A dynamic closure modeling framework for large eddy simulation using approximate deconvolution: Burgers equation

Abstract

We put forth a dynamic closure modeling framework for the large eddy simulations of the Burgers equation based upon the use of the approximate deconvolution (AD) procedure to compute the Smagorinsky constant self-adaptively from the resolved flow quantities. In our proposed framework, the test filtering process of the standard dynamic model is replaced by the AD procedure. The robustness of the model has been tested considering the Burgers equation in its conservative and skew-symmetric forms. Our numerical assessments for solving the single-mode sine wave and the decaying Burgers turbulence problems show that the present framework effectively damps grid-to-grid oscillations and yields an improved shock capturing property for central numerical schemes as underlying discretizations.

Keywords:

• approximate deconvolution
• dynamic model
• Smagorinsky model
• large eddy simulation
• Burgers turbulence

Public interest statement

Multiple physical processes in the engineering and environmental sciences are tightly coupled with turbulent flows where the accuracy and generalizability of closure models play a key role. Large eddy simulation (LES) is a popular technique for simulating turbulent flows. In practice, direct numerical simulation (DNS), which resolves every scale of the solution, is prohibitively expensive for nearly all systems with complex geometry or flow configurations. To achieve the same order of resolved physical accuracy as DNS, however, LES requires to correctly treat the well-known closure problem: the effect of the small scales on the large ones needs to be modeled. Therefore, there has been a substantial effort in developing these LES closure models in the past few decades. The present study investigates the feasibility of a dynamic eddy viscosity model for solving the decaying Burgers turbulence problem with quadratic nonlinearity, which can be considered a simplified prototype integrable system for more complex flow dynamics.

Competing interests

The authors declare no competing interest.

Acknowledgements

This work was completed utilizing the High Performance Computing Center facilities of Oklahoma State University at Stillwater.

Additional information

Funding

The authors received no direct funding for this research.

Notes on contributors

Romit Maulik

Romit Maulik is a PhD candidate at the School of Mechanical and Aerospace Engineering at Oklahoma State University (OSU). He received his BSc degree from Birla Institute of Technology and MSc degree from the School of Mechanical and Aerospace Engineering at OSU. He is interested in mathematical modeling of turbulent flows and machine learning applications in fluid dynamics.

Omer San

Omer San is an assistant professor at the School of Mechanical and Aerospace Engineering at OSU. He received his PhD in Engineering Mechanics from Virginia Tech in 2012. He held two postdoctoral research positions, first in the Interdisciplinary Center for Applied Mathematics (ICAM) at Virginia Tech from 2012–’14, then from 2014–’15 in the Center for Shock Wave-processing of Advanced Reactive Materials (C-SWARM) at the University of Notre Dame, Indiana. Since 2015, he has been with the faculty of the School of Mechanical and Aerospace Engineering at OSU-Stillwater. His research interests include multiscale modeling and simulation, fluid dynamics, and high performance computing.