Journal of Computational and Applied Mathematics - Orthogonal polynomials and numerical methods
Numerical study of pseudospectral methods in shock wave applications
Journal of Computational Physics
A note on the accuracy of spectral method applied to nonlinear conservation laws
Journal of Scientific Computing
Zonal embedded grids for numerical simulations of wall-bounded turbulent flows
Journal of Computational Physics
An adaptive wavelet-vaguelette algorithm for the solution of PDEs
Journal of Computational Physics
Journal of Computational Physics
Vortex methods with spatially varying cores
Journal of Computational Physics
Blending Finite-Difference and Vortex Methods for Incompressible Flow Computations
SIAM Journal on Scientific Computing
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Fourier Spectral Solver for the Incompressible Navier-Stokes Equations with Volume-Penalization
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Journal of Computational Physics
Journal of Computational Physics
GPU accelerated simulations of bluff body flows using vortex particle methods
Journal of Computational Physics
A spectral fictitious domain method with internal forcing for solving elliptic PDEs
Journal of Computational Physics
Simulations of single and multiple swimmers with non-divergence free deforming geometries
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.49 |
In this study, we use volume-penalization to mimic the presence of obstacles in a flow or a domain with no-slip boundaries. This allows in principle the use of fast Fourier spectral methods and coherent vortex simulation techniques (based on wavelet decomposition of the flow variables) to compute turbulent wall-bounded flow or flows around solid obstacles by simply adding one term in the equation. Convergence checks are reported using a recently revived, and unexpectedly difficult dipole-wall collision as a benchmark computation. Several quantities, like the vorticity isolines, truncation error, kinetic energy and enstrophy are inspected for a collision of a dipole with a no-slip wall and compared with available benchmark data obtained with a standard Chebyshev pseudospectral method. We quantify the possible deteriorating effects of the Gibbs phenomenon present in the Fourier based schemes due to continuity restrictions of the penalized Navier-Stokes equations on the wall. It is found that Gibbs oscillations have a negligible effect on the flow evolution allowing higher-order recovery of the accuracy on a Fourier basis by means of postprocessing. An advantage of coherent vortex simulations, on the other hand, is that the degrees of freedom of the flow computation can strongly be reduced. In this study, we quantify the possible reduction of degrees of freedom while keeping the accuracy. For an optimal convergence scenario the penalization parameter has to scale with the number of Fourier and wavelet modes. In addition, an implicit treatment of the Darcy drag term in the penalized Navier-Stokes equations is beneficial since this allows one to set the time step independent from the penalization parameter without additional computational or memory requirements.