Multigrid methods with PSTS- and HSS-smoothers for solving the unsteady Navier-Stokes equations

Authors

  • Tatiana Martynova Southern Federal University, Vorovich Institute of Mathematics, Mechanics and Computer Science
  • Galina Muratova Southern Federal University, Vorovich Institute of Mathematics, Mechanics and Computer Science
  • Evgeniya Andreeva Southern Federal University, Vorovich Institute of Mathematics, Mechanics and Computer Science
  • Vadim Bavin Southern Federal University, Vorovich Institute of Mathematics, Mechanics and Computer Science
  • Zeng-Qi Wang Shanghai Jiao Tong University, School of Mathematical Sciences, Shanghai, 200000, P.R. China

Keywords:

multigrid methods, product-type skew-Hermitian triangular splitting methods, Hermitian/skew-Hermitian splitting methods, incompressible Navier-Stokes equations.

Abstract

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.

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Published

2020-12-25

Issue

Vol. 17 (2020)

Section

Computational mathematics