关于鲁棒α阻尼粘性格式的研究
On Robust Alpha-Damping Viscous Scheme
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中文总结 AI 辅助
本文针对非结构网格粘性离散化的隐式缺陷修正求解器，发现采用边中点计算阻尼项可提升鲁棒收敛性，经二维粘性流动问题数值验证有效。
中文摘要 AI 辅助
本文研究了基于α阻尼格式的非结构网格粘性离散化的隐式缺陷修正求解器的收敛性。我们表明，与在面心处计算阻尼项相比，在两个相邻单元中心的中点（边中点）处计算阻尼项可实现显著更鲁棒的迭代收敛性。一维傅里叶分析显示，当残差中的阻尼项小于构建雅可比矩阵所用的阻尼项时，隐式求解器趋于稳定。该观察结果表明，可通过有效减小残差中阻尼项的幅值来稳定求解器，边中点计算即可实现此效果。针对高度不规则的混合单元网格和三角形网格上的二维粘性流动问题，数值验证了鲁棒收敛性。
英文摘要
In this paper, we investigate the convergence of an implicit defect-correction solver for a viscous discretization based on the alpha-damping scheme for unstructured grids. We show that significantly more robust iterative convergence is achieved by evaluating the damping term at the midpoint between two adjacent cell centers (edge midpoint) rather than at the face centroid. A one-dimensional Fourier analysis reveals that the implicit solver tends to be stable when the damping term in the residual is smaller than that used to construct the Jacobian. This observation suggests that the solver can be stabilized by effectively reducing the magnitude of the damping term in the residual - an effect achieved by the edge-midpoint evaluation. Robust convergence is demonstrated numerically for two-dimensional viscous-flow problems on highly irregular mixed-element and triangular grids.
