Embedded boundary methods (EBMs) are robust solution methods for highly nonlinear fluid‐structure interaction (FSI) problems. They suffer, however, some disadvantages because they perform their computations on embedding, nonbody‐fitted fluid meshes. In particular, they tend to generate discrete events that introduce discontinuities in the semi‐discretization process and lead to numerical solutions that are insufficiently smooth for differentiation with respect to the evolution of a discrete, fluid/structure interface ${\mathrm{\Gamma }}_h^{F/S}$. This hinders their application to the gradient‐based solution of fluid‐structure optimization problems. Discrete events also promote spurious oscillations in the post‐processing of time‐dependent results computed at ${\mathrm{\Gamma }}_h^{F/S}$.z This paper addresses these issues in the context of Finite Volume method with Exact two‐material Riemann problems (FIVER), a comprehensive framework for developing EBMs for highly nonlinear, compressible, FSI problems. It revisits the concept of the status of a node of an embedding fluid mesh and introduces that of a smoothness indicator nodal function, to eliminate discrete events and achieve smoothness in the semi‐discretization process. It also introduces a moving least squares approach in the loads evaluation algorithm, to suppress spurious oscillations from integral quantities computed on ${\mathrm{\Gamma }}_h^{F/S}$. Equipped with these enhancements, FIVER is shown to deliver, for three different FSI applications, smooth results that are differentiable with respect to evolutions of ${\mathrm{\Gamma }}_h^{F/S}$.

中文翻译：

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离散嵌入边界法，平滑依赖于流体-结构界面的演化

嵌入式边界方法（EBM）是解决高度非线性流体-结构相互作用（FSI）问题的可靠方法。但是，它们会遭受一些不利影响，因为它们是在嵌入的，不适合人体的流体网格上执行计算的。特别是，它们往往会产生离散事件，从而在半离散化过程中引入不连续性，并导致数值解相对于离散的流体/结构界面的演化而言不够平滑，难以区分。${\mathrm{\Gamma }}_H^{F/\mathrm{小号}}$。这阻碍了它们在基于梯度的流体结构优化问题解决方案中的应用。离散事件还会在对以${\mathrm{\Gamma }}_H^{F/\mathrm{小号}}$.z本文在具有精确两种材料黎曼问题（FIVER）的有限体积方法的背景下解决了这些问题，这是开发用于解决高度非线性，可压缩FSI问题的EBM的全面框架。它重新审视了嵌入流体网格的节点状态的概念，并引入了平滑度指示器节点函数的概念，以消除离散事件并在半离散化过程中实现平滑度。它还在负载评估算法中引入了移动最小二乘法，以抑制由计算出的积分量产生的虚假振荡。${\mathrm{\Gamma }}_H^{F/\mathrm{小号}}$。配备了这些增强功能后，FIVER被证明可以为三种不同的FSI应用提供平滑的结果，这些结果在不同方面会有所不同。${\mathrm{\Gamma }}_H^{F/\mathrm{小号}}$。