The immersed boundary method (IBM) has been extensively utilized in fluid dynamics simulations with various numerical methods. There are two key steps in IBM, namely the force distribution and velocity interpolation steps; and the kernel function ϕ plays important roles in both steps. The purpose for the velocity interpolation is to enhance the no-slip condition between fluid and boundary surface. However, with the kernel function designed to satisfy the basic requirements for the force distribution, the boundary velocity calculation process in traditional IBM simulations is actually a weighted averaging operation instead of an interpolation. This induces large errors in the calculated boundary velocity for general nonlinear velocity distributions. In this paper, we propose to release the kernel function's role from the boundary velocity calculation, and replace it with the classical Lagrangian interpolation schemes to obtain the boundary velocity from the local flow field. This idea has been tested in several two-dimensional periodic systems, and both flat and curved surfaces and steady and unsteady flows have been considered. Our simulation results show that in general a 20~30% accuracy improvement in velocity and flow-structure interaction can be achieved with no extra cost in computational complexity and efficiency, thanks to the simple mathematical formulation and computational algorithm.

沉浸边界方法（IBM）已通过各种数值方法广泛用于流体动力学模拟中。IBM中有两个关键步骤，即力分布和速度插值步骤；和内核功能ϕ在这两个步骤中都起着重要作用。速度插值的目的是增强流体与边界表面之间的防滑条件。但是，由于内核函数旨在满足力分布的基本要求，因此传统IBM仿真中的边界速度计算过程实际上是加权平均运算，而不是插值运算。对于一般的非线性速度分布，这会在计算的边界速度中引起较大的误差。在本文中，我们建议从边界速度计算中释放核函数的作用，并用经典的拉格朗日插值方案代替它，以从局部流场获得边界速度。这个想法已经在几个二维周期系统中得到验证，同时考虑了平坦和弯曲的表面以及稳定和不稳定的流动。我们的仿真结果表明，由于简单的数学公式和计算算法，总体而言，速度和流-固相互作用的精度可提高20％至30％，而不会增加计算复杂性和效率。