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 Nonlinear Numerical Schemes for Evolutionary PDEs - Proceedings of the European Workshop, HONOM 2013

BASSI, Francesco;
2014-01-01

Abstract

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.
book chapter - capitolo di libro
2014
Nigro, Alessandra; De Bartolo, Carmine; Bassi, Francesco; Ghidoni, Antonio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10446/71941
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