The immersed boundary (IB) method is a non-body conforming approach to fluid-structure interaction (FSI) that uses an Eulerian description of the momentum, viscosity, and incompressibility of a coupled fluid-structure system and a Lagrangian description of the deformations, stresses, and resultant forces of the immersed structure. Integral transforms with Dirac delta function kernels couple Eulerian and Lagrangian variables. In practice, discretizations of these integral transforms use regularized delta function kernels, and although a number of different types of regularized delta functions have been proposed, there has been limited prior work to investigate the impact of the choice of kernel function on the accuracy of the methodology. This work systematically studies the effect of the choice of regularized delta function in several fluid-structure interaction benchmark tests using the immersed finite element/difference (IFED) method, which is an extension of the IB method that uses finite element structural discretizations combined with a Cartesian grid finite difference method for the incompressible Navier-Stokes equations. Further, many IB-type methods evaluate the delta functions at the nodes of the structural mesh, and this requires the Lagrangian mesh to be relatively fine compared to the background Eulerian grid to avoid leaks. The IFED formulation offers the possibility to avoid leaks with relatively coarse structural meshes by evaluating the delta function on a denser collection of interaction points. This study investigates the effect of varying the relative mesh widths of the Lagrangian and Eulerian discretizations. Although this study is done within the context of the IFED method, the effect of different kernels could be important not just for this method, but also for other IB-type methods more generally.
翻译:淡化边界(IB) 方法是一种对流体结构互动(FSI)的非机体兼容的方法,它使用 Eullian 描述一个混合流体结构系统的势头、粘度和不压缩性, 以及Lagrangian 描述浸入结构的变形、 压力和随之产生的力量。 Dirac 三角洲函数内核的整合变异结合 Eulelirian 和 Lagrangian 变量。 在实践中, 这些整体变异的离异使用固定化的 三角体内核, 虽然已经提出了不同种类的正规化三角体功能, 但是在调查一个混合的流体结构结构结构结构结构结构结构结构结构的变异性时, 已经做了一些系统化三角体函数选择的效果, 使用沉化的固定元素/变异变(IFED) 方法, 这是IB 方法的一种延伸, 使用较固定的离异元素结合一种碳化的三角体内核分解, 提出了若干不同类型的三角形变异功能, 而这种结构变异的变异的变形法则由IB 的变异的变形变形变式变式的变形法 。