  A novel sharp interface ghost-cell based immersed boundary method has been
proposed and its parameters have been optimized against an analytical model in
diffusion applications. The proposed embedded constrained moving least-squares
(ECMLS) algorithm minimizes the error of the interpolated concentration at the
image point of the ghost point by applying a moving least-squares method on all
internal nodes, near the ghost image point, and the associated mirrored image
points of these internal nodes through the corresponding boundary conditions.
Using an analytical model as a reference, the ECMLS algorithm is compared to
the constrained moving least-squares (CMLS) algorithm and the staircase model
using various grid sizes, interpolation basis functions, weight functions, and
the penalty parameter of the constraint. It is found that using ECMLS algorithm
in the investigated diffusion application, the incomplete quartic basis
function yields the best performance while the quadratic, cubic, and bicubic
basis functions also produce results better than the staircase model. It is
also found that the linear and bilinear basis functions cannot produce results
better than the staircase model in diffusion applications. It is shown that the
optimal radius of the region of internal nodes used for interpolation scales
with the logarithm of the boundary radius of curvature. It is shown that for
the diffusion application, the proposed ECMLS algorithm produces lower errors
at the boundary with better numerical stability over a wider range of basis
functions, weight functions, boundary radius of curvature, and the penalty
parameter than the CMLS algorithm.
