Convergence Analysis of Fractional Time-Stepping Techniques for Incompressible Fluids with Microstructure

We present and analyze fully discrete fractional time stepping techniques for the solution of the micropolar Navier Stokes equations, which is a system of equations that describes the evolution of an incompressible fluid whose material particles possess both translational and rotational degrees of f...

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Bibliographic Details
Published in:	Journal of scientific computing Vol. 64; no. 1; pp. 216 - 233
Main Author:	Salgado, Abner J.
Format:	Journal Article
Language:	English
Published:	New York Springer US 01-07-2015 Springer Nature B.V
Subjects:	Algorithms Angular velocity Approximation Computational Mathematics and Numerical Analysis Convergence Fluid flow Incompressible flow Incompressible fluids Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Navier-Stokes equations Theoretical Velocity 65N15 65N12 Micropolar flows Fluids with microstructure Micropolar Navier Stokes 76A05 35Q30 76M10 Fractional time stepping 65N30
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Summary:	We present and analyze fully discrete fractional time stepping techniques for the solution of the micropolar Navier Stokes equations, which is a system of equations that describes the evolution of an incompressible fluid whose material particles possess both translational and rotational degrees of freedom. The proposed schemes uncouple the computation of the linear and angular velocity and the pressure. We develop a first order scheme which is unconditionally stable and delivers optimal convergence rates, and an almost unconditionally stable second order scheme.
ISSN:	0885-7474 1573-7691
DOI:	10.1007/s10915-014-9926-x