The penalization method is used to simulate the effect of boundaries on fluid flows without body-fitted mesh. It is introduced here in a three-dimensional Fourier pseudo-spectral code with periodic boundary conditions. We propose an implicit implementation for the penalization term, thus getting rid of the strong stability constraint stemming from the stiffness of the penalized equations. The convergence of this implicit penalized method is shown by comparison with solutions of Navier-Stokes equations with explicit boundary conditions. Different test-cases are used, among which a comparison with channel flow simulations with a Chebyshev-Fourier pseudo-spectral code in which the projection base automatically ensures the no-slip boundary condition and the divergence-free condition. We consider inertial or internal gravity waves reflection on solid walls, hence assessing the correct account of pressure coupling for wave-propagation and reflection by the implicit penalized algorithm, and the common benchmark of a Gaussian vortex ring impacting on a normal flat plane solid boundary. Numerical convergence is characterized by increasing the grid resolution and by reducing the penalization parameter η.