POD-Galerkin method for Finite Volume approximation of Navier-Stokes and turbulent RANS equations


Tuesday, 30 June, 2015 - 11:30

Speaker: Stefano Lorenzi (Dep. of Energy, CESNEF, Politecnico di Milano, Italy)

Room: SISSA - Santorio A - room 133


Model order reduction can be employed whenever fast simulations are required in engineering. A typical application of this approach is the control context. In this field, accurate and fast running simulation tools are devoted to the control system development for both its realization and validation.

Reduced order techniques have so far mainly been applied to finite element scheme. Nevertheless, in many engineering fields, the Finite Volume Method (FVM) may be preferred to other approaches due to its robust and inexpensive discretization of conservation laws. Besides the FVM can be used on arbitrary geometries, the main numerical feature of this method is the local conservation of the numerical fluxes. Since the numerical flux is conserved form one cell to the neighbour ones, the FVM is quite attractive for those problems that require the conservation of some quantities. This is a relevant characteristic of Computational Fluid Dynamics (CFD) problem. Moreover, in many engineering applications, the model should deal with high-Reynolds-number fluids which require the adoption of turbulence models. In particular, the classic modelling option in industrial field is the Reynolds-Averaged Navier–Stokes (RANS) equations with the Boussinesq assumption of the turbulent (eddy) viscosity.

In this work, a POD-Galerkin method for Finite Volume approximation is proposed to be employed in CFD applications, both for laminar and turbulent flows. The typical test case of the lid-driven cavity with Re = 1.000 and Re = 10.000 is employed to assess the performance of the approach. Finally, an application related to a nuclear engineering problem is also presented.