| Resumo : |
This study considers the properties of accuracy and stability of the spectral/hp continuous Galerkin (CG) formulation for under-resolved nonlinear problems. The theme's relevance lies in the fact that, in recent years, CG has been used in LES-type computations of turbulent flows without explicit turbulence modelling. In this scenario, an appropriate balance between numerical dissipation and spectral resolution power (i.e. eddy-resolving capability) is very important. Here, a modified Burgers' equation is proposed, in which discontinuities are prevented while large wavenumbers remain significantly energised. This model problem is analysed with fully-resolved and under-resolved simulations. In the latter, a modern spectral vanishing viscosity (SVV) operator is used for stability. Different polynomial orders are considered in a same-DOF setting. Sensible choices of polynomial orders and SVV parameters are shown to provide accurate resolution of the inertial range at a fraction of the cost of fully resolved cases. |