Towards a new model-free simulation of high-Reynolds-flows: Local average direct numerical simulation

Studies on the numerical simulation of high-Reynolds-number flows encounter difficulties due to the wide range of characteristic length and time scales existing in the flow field. These are often much smaller than the computational grid size. A new approach based on a 'model-free' local average direct numerical simulation is presented which incorporates a strategy to filter the non-resolvable scales by means of an integration over the domain and to recover the contribution of the subgrid scales by using an integral formulation developed for them. The resulting weak formulation allows us to define a numerical flux that, thanks to the filtering operation, is highly accurate. Several computation test-cases concerning theoretical accuracy and the Navier-Stokes equations at high Reynolds number are carried out without using any turbulence model. The obtained accuracy for all computations confirms that this approach can be considered a valid contribution in the field of direct numerical simulation.