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.
翻译:在对流体结构互动建模的淡化边界(IB)方法中,流体和结构变量之间的混合利用一个正规版本的Dirac delta函数进行介介质。在 IB 文献中,正规化的三角形函数,也指 IB 内核函数,或者从一组假设中分析衍生出来,或者使用移动最小方(MLS)法进行数字计算。虽然分析衍生方法通常假定一种正常的碳酸盐格,但MLS 方法是一种无线技术,可用于在复杂域和无结构的meshes 上生成内核函数。在本说明中,我们认为,IB 内核生成,无论是分析性的还是通过 MLS,都是一个受限的二次最小化问题。受限的二次函数的极限比内核生成更为广泛,而且有公认的数字优化技术来解决这个问题。例如,我们表明,受限的二次最小化技术可以用来产生单面(氮基) IB内核和/或捆绑定的数值。