Linearized Navier-Stokes Equations and their Numerical Solution

摘要

A propagation model, based on the linearized Navier-Stokes (LNS) equations, is proposed. It includes hydrodynamic-acoustic interactions, coupling acoustic waves and vortical modes, the mechanism responsible of the generation of vorticity associated with the hydro-dynamic modes. The linearized Navier-Stokes equations are discretized in space using a Discontinuous Galerkin formulation for unstructured grids. Explicit time integration and non-reflecting Perfectly Matched Layers boundary conditions are introduced. To reduce the computational overhead given by the presence of the viscous terms, the diffusive fluxes are evaluated only during the first stage of the Runge-Kutta time stepping and kept frozen for the successive stages. The solution of the LNS equations increases the computational time of approximately the 85% with respect to the linearized Euler equations (LEE), while adopting the freezing technique the computational overhead is reduced to the 15%. The LNS model is applied to the acoustic radiation from a straight circular semi-infinite hard-wall duct with several mean flow configurations, the so-called Munt problem. The mechanism of vortex shedding from the duct trailing edge is analyzed and the solution of the LNS model is compared with the results obtained with the LEE simulations.