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Immersed Interface Method for Solving the Incompressible Navier-Stokes Equations with Moving Boundaries

机译:求解带运动边界的不可压缩Navier-Stokes方程的沉浸接口方法

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Immersed interface methods have reached a level of maturity where they can now be considered a viable alternative to conventional numerical approaches. One considerable advantage of these methods is their simplicity in generating grids independent of the complexity of the geometry. For flows containing moving boundaries, immersed interface methods facilitate the numerical solution procedure by using stationary, non-deforming Cartesian" grids. In contrast, current body-fitted grid approaches are confronted with immense difficulties in the solution procedure, especially in cases where the boundary exhibits large displacements. This paper will outline the main ideas of a novel immersed interface method for the incompressible Navier-Stokes equation including boundary motion. The underlying immersed interface method without moving boundaries was presented and validated in Brehm and Fasel.1'3 In the present paper the previous method is extended to include moving boundaries. The enhanced immersed interface method which is applied to the transport step of the numerical solver of the incompressible Navier-Stokes equation is rigorously derived and validated for the one-dimensional Burgers' equation. The validation results for the full Navier-Stokes equation presented herein indicate that this approach provides outstanding characteristics with respect to accuracy, robustness, and computational cost. In the final application of the immersed boundary Navier-Stokes solver, a fully-coupled fluid structure interaction problem is studied in great detail.
机译:沉浸式接口方法已达到成熟水平,现在可以认为它们是常规数值方法的可行替代方案。这些方法的一大优势是它们在生成网格方面的简便性,而与几何图形的复杂性无关。对于包含移动边界的流,沉浸式界面方法通过使用固定的,不变形的笛卡尔网格简化了数值求解过程。相比之下,当前的人体拟合网格方法在求解过程中面临着巨大的困难,尤其是在边界存在的情况下表现出大的位移。本文将概述一种新的包含边界运动的不可压缩Navier-Stokes方程的沉浸界面方法的主要思想。在Brehm和Fasel中提出并验证了没有移动边界的底层沉浸界面方法.1'3本文将先前的方法扩展为包括移动边界,并严格推导了应用于不可压缩Navier-Stokes方程数值求解器的传递步骤的增强型沉浸界面方法,并针对一维Burgers方程进行了验证。本文介绍的完整Navier-Stokes方程的验证结果n表示此方法在准确性,鲁棒性和计算成本方面提供了出色的特性。在浸入式边界Navier-Stokes求解器的最终应用中,将对全耦合流体结构相互作用问题进行详细研究。

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