Structured, unstructured, and zonal embedded grid finite volume formulations have been developed to solve the Favre filtered Navier-Stokes equations for performing large eddy simulation of turbulent flows. These compressible formulations were developed using a dual time stepping approach with low Mach number preconditioning. For the structured and zonal embedded grid formulations, time marching was done with either an explicit Runge-Kutta scheme or an implicit lower-upper symmetric-Gauss-Seidel scheme. For the unstructured formulation, time marching used either an explicit Runge-Kutta scheme or traditional Gauss-Seidel scheme. All codes were parallelized to reduce the overall time required for simulations. These schemes were second-order accurate in space and time. Validations were performed using laminar and turbulent incompressible benchmark flows.

Large eddy simulation methods have been developed to compute compressible turbulent flows with heat transfer. The formulation employs preconditioning to permit efficient use in the low Mach number regime. Efficient algorithms have been developed for both vector and parallel processing computer systems. Simulation results have been obtained using a dynamic subgrid-scale model for a channel heated and cooled at temperature ratios as high as 3. Results were also obtained for a channel with uniform wall heat flux heating and cooling with wall to bulk temperature ratios as high as 1.5 for heating and 0.56 for cooling. Density rms fluctuations as high as 9% have been observed for very low Mach number flows with heat transfer. Mean and rms velocity and temperature data were observed to collapse toward incompressible results when plotted in semi-local coordinates. Preliminary results have also been obtained for flow in a rib-roughened channel. The large eddy simulation algorithms were extended to include the use of unstructured and zonal embedded grids. Particularly, the use of zonal embedded grids show much promise for extending the Reynolds number range for which large eddy simulation can be employed with existing computers.

This book presents a comprehensive overview of the mathematics and physics behind the simulation of turbulent flows and discusses in detail (i) the phenomenology of turbulence in fluid dynamics, (ii) the role of direct and large-eddy simulation in predicting these dynamics, (iii) the multiple considerations underpinning subgrid modelling, and, (iv) the issue of validation and reliability resulting from interacting modelling and numerical errors.

This book gathers the proceedings of the 11th workshop on Direct and Large Eddy Simulation (DLES), which was held in Pisa, Italy in May 2017. The event focused on modern techniques for simulating turbulent flows based on the partial or full resolution of the instantaneous turbulent flow structures, as Direct Numerical Simulation (DNS), Large-Eddy Simulation (LES) or hybrid models based on a combination of LES and RANS approaches. In light of the growing capacities of modern computers, these approaches have been gaining more and more interest over the years and will undoubtedly be developed and applied further. The workshop offered a unique opportunity to establish a state-of-the-art of DNS, LES and related techniques for the computation and modeling of turbulent and transitional flows and to discuss about recent advances and applications. This volume contains most of the contributed papers, which were submitted and further reviewed for publication. They cover advances in computational techniques, SGS modeling, boundary conditions, post-processing and data analysis, and applications in several fields, namely multiphase and reactive flows, convection and heat transfer, compressible flows, aerodynamics of airfoils and wings, bluff-body and separated flows, internal flows and wall turbulence and other complex flows.

It is a truism that turbulence is an unsolved problem, whether in scientific, engin eering or geophysical terms. It is strange that this remains largely the case even though we now know how to solve directly, with the help of sufficiently large and powerful computers, accurate approximations to the equations that govern tur bulent flows. The problem lies not with our numerical approximations but with the size of the computational task and the complexity of the solutions we gen erate, which match the complexity of real turbulence precisely in so far as the computations mimic the real flows. The fact that we can now solve some turbu lence in this limited sense is nevertheless an enormous step towards the goal of full understanding. Direct and large-eddy simulations are these numerical solutions of turbulence. They reproduce with remarkable fidelity the statistical, structural and dynamical properties of physical turbulent and transitional flows, though since the simula tions are necessarily time-dependent and three-dimensional they demand the most advanced computer resources at our disposal. The numerical techniques vary from accurate spectral methods and high-order finite differences to simple finite-volume algorithms derived on the principle of embedding fundamental conservation prop erties in the numerical operations. Genuine direct simulations resolve all the fluid motions fully, and require the highest practical accuracy in their numerical and temporal discretisation. Such simulations have the virtue of great fidelity when carried out carefully, and repre sent a most powerful tool for investigating the processes of transition to turbulence.

Large eddy simulation (LES) seeks to simulate the large structures of a turbulent flow. This is the first monograph which considers LES from a mathematical point of view. It concentrates on LES models for which mathematical and numerical analysis is already available and on related LES models. Most of the available analysis is given in detail, the implementation of the LES models into a finite element code is described, the efficient solution of the discrete systems is discussed and numerical studies with the considered LES models are presented.