Progress in the numerical simulation of turbulence has been rapid in the 1990s. New techniques both for the numerical approximation of the Navier-Stokes equations and for the subgrid-scale models used in large-eddy simulation have emerged and are being widely applied for both fundamental and applied engineering studies, along with ideas for the performance and use of simulation for compressible, chemically reacting and transitional flows. This collection of papers from the second ERCOFTAC Workshop on Direct and Large-Eddy Simulation, held in Grenoble in September 1996, presents the research being undertaken in Europe and Japan on these topics. Describing in detail the ambitious use of DNS for fundamental studies and of LES for complex flows of potential and actual engineering importance, this volume should be of interest to researchers active in the area.

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."

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.

Progress in the numerical simulation of turbulence has been rapid in the 1990s. New techniques both for the numerical approximation of the Navier-Stokes equations and for the subgrid-scale models used in large-eddy simulation have emerged and are being widely applied for both fundamental and applied engineering studies, along with novel ideas for the performance and use of simulation for compressible, chemically reacting and transitional flows. This collection of papers from the second ERCOFTAC Workshop on Direct and Large-Eddy Simulation, held in Grenoble in September 1996, presents the key research being undertaken in Europe and Japan on these topics. Describing in detail the ambitious use of DNS for fundamental studies and of LES for complex flows of potential and actual engineering importance, this volume will be of interest to all researchers active in the area.