A divergence-free velocity reconstruction for incompressible flows
Please always quote using this URN:urn:nbn:de:0296-matheon-11738
- In incompressible flows with vanishing normal velocities at the boundary, irrotational forces in the momentum equations should be balanced completely by the pressure gradient. Unfortunately, nearly all available discretization methods for incompressible flows violate this property. The origin of the problem is that discrete velocity approximations of incompressible flows are usually not divergence-free. Hence, the use of divergence-free velocity reconstructions is proposed wherever an $L^2$ scalar product appears in the discrete variational formulation. The approach is illustrated and applied to a nonconforming MAC-like discretization for unstructured Delaunay grids. It is numerically demonstrated that a divergence-free velocity reconstruction based on the lowest-order Raviart-Thomas element increases the robustness and accuracy of an existing convergent discretization, when irrotational forces appear in the momentum equations.
Author: | Alexander Linke |
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URN: | urn:nbn:de:0296-matheon-11738 |
Referee: | Alexander Mielke |
Document Type: | Preprint, Research Center Matheon |
Language: | English |
Date of first Publication: | 2012/10/10 |
Release Date: | 2012/10/10 |
Tag: | Navier-Stokes equations; divergence-free velocity reconstruction; incompressible flows |
Institute: | Freie Universität Berlin |
MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N08 Finite volume methods |
76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX) / 76Dxx Incompressible viscous fluids / 76D05 Navier-Stokes equations [See also 35Q30] | |
Preprint Number: | 986 |