This paper presents a one-sided immersed boundary (IB) method using kernel functions constructed via a moving least squares (MLS) method. The resulting kernels effectively couple structural degrees of freedom to fluid variables on only one side of the fluid-structure interface. This reduces spurious feedback forcing and internal flows that are typically observed in IB models that use isotropic kernel functions to couple the structure to fluid degrees of freedom on both sides of the interface. The method developed here extends the original MLS methodology introduced by Vanella and Balaras (2009) [27]. Prior IB/MLS methods have used isotropic kernel functions that coupled fluid variables on both sides of the boundary to the interfacial degrees of freedom. The original IB/MLS approach converts the cubic spline weights typically employed in MLS reconstruction into an IB kernel function that satisfies particular discrete moment conditions. This paper shows that the same approach can be used to construct one-sided kernel functions (kernel functions are referred to as generating functions in the MLS literature). We also examine the performance of the new approach for a family of kernel functions introduced by Peskin. It is demonstrated that the one-sided MLS construction tends to generate non-monotone interpolation kernels with large over- and undershoots. We present two simple weight shifting strategies to construct generating functions that are positive and monotone, which enhances the stability of the resulting IB methodology. Benchmark cases are used to test the order of accuracy and verify the one-sided IB/MLS simulations in both two and three spatial dimensions. This new IB/MLS method is also used to simulate flow over the Ahmed car model, which highlights the applicability of this methodology for modeling complex engineering flows.

本文提出了一种使用通过最小二乘法（MLS）方法构造的核函数的单侧浸入边界（IB）方法。所得的核仅将结构自由度与流体-结构界面的一侧上的流体变量有效地耦合。这样可以减少在使用各向同性内核函数将结构耦合到界面两侧的流体自由度的IB模型中通常观察到的虚假反馈强迫和内部流动。这里开发的方法扩展了Vanella和Balaras（2009）引入的原始MLS方法[27]。先前的IB / MLS方法使用了各向同性的核函数，该函数将边界两侧的流体变量耦合到界面自由度。原始的IB / MLS方法将通常在MLS重建中使用的三次样条权重转换为满足特定离散矩条件的IB核函数。本文表明，可以使用相同的方法来构造单面内核函数（内核函数在MLS文献中称为生成函数）。我们还将检查Peskin引入的一系列内核函数的新方法的性能。结果表明，单侧MLS构造倾向于生成具有较大过冲和下冲的非单调插值内核。我们提出了两种简单的权重转移策略，以构建正和单调的生成函数，从而增强了所得IB方法的稳定性。基准案例用于测试准确性的顺序，并在两个和三个空间维度上验证单边IB / MLS仿真。这种新的IB / MLS方法还用于模拟艾哈迈德汽车模型上的流动，这突显了这种方法对复杂工程流进行建模的适用性。