A New Approach for Error Reduction in the Volume Penalization Method (Communications in Computational Physics, 2014)
A new approach for reducing error of the volume penalization method isproposed. The mask function is modified by shifting the interface between solid andfluid by $√νη$ toward the fluid region, where ν and η are the viscosity and the permeability, respectively. The shift length $√νη$ is derived from the analytical solution of theone-dimensional diffusion equation with a penalization term. The effect of the errorreduction is verified numerically for the one-dimensional diffusion equation, Burgers' equation, and the two-dimensional Navier-Stokes equations. The results show thatthe numerical error is reduced except in the vicinity of the interface showing overallsecond-order accuracy, while it converges to a non-zero constant value as the numberof grid points increases for the original mask function. However, the new approach iseffective when the grid resolution is sufficiently high so that the boundary layer, whosewidth is proportional to $√νη$, is resolved. Hence, the approach should be used whenan appropriate combination of ν and η is chosen with a given numerical grid.