Geodesic
Multigrid methods with PSTS- and HSS-smoothers for solving the unsteady Navier-Stokes equations
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 2190-2203

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Multigrid methods are considered for staggered grid discretizations of the incompressible unsteady Navier-Stokes equations. After discretization and linearization of the problem, systems of linear algebraic equations with a strongly nonsymmetric matrix appear. Product-type skew-Hermitian triangular splitting and Hermitian/skew-Hermitian splitting methods are used as smoothers in the multigrid methods for solving the linear equation systems. Numerical experiments on a 2-D model problem were carried out using algebraic multigrid methods and indicated that these smoothers are robust with respect to the different Reynolds numbers.
Keywords: multigrid methods, product-type skew-Hermitian triangular splitting methods, Hermitian/skew-Hermitian splitting methods, incompressible Navier-Stokes equations. 
@article{SEMR_2020_17_a124,
     author = {G. V. Muratova and T. S. Martynova and E. M. Andreeva and V. V. Bavin and Z.-Q. Wang},
     title = {Multigrid methods with {PSTS-} and {HSS-smoothers} for solving the unsteady {Navier-Stokes} equations},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {2190--2203},
     publisher = {mathdoc},
     volume = {17},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2020_17_a124/}
}
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G. V. Muratova; T. S. Martynova; E. M. Andreeva; V. V. Bavin; Z.-Q. Wang. Multigrid methods with PSTS- and HSS-smoothers for solving the unsteady Navier-Stokes equations. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 2190-2203. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a124/