湍流N-S方程数值模拟的FEniCS-Based程序框架
A FEniCS-Based Programming Framework for Modeling Turbulent Flow by the Reynolds-Averaged Navier-Stokes Equations
摘要：
为给定的流动情况找到合适的湍流模型通常需要对模型和数值解方法进行大量的实验。这项工作提出了一个灵活的，可编程的软件框架的设计和实施，以协助计算湍流的数值实验。该框架的目标是采用有限元法离散化的雷诺平均Navier-Stokes模型。新的实现利用了Python和FeNiCS包，两者的结合导致了紧凑和可重用的代码，其中模型和求解器特定的代码非常类似于方程和算法的数学公式。所提出的思想和编程技术也适用于其他领域，涉及系统的非线性偏微分方程。我们展示了两个应用程序的框架，并探讨了各种线性化的非线性求解器的收敛性能的影响，平均Navier-Stokes模型。
英文摘要：
Finding an appropriate turbulence model for a given flow case usually calls for extensive experimentation with both models and numerical solution methods. This work presents the design and implementation of a flexible, programmable software framework for assisting with numerical experiments in computational turbulence. The framework targets Reynolds-averaged Navier-Stokes models, discretized by finite element methods. The novel implementation makes use of Python and the FEniCS package, the combination of which leads to compact and reusable code, where model- and solver-specific code resemble closely the mathematical formulation of equations and algorithms. The presented ideas and programming techniques are also applicable to other fields that involve systems of nonlinear partial differential equations. We demonstrate the framework in two applications and investigate the impact of various linearizations on the convergence properties of nonlinear solvers for a Reynolds-averaged Navier-Stokes model.
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