A high-order accurate discontinuous Galerkin finite element method for laminar low Mach number flows

• Published in: International journal for numerical methods in fluids Vol. 72; no. 1; pp. 43 - 68
• Main Authors: Nigro, A., Renda, S., De Bartolo, C., Hartmann, R., Bassi, F.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 10.05.2013; Wiley Subscription Services, Inc
• Subjects: Accuracy; BR2-scheme; Computer simulation; discontinuous Galerkin finite element method; Flux; Galerkin methods; low Mach number; Mach number; Mathematical models; Navier-Stokes equations; Preconditioning; Unsteady flow
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.3732

SUMMARYIn this paper we present a discontinuous Galerkin (DG) method designed to improve the accuracy and efficiency of laminar flow simulations at low Mach numbers using an implicit scheme. The algorithm is based on the flux preconditioning approach, which modifies only the dissipative terms of the numerical flux. This formulation is quite simple to implement in existing implicit DG codes, it overcomes the time‐stepping restrictions of explicit multistage algorithms, is consistent in time and thus applicable to unsteady flows. The performance of the method is demonstrated by solving the flow around a NACA0012 airfoil and on a flat plate, at different low Mach numbers using various degrees of polynomial approximations. Computations with and without flux preconditioning are performed on different grid topologies to analyze the influence of the spatial discretization on the accuracy of the DG solutions at low Mach numbers. The time accurate solution of unsteady flow is also demonstrated by solving the vortex shedding behind a circular cylinder at the Reynolds number of 100. Copyright © 2012 John Wiley & Sons, Ltd. A DG method designed to improve the performance of steady and unsteady laminar flow simulations at low Mach numbers is proposed. The figure shows the influence on the accuracy of the following: (i) high‐order discretization (top row: flat plate, u‐velocity component), (ii) grid topology (middle row: NACA0012 airfoil, contours of normalized pressure), for steady‐state computations, and of the (iii) flux preconditioning approach for unsteady flow simulations (bottom row: vortex shedding behind a circular cylinder, snapshots of normalized pressure).