On immersed boundary kernel functions: a constrained quadratic minimization perspective
Abstract
In the immersed boundary (IB) approach to fluid-structure interaction modeling, the coupling between the fluid and structure variables is mediated using a regularized version of Dirac delta function. In the IB literature, the regularized delta functions, also referred to IB kernel functions, are either derived analytically from a set of postulates or computed numerically using the moving least squares (MLS) approach. Whereas the analytical derivations typically assume a regular Cartesian grid, the MLS method is a meshless technique that can be used to generate kernel functions on complex domains and unstructured meshes. In this note we take a viewpoint that IB kernel generation, either analytically or via MLS, is a constrained quadratic minimization problem. The extremization of a constrained quadratic function is a broader concept than kernel generation, and there are well-established numerical optimization techniques to solve this problem. For example, we show that the constrained quadratic minimization technique can be used to generate one-sided (anisotropic) IB kernels and/or to bound their values.
Cite
@article{arxiv.2111.11025,
title = {On immersed boundary kernel functions: a constrained quadratic minimization perspective},
author = {Amneet Pal Singh Bhalla},
journal= {arXiv preprint arXiv:2111.11025},
year = {2021}
}