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A comparison of time-discretization/linearization approaches for the incompressible Navier-Stokes equations. (English) Zbl 1124.76041
Summary: This paper presents a numerical study of two ways for discretizing and linearizing the time-dependent incompressible Navier-Stokes equations. One approach consists in first applying a semi-discretization in time by a fully implicit \(\theta \)-scheme. Then, at each discrete time, the equations are linearized by a fixed point iteration. The number of iterations to reach a given stopping criterion is a priori unknown in this approach. In the second approach, Rosenbrock schemes with \(s\) stages are used as temporal discretization. The nonlinearity of Navier-Stokes equations is treated internally in Rosenbrock methods. At discrete time, exactly \(s\) linear systems of equations have to be solved. The numerical study considers five two-dimensional problems with distinct features. Four implicit time stepping schemes and five Rosenbrock methods are involved.

76M25 Other numerical methods (fluid mechanics) (MSC2010)
76D05 Navier-Stokes equations for incompressible viscous fluids
65M20 Method of lines for initial value and initial-boundary value problems involving PDEs
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