  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 ({\nu}{\eta})^0.5 toward the fluid region, where {\nu} and {\eta}
are the viscosity and the permeability, respectively. The shift length
({\nu}{\eta})^0.5 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' 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
({\nu}{\eta})^0.5, is resolved. Hence, the approach should be used when an
appropriate combination of {\nu} and {\eta} is chosen with a given numerical
grid.
