Algebraic pressure segregation methods for the incompressible Navier-Stokes equations. (English) Zbl 1144.76027
Summary: This work is an overview of algebraic pressure segregation methods for incompressible Navier-Stokes equations. These methods can be understood as an inexact \(LU\) block factorization of the original system matrix. We have considered a wide set of methods: algebraic pressure correction methods, algebraic velocity correction methods and Yosida method. Higher-order schemes, based on improved factorizations, are also introduced. We have also explained the relationship between these pressure segregation methods and some widely used preconditioners, and we have introduced predictor-corrector methods, one-loop algorithms where nonlinearity and iterations towards the monolithic system are coupled.
MSC:
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |
Keywords:
inexact \(LU\) block factorization; algebraic velocity correction methods; predictor-corrector methodsReferences:
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