Numerical methods for Computational Fluid Dynamics Physical consistency of high-resolution CFD

Instantaneous contours of temperature (top) of Ma=3 shock impinging on a turbulent boundary layer,and corresponding mean flow (bottom)

Motivation and Objectives

CFD tools in physical or engineering applications never can reach numerical resolution levels where the truncation error of the discretization schemes enters its asymptotic limit. It thus is of high practical relevance to design schemes that have good scale resolution properties whenever numerical resolution is sufficient for relevant flow scales, and whose truncation error functions as physically consistent subgrid-scale model when not. In the past, this research concept has led to the development of the first physically consistent and practically successful implicit LES model. Currently, the notion of employing model uncertainty and truncation errors as physical-model surrogates is being pursued on several levels.

Approach to Solution

Concepts of physical design of modeling and discretization error have been successfully employed for further development of high-resolution schemes targeted ENO schemes that are suitable for underresolved computations of turbulent and non-turbulent flows. The physically consistent implicit LES models ALDM has been applied to turbulent shock-boundary-layer interaction at unprecedented Reynolds numbers. Extending the general concept to numerical models for fluctuating hydrodynamics, the manipulation of modeling errors within the dissipative-particle-dynamics model is investigated to explore spontaneous long-range correlations in turbulent flows. Physical effects of truncation errors in particle-discretizations may also lead to relaxation processes that allow for highly effective mesh generation and domain partitioning methods. Both have been developed to apre-commercialization demonstration level.

Automatic generation of unstructured meshes with high mesh quality based on physical-particle advection anaology
Vortex-ring evolution for reacting shock-bubble interaction, grey shades correspond to inert-gas mass fraction and red is isosurface of vorticity v