A FEniCS-Based Programming Framework for Modeling Turbulent Flow by the Reynolds-Averaged Navier-Stokes Equations

TL;DR

This paper introduces a flexible, Python-based FEniCS framework for modeling turbulent flow using Reynolds-Averaged Navier-Stokes equations, enabling efficient experimentation with turbulence models and numerical methods.

Contribution

It presents a novel, reusable software framework that closely aligns code with mathematical formulations, facilitating computational turbulence research and potentially other nonlinear PDE systems.

Findings

Framework simplifies turbulence modeling experiments

Investigates solver convergence with different linearizations

Demonstrates applicability in two turbulence cases

Abstract

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.