By Pierre Sagaut
This specific publication offers a basic unified presentation of using the multiscale/multiresolution methods within the box of turbulence. The assurance levels from statistical versions constructed for engineering reasons to multiresolution algorithms for the direct computation of turbulence. It presents the one to be had updated studies facing the most recent and such a lot complex turbulence versions (including LES, VLES, hybrid RANS/LES, DES) and numerical strategies.The publication goals at supplying the reader with a entire description of contemporary techniques for turbulent stream simulation, starting from turbulence modeling to the main complex multilevel numerical tools.
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Additional info for Multiscale and Multiresolution Approaches in Turbulence
A Brief Introduction to Turbulence 15 scales by non-linear interaction with no action by viscosity or condition of formation. The extent of this inertial subrange depends on the Reynolds number. In that region, the only relevant parameters are the length scale under investigation K = 1/7 and the mean dissipation rate of turbulent energy ET- Since energy is transferred without loss, ST remains constant and equal to the finite mean energy 8 dissipation rate: eT « ej. 7. • The last region contains the smallest scales for which viscous effects become important and where the kinetic energy is dissipated into heat.
For several years it has thus clearly appeared necessary to develop some specific approaches to reduce the cost associated with the simulation of turbulent flows, leading to the emergence of several numerical techniques. The global idea of such approaches is to reduce the number of degrees of freedom of the problem, by resolving only some specific scales of the flow. T h e principle is then to perform a scale segregation, and to separate the structures of the flow which are identified as being of direct practical interest from other scales which can remain unresolved, and only accounted for t h r o u g h the use of a mathematical model.
Here, a two-level decomposition of the flow variables is considered, between a filtered (LES) part, and an averaged (RANS) part. In this case, the multilevel 10 The term multigrid is introduced to designate a method using different computational grids, and not to the multigrid methods used in steady CFD algorithms to speed up the convergence to a steady state. Multiscale and Multiresolution 44 Approaches in Turbulence method then becomes a multiresolution method, since the different resolution levels are obtained with some scale separation operators of different natures.