Numerical analysis of a 1/2-equation model of turbulence

TL;DR

This paper provides the first numerical analysis of a simplified 1/2-equation turbulence model, proving stability, convergence, and error estimates, and validating these with numerical tests.

Contribution

It introduces the first rigorous numerical analysis of the 1/2-equation turbulence model, including stability, convergence, and error bounds.

Findings

The 1/2-equation model produces comparable velocity statistics to more complex models.

Stability, convergence, and error estimates are established for semi-discrete and fully discrete schemes.

Numerical tests confirm the theoretical convergence results.

Abstract

The recent 1/2-equation model of turbulence is a simplification of the standard Kolmogorov-Prandtl 1-equation URANS model. Surprisingly, initial numerical tests indicated that the 1/2-equation model produces comparable velocity statistics at reduced cost. It is also a test problem and first step for developing numerical analysis to address a full 1-equation model. This report begins the numerical analysis of the 1/2 equation model. Stability, convergence and error estimates are proven for a semi-discrete and fully discrete approximation. Finally, numerical tests are conducted to validate our convergence theory.