Morphing Continuum Theory for Turbulence: Theory, Computation and Visualization

TL;DR

This paper introduces a high-order morphing continuum theory (MCT) for modeling compressible turbulence, formulated within rational continuum mechanics, and demonstrates its superior predictive capability over traditional Navier-Stokes-based methods in simulating transonic flow.

Contribution

The paper develops a novel high-order MCT framework for turbulence modeling, including constitutive equations and conservation laws, and applies it to computational simulations showing improved accuracy.

Findings

MCT-based DNS outperforms NS-based DNS in predicting transonic flow.

MCT requires less than 10% of the mesh size compared to traditional methods.

A new frame-indifferent Q-criterion derived from MCT effectively visualizes turbulence structures.

Abstract

A high order morphing continuum theory (MCT) is introduced to model highly compressible turbulence. The theory is formulated under the rigorous framework of rational continuum mechanics. A set of linear constitutive equations and balance laws are deduced and presented from the Coleman-Noll procedure and Onsager's reciprocal relations. The governing equations are then arranged in conservation form and solved through the finite volume method with a second order Lax-Friedrichs scheme for shock preservation. A numerical example of transonic flow over a three-dimensional bump is presented using MCT and the finite volume method. The comparison shows that MCT-based DNS provides a better prediction than NS-based DNS with less than 10% of the mesh number when compared with experiments. A MCT-based and frame-indifferent Q-criterion is also derived to show the coherent eddy structure of the downstream turbulence in the numerical example. It should be emphasized that unlike the NS-based G-criterion, the MCT-based Q-criterion is objective without the limitation of Galilean-invariance.