document: Similar numerical oscillations to those described above also emerge in the ISPM when utilising classical IBM kernels due to their lack of regularity (with discontinuous second derivatives). Furthermore, it is important to remark that the immersed structure stresses are captured in the Lagrangian description and hence, in order to compute them accurately, it is important to ensure that these spurious oscillations are not introduced via the kernel interpolation functions. In this paper, the authors have specifically designed a new family of kernel functions which do not introduce these spurious oscillations. The kernel functions are obtained by taking into account discrete reproducibility conditions as originally introduced by Peskin [14] (in our case, tailor-made for Cartesian staggered grids) and regularity requirements to prevent the appearance of spurious oscillations when computing derivatives. A Maple computer program has been developed to obtain explicit expressions for the new kernels.
extractive_keyphrases: oscillations maple computer program computing derivatives lagrangian description ispm kernel functions kernel interpolation functions ibm kernels obtain explicit expressions for the new kernels cartesian staggered grids
abstractive_keyphrases: numerical oscillations a new family of kernel functions which do not introduce these spurious oscillations kernels