ERROR ESTIMATION, GRID SELECTION AND CONVERGENCE VERIFICATION IN LARGE EDDY SIMULATION

Abstract

Large eddy simulation (LES) is a modeling approach to simulation of turbulence, in which the large and energy containing eddies are directly resolved, while the smaller scales are modeled. The ``coarse-graining'' length scale (the length scale below which the turbulent eddies are modeled) is an important modeling parameter that is directly tied to the computational grid. As a result, the LES grid controls both the numerical and modeling errors and in most cases (given that the LES model is consistent) becomes the most important factor in determining the accuracy of the solution. The main goal of this dissertation is to enable a systematic approach to grid selection and convergence-verification in LES.

Systematic grid selection consists of five essential ingredients: (i) an ``error-indicator'' that identifies the regions of error generation, (ii) some knowledge of the directional structure of error generation (i.e., an anisotropic measure of error generation at each location), (iii) a model that describes the connection between the error generation and the filter/grid resolution (i.e., how it changes with a change in the resolution), (iv) criteria that describe the most ``optimal'' distribution of the error-indicator in space and in direction, and (v) a robust method for convergence-verification. Items (i), (ii), (iv) and (v) are all addressed in this dissertation, while item (iii) has not been a subject of extensive research here (because of its somewhat lower importance compared to the other four).

Three error-indicators are introduced that are different in terms of their underlying assumptions, complexity, potential accuracy, and extensibility to more complex flows and more sophisticated formulations of the problem of ``optimal'' grid selection. Two of these error-indicators are inherently anisotropic, while the third one is only a scalar but can be combined with either of the other two to enable anisotropic error-estimation. The ``optimal'' distributions of these error-indicators are discussed in detail, that, combined with a model to connect the error-indicator and the grid/filter resolution, describe our ``optimal'' grid selection criteria. Additionally, a more robust approach for convergence-verification in LES is proposed, and is combined with error-estimation and ``optimal'' grid selection/adaptation to form a systematic algorithm for large eddy simulation.

The proposed error-estimation, grid selection, and convergence-verification methods are tested on the turbulent channel flow and the flow over a backward-facing step, with good results in all cases, and grids that are quite close to what is know as ``best practice'' for LES of these flows.