变黏度不可压缩Navier--Stokes方程的应力散度、Laplacian和旋转形式

中文摘要 AI 辅助

在Navier--Stokes方程中，不可压缩性允许将黏性项改写为多种形式，从而产生不同的数值特性和流动描述。此外，考虑非牛顿、热或湍流效应的模型常常打破常黏度假设，从而产生额外的一致性项。在此背景下，本工作比较了经典的对称梯度扩散项与更近期的变黏度Laplacian和旋转形式的推广。我们讨论、分析并测试了它们在实现、效率、数值稳定性和出流边界条件方面的差异。着眼于时间依赖流动，我们考虑二阶隐式-显式（IMEX）时间离散化，旨在提高效率和数值稳定性。通过严格的稳定性分析，我们展示了选定的显式处理如何绕过算法非线性而不引发CFL条件。我们的数值结果突出了三种黏性公式之间的重要差异——尤其是在存在出流边界的情况下，此时广义Laplacian形式在扩散主导区域被证明更为适用。

英文摘要

In the Navier--Stokes equations, incompressibility allows rewriting the viscous term in various forms leading to distinct numerical properties and flow descriptions. Furthermore, models accounting for non-Newtonian, thermal or turbulent effects often break the constant-viscosity assumption, thereby producing additional consistency terms. In this context, the present work compares the classical symmetric-gradient diffusion term with more recent variable-viscosity generalizations of the Laplacian and rotational forms. We discuss, analyze and test their differences with respect to implementation, efficiency, numerical stability and outflow boundary conditions. With a focus on time-dependent flows, we consider second-order implicit-explicit (IMEX) temporal discretizations aimed at improving efficiency and numerical stability. Through a rigorous stability analysis, we show how selected explicit treatments can bypass algorithmic nonlinearities without inducing CFL conditions. Our numerical results highlight important differences between the three viscous formulations---especially in the presence of outflow boundaries, for which the generalized Laplacian form proves more suitable in diffusion-dominated regimes. %(as widely known for constant viscosity).

发表机构

• Pontificia Universidad Católica de Valparaíso（天主教瓦拉帕莱索大学）
• RWTH Aachen University（亚琛工业大学）
• University of Santiago de Chile（智利圣地亚哥大学）

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