The Large Eddy Simulation Arithmetic Design Based On Turbulence Self-similar Structure

Large eddy simulation(LES) is very important to the numerical simulationof turbulence, its key is the construction of reasonable subgrid stress model. Anew LES Model based on turbulence self-similar structure is brought forwardin this dissertation. The model is actually a dynamic model, its coe?cientsare calculated dynamically in simulation in order to be self-adaptive with ?ow.The kernel thought of dynamic model is the assumption that the coe?cients ofbenchmark model are scale-invariable,hence the coe?cients can be calculatedthrough Germano equation. However, the scale invariance hasn't a detailed crite-rion at present, so we first elect a criterion for the selecting of benchmark modelof dynamic model, that is filtered large scale quantity satisfying which kind ofcondition can be taken as benchmark model of dynamic model.We analyze self-similar structure in turbulence and discover every velocityfluctuation in turbulence possesses a similar structure in large scale by usingIFS anti-problem,hence present concrete description of turbulence self-similarstructure. By using the similarity of velocity ?uctuation in two levels, we presentsubgrid stress in similar structure takes on a simple similar relation, moreoverfiltered large scale quantities also satisfy the same linear relation. Hence subgridstress can be modeled by the large scale quantities, furthermore the coe?cientscan be dynamically calculated using Germano equation.The method of constructing subgrid stress model in this dissertation canconstruct a mixed model consisting of Smagorinsky model, scale-similar modeland fractal model, furthermore the coe?cients of model can be dynamically cal-culated. The multi-parameter fit of subgrid stress can improve the correlationcoe?cient of LES model. We advance a method of dissipation restriction whichcan make the model not only take on upper subgrid stress correlation coe?-cient, but also provide su?cient subgrid stress dissipation. The method replacesone-equation model of providing dissipation and has better practicability.After constructing our LES model, we perform large eddy simulation of ran-dom forced and decaying Burgers equation as well as nonlocal Burgers equation.The results show our LES model is e?ective and perform a new thought for theconstruction of subgrid stress model in other ?ow.