The aim of this paper is to investigate and evaluate a multi-stage and multi-step method that is an evolution of the more common Backward Differentiation Formulae (BDF). This new class of formulae, called Two Implicit Advanced Step-point (TIAS), has been applied to a high-order Discontinuous Galerkin (DG) discretization of the Navier-Stokes equations, coupling the high temporal accuracy gained by the TIAS scheme with the high space accuracy of the DG method. The performance of the DG-TIAS scheme has been evaluated by means of two test cases: an inviscid isentropic convecting vortex and a laminar vortex shedding behind a circular cylinder. The advantages of the high-order time discretization are illustrated comparing the sixth-order accurate TIAS scheme with the second-order accurate BDF scheme using the same spatial discretization.
High-order discontinuous Galerkin solution of unsteady flows by using an advanced implicit method / Nigro, A.; De Bartolo, C.; Bassi, F.; Ghidoni, A.. - ELETTRONICO. - 99:(2014), pp. 135-149. (Intervento presentato al convegno European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs, HONOM 2013 tenutosi a fra nel 2013) [10.1007/978-3-319-05455-1_8].