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Petrov-Galerkin solutions of the incompressible Navier-Stokes equations in primitive variables with adaptive remeshing. (English) Zbl 0783.76053

Summary: The solution of the incompressible Navier-Stokes equations in primitive variables is addressed. A Petrov-Galerkin formulation which automatically introduces streamline upwinding and allows equal order interpolation for all flow variables is presented. The solution algorithm is segregated, involving a series of updatings of the velocity and pressure fields. Error estimation and adaptive remeshing strategies for both steady and unsteady problems are demonstrated in some representative numerical examples.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76M30 Variational methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
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