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...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2011 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/14695 |
| Acceso en línea: | https://hdl.handle.net/2117/14695 https://dx.doi.org/10.1002/fld.2703 |
| Access Level: | acceso abierto |
| Palabra clave: | 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 |
| Sumario: | 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. |
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