@Article{CiCP-16-1181,
author = {Wakana Iwakami, Yuzuru Yatagai, Nozomu Hatakeyama and Yuji Hattori},
title = {A New Approach for Error Reduction in the Volume Penalization Method},
journal = {Communications in Computational Physics},
year = {2014},
volume = {16},
number = {5},
pages = {1181--1200},
abstract = {<p style="text-align: justify;">A new approach for reducing error of the volume penalization method is
proposed. The mask function is modified by shifting the interface between solid and
fluid 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 the
one-dimensional diffusion equation with a penalization term. The effect of the error
reduction is verified numerically for the one-dimensional diffusion equation, Burgers&#39; equation, and the two-dimensional Navier-Stokes equations. The results show that
the numerical error is reduced except in the vicinity of the interface showing overall
second-order accuracy, while it converges to a non-zero constant value as the number
of grid points increases for the original mask function. However, the new approach is
effective when the grid resolution is sufficiently high so that the boundary layer, whose
width is proportional to $√νη$, is resolved. Hence, the approach should be used when
an appropriate combination of ν and η is chosen with a given numerical grid.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.220513.070514a},
url = {http://global-sci.org/intro/article_detail/cicp/7077.html}
}