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首页> 外文期刊>Journal of Computational Physics >Spectrally-accurate algorithm for moving boundary problems for the Navier-Stokes equations
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Spectrally-accurate algorithm for moving boundary problems for the Navier-Stokes equations

机译：Navier-Stokes方程的运动边界问题的频谱精确算法

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摘要

A spectral algorithm based on the immersed boundary conditions (IBC) concept is developed for simulations of viscous flows with moving boundaries. The algorithm uses a fixed computational domain with flow domain immersed inside the computational domain. Boundary conditions along the edges of the time-dependent flow domain enter the algorithm in the form of internal constraints. Spectral spatial discretization uses Fourier expansions in the stream-wise direction and Chebyshev expansions in the normal-to-the-wall direction. Up to fourth-order implicit temporal discretization methods have been implemented. It has been demonstrated that the algorithm delivers the theoretically predicted accuracy in both time and space. Performances of various linear solvers employed in the solution process have been evaluated and a new class of solver that takes advantage of the structure of the coefficient matrix has been proposed. The new solver results in a significant acceleration of computations as well as in a substantial reduction in memory requirements.
机译：开发了一种基于沉浸边界条件（IBC）概念的光谱算法，用于模拟具有移动边界的粘性流。该算法使用固定的计算域，将流域浸入计算域中。沿时变流域边缘的边界条件以内部约束的形式进入算法。频谱空间离散化使用在流方向上的傅立叶展开和在法线到墙方向上的Chebyshev展开。已经实现了多达四阶隐式时间离散化方法。已经证明该算法在时间和空间上都提供了理论上预测的准确性。评估了求解过程中使用的各种线性求解器的性能，并提出了一种利用系数矩阵结构的新型求解器。新的求解器可显着加快计算速度，并显着减少内存需求。

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