Large eddy simulation of three-dimensional turbulent flows by the finite element method

Abstract

The main objectives of this work are the formulation, implementation and applications of a numerical algorithm to simulate turbulent, incompressible, isothermal flows. The transient three-dimensional flow is analyzed using an explicit Taylor-Galerkin scheme and the finite element method with hexahedrical eight-node element. Turbulence is simulated using Large Eddy Simulation. For sub-grid scales two models were implemented, the classical Smagorinsky's model and the dynamic eddy viscosity model. For the second filtration, which is necessary in the dynamic model, a new method was developed based on independent finite elements that involve each node in the original mesh. The implemented scheme is efficient and good results with low additional computational cost were obtained. Results for two classical problems, the driven cavity and the backward facing step are presented. Comments about the model applicability for flows with high Reynolds numbers are also presented

Explicit filtering and exact reconstruction of the sub-filter stresses in large eddy simulation

“…By contrast, integral filters, which essentially perform a weighted average over a patch of cells surrounding a node, are somewhat complicated to construct on unstructured meshes and in parallelised codes. Methods for constructing integral filters on unstructured meshes rely on complicated logic [26,27].…”

Estudio Numérico de Flujos Turbulentos Isotérmicos en Canales y Flujos Laminares con Convección Mixta en Cavidades

“…Puede ser citado como ejemplo la imposibilidad del uso de métodos de integración temporales puramente explícitos debido a la ausencia de la derivada temporal de la presión en la ecuación de la continuidad (Reddy y Gartling, 1994). Con el objetivo de superar esa dificultad es usado el método de seudo-compresibilidad (Kawahara y Hirano, 1983) donde la derivada de la presión en el tiempo permanece en la ecuación de la continuidad (Petry y Awruch, 2006).…”