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首页> 外文期刊>Numerical Heat Transfer, Part B. Fundamentals: An International Journal of Computation and Methodology >A Least-Squares-Based Immersed Boundary Approach for Complex Boundaries in the Lattice Boltzmann Method
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A Least-Squares-Based Immersed Boundary Approach for Complex Boundaries in the Lattice Boltzmann Method

机译：格子Boltzmann方法中基于最小二乘的浸入边界方法求解复杂边界

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摘要

A least-squares algorithm for handling complex boundaries with the lattice Boltzmann method is proposed. The method is an extension to an immersed boundary implementation of the solver. We impose additional rules that are designed to conserve the mass flux through cut-cell control volumes and also to satisfy the continuity condition on the numerical boundary points. Then, we use the least-squares method to find the best achievable solution of the overdetermined system. Further, computational cost assessments are considered. The qualitative and quantitative results show that the velocity values obtained from simulation of a flow with curved and moving boundaries, i.e., the Taylor-Couette flow, are closer to the exact solution than the values found from the traditional approach. Finally, we present some statistical analysis to show that the velocities are obtained confidently.
机译：提出了一种用格子玻尔兹曼方法处理复杂边界的最小二乘算法。该方法是求解器的浸入边界实现的扩展。我们强加了附加规则，这些规则旨在保留通过切割单元控制体积的质量通量，并满足数字边界点上的连续性条件。然后，我们使用最小二乘方法找到超定系统的最佳可实现解。此外，考虑了计算成本评估。定性和定量结果表明，通过模拟具有弯曲和移动边界的流（即泰勒-库埃特流）获得的速度值比从传统方法中获得的值更接近精确解。最后，我们提出一些统计分析，以显示速度是自信地获得的。

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