High-order implicit time integration for unsteady incompressible flows

Author (s): Montlaur, A.; Fernández-Méndez, S. and Huerta, A.
Journal: International Journal for Numerical Methods in Fluids

Volume: 70, Issue 5
Pages: 603 – 626
Date: 2012

The spatial discretization of unsteady incompressible Navier-Stokes equations is stated as a system of Differential Algebraic Equations (DAEs), corresponding to the conservation of momentum equation plus the constraint due to the incompressibility condition. Asymptotic stability of Runge-Kutta and Rosenbrock methods applied to the solution of the resulting index-2 DAE system is analyzed. A critical comparison of Rosenbrock, semi-implicit and fully implicit Runge-Kutta methods is performed, in terms of order of convergence and stability. Numerical examples, considering a Discontinuous Galerkin formulation with piecewise solenoidal approximation, demonstrate the applicability of the approaches, and compare their performance with classical methods for incompressible flows.



	Author = {Montlaur, Adeline and Fern{{\'a}}ndez-M{{\'e}}ndez, Sonia and Huerta, Antonio},
	Title = {High-order implicit time integration for unsteady incompressible flows},
	Fjournal = {International Journal for Numerical Methods in Fluids},
	Journal = {Internat. J. Numer. Methods Fluids},
	Volume = {70},
	Number = {5},
	Pages = {603--626},
	Year = {2012},
	Doi = {10.1002/fld.2703},
	Url = {http://onlinelibrary.wiley.com/doi/10.1002/fld.2703/pdf}