ADAPTIVITY IN WALL-MODELED LARGE EDDY SIMULATION

Abstract

In turbulence-resolving simulations, smaller eddies account for most of the computational cost. This is especially true for a wall-bounded turbulent flow, where a wall-resolved large eddy simulation might use more than 99% of the computing power to resolve the inner 10% of the boundary layer in realistic flows.The solution is to use an approximate model in the inner 10% of the boundary layer where the turbulence is expected to exhibit universal behavior, a technique generally called wall-modeled large eddy simulation.

Wall-modeled large-eddy simulation introduces a modeling interface (or exchange location) separating the wall-modeled layer from the rest of the domain. The current state-of-the-art is to rely on user expertise when choosing where to place this modeling interface, whether this choice is tied to the grid or not. This dissertation presents three post-processing algorithms that determine the exchange location systematically.

Two algorithms are physics-based, derived based on known attributes of the turbulence in attached boundary layers. These algorithms are assessed on a range of flows, including flat plate boundary layers, the NASA wall-mounted hump, and different shock/boundary-layer interactions. These algorithms in general agree with what an experienced user would suggest, with thinner wall-modeled layers in nonequilibrium flow regions and thicker wall-modeled layers where the boundary layer is closer to equilibrium, but are completely ignorant to the cost of the simulation they are suggesting.

The third algorithm is based on the sensitivity of the wall-model with the predicted wall shear stress and a model of the subsequent computational cost, finding the exchangelocation that minimizes a combination of the two. This algorithm is tested both a priori and a posteriori using an equilibrium wall model for the flow over a wall-mounted hump, a boundary layer in an adverse pressure gradient, and a shock/boundary-layer interaction. This third algorithm also produces exchange locations that mostly agree with what an experienced user would suggest, with thinner layers where the wall-model sensitivity is high and thicker layers where this sensitivity is low. This suggests that the algorithm should be useful in simulations of realistic and highly complex geometries.