A high order characteristics method for the incompressible Navier-Stokes equations. (English) Zbl 0824.76060

Boukir, Karima; Maday, Yvon; Métivet, Brigitte

Comput. Methods Appl. Mech. Eng. 116, 211-218 (1994).

Summary: We analyze a high order characteristics method for the Navier-Stokes equations. We focus on the cases of the first, second and third order in time schemes with finite element spatial discretization. A numerical comparison between the first and second order schemes is done for steady or transient flows.

MSC:

76M25	Other numerical methods (fluid mechanics) (MSC2010)
76D05	Navier-Stokes equations for incompressible viscous fluids
76R10	Free convection
65M25	Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs

Keywords:

consistency error; first order scheme; stability; convergence; second and third order schemes; spectral spatial discretization; finite element spatial discretization

References:

[1]	Maday, Y.; Patera, A.; Ronquist, E., An operator integration factor splitting method for time dependent problems, (Application to incompressible fluid flows. Application to incompressible fluid flows, J. Sci. Comput., 5 (1990)), 263-292 · Zbl 0724.76070
[2]	Benque, J. P.; Ibler, B.; Kerami, A.; Labadie, G., A finite element method for the Navier—Stokes equations, (Proc. 3rd Internat. Conf. on Finite Elements in Flow Problems. Proc. 3rd Internat. Conf. on Finite Elements in Flow Problems, Banff. Alberta, Canada (1980)) · Zbl 0457.76023
[3]	Pironneau, O., On the transport diffusion algorithm and its applications to the Navier—Stokes equations, Numer. Math., 38, 309-332 (1982) · Zbl 0505.76100
[4]	Suli, E., Convergence and nonlinear stability of the Lagrange—Galerkin method for the Navier—Stokes equations, Numer. Math., 53, 459-483 (1988) · Zbl 0637.76024
[5]	Ewing, R. E.; Russell, T. F., Multistep Galerkin method along characteristics for convection-diffusion problems, (Vichnevetsky, R.; Stepleman, R. S., Advances in Computer Methods for P.D.E (1981), IMACS, Rutgers Univ.: IMACS, Rutgers Univ. Braunschweig), 28-36
[9]	Girault, V.; Raviart, P. A., Finite Element Methods for the Navier—Stokes Equations, (Theory and Algorithms (1986), Springer: Springer New Brunswick, NJ) · Zbl 0396.65070
[10]	Chabard, J. P.; Métivet, B.; Pot, G.; Thomas, B., An efficient finite element method for the computation of 3D turbulent incompressible flows, (Finite Element in Fluids, 8 (1994), Wiley: Wiley Berlin), in press
[11]	Métivet, B.; Razafindrakoto, E., Projet N3S de mécanique des fluides, (Etude d’un schema aux caractéristiques d’ordre 2 pour la resolution des equations de Navier—Stokes. Etude d’un schema aux caractéristiques d’ordre 2 pour la resolution des equations de Navier—Stokes, Rapport EDF. H172/7094 (1990))
[12]	(Roux, B., Numerical Simulation of Oscillatory Convection in low-Pr fluids. Numerical Simulation of Oscillatory Convection in low-Pr fluids, Notes on Numerical Mechanics, 27 (1990), Vieweg: Vieweg New York) · Zbl 0712.00022