High-order implicit time integration for unsteady incompressible flows

The spatial discretization of unsteady incompressible Navier–Stokes equations is stated as a system of differential algebraic equations, corresponding to the conservation of momentum equation plus the constraint due to the incompressibility condition. Asymptotic stability of Runge–Kutta and Rosenbro...

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Detalhes bibliográficos
Autores: Villardi de Montlaur, Adeline de|||0000-0002-0243-668X, Fernández Méndez, Sonia|||0000-0002-9305-7684, Huerta, Antonio|||0000-0003-4198-3798
Formato: artículo
Fecha de publicación:2011
País:España
Recursos:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/14695
Acesso em linha:https://hdl.handle.net/2117/14695
https://dx.doi.org/10.1002/fld.2703
Access Level:acceso abierto
Palavra-chave:Galerkin methods
Navier-Stokes equations
Differential algebraic equations
Incompressible Navier–Stokes
High-order time integrators
Runge–Kutta
Rosenbrock
Discontinuous Galerkin
Equacions
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
Descrição
Resumo:The spatial discretization of unsteady incompressible Navier–Stokes equations is stated as a system of differential algebraic equations, 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 differential algebraic equations 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.