F. Bassi, N. Franchina, A. Ghidoni and S. Rebay A numerical investigation of a spectral-type nodal collocation discontinuous Galerkin approximation of the Euler and Navier–Stokes equations International Journal for Numerical Methods in Fluids 71
In this paper, we aim at clarifying, by numerical investigation, the behaviour of spectral discontinuous Galerkin collocation approximations defined on Legendre–Gauss–Lobatto and Legendre–Gauss nodes. Numerical results have shown that the discretization based upon the former set of nodes may suffer from unstable behaviours due to aliasing driven instabilities that can be triggered by particular flow regions such as stagnation points.
The discretization is affected by aliasing errors due to inexact integration of nonlinearities, but it is also subject to the effects of DOFs decoupling typical of this kind of approximations. Establishing which phenomenon is the source of the unstable behaviour noted near stagnation points is not possible a priori because the influence of the two aspects cannot be considered separately. In fact, for the Lobatto-DG scheme, the aspects are both influential, whereas for the Gauss-DG scheme, they are not, being the discretization accurate enough at least for the integration of linear terms and being the scheme free of DOFs decoupling effects. Computations indicate that, for a sufficient high-order accurate approximation, the Lobatto-based scheme can obtain satisfactory results. This fact suggests that the DOFs decoupling typical of nodal collocation approximations is not the cause per se of the observed instabilities. Instead, satisfactory results have shown a great reliability of the Gauss-DG discretization even in the presence of stretched meshes and relatively high Reynolds number.
Complete the form below and we will send an e-mail message containing a link to the selected article on your behalf