This paper deals with preconditioners for the iterative solution of the discrete Oseen problem with variable viscosity. The motivation of this work originates from numerical simulations of multiphase flow, governed by...This paper deals with preconditioners for the iterative solution of the discrete Oseen problem with variable viscosity. The motivation of this work originates from numerical simulations of multiphase flow, governed by the coupled Cahn-Hilliard and incompressible Navier-Stokes equations. The impact of variable viscosity on some known precondition- ing technique is analyzed. Theoretical considerations and numerical experiments show that some broadly used preconditioning techniques for the Oseen problem with constant viscosity are also efficient when the viscosity is vaxving.展开更多
In this paper multigrid smoothers of Vanka-type are studied in the context of Computational Solid Mechanics(CSM).These smoothers were originally developed to solve saddle-point systems arising in the field of Comput...In this paper multigrid smoothers of Vanka-type are studied in the context of Computational Solid Mechanics(CSM).These smoothers were originally developed to solve saddle-point systems arising in the field of Computational Fluid Dynamics(CFD),particularly for incompressible flow problems.When treating(nearly)incompressible solids,similar equation systems arise so that it is reasonable to adopt the‘Vanka idea’for CSM.While there exist numerous studies about Vanka smoothers in the CFD literature,only few publications describe applications to solid mechanical problems.With this paper we want to contribute to close this gap.We depict and compare four different Vanka-like smoothers,two of them are oriented towards the stabilised equal-order Q_(1)/Q_(1)finite element pair.By means of different test configurations we assess how far the smoothers are able to handle the numerical difficulties that arise for nearly incompressible material and anisotropic meshes.On the one hand,we show that the efficiency of all Vanka-smoothers heavily depends on the proper parameter choice.On the other hand,we demonstrate that only some of them are able to robustly deal with more critical situations.Furthermore,we illustrate how the enclosure of the multigrid scheme by an outer Krylov space method influences the overall solver performance,and we extend all our examinations to the nonlinear finite deformation case.展开更多
文摘This paper deals with preconditioners for the iterative solution of the discrete Oseen problem with variable viscosity. The motivation of this work originates from numerical simulations of multiphase flow, governed by the coupled Cahn-Hilliard and incompressible Navier-Stokes equations. The impact of variable viscosity on some known precondition- ing technique is analyzed. Theoretical considerations and numerical experiments show that some broadly used preconditioning techniques for the Oseen problem with constant viscosity are also efficient when the viscosity is vaxving.
基金has been supported by DFG,under grant TU 102/11-3。
文摘In this paper multigrid smoothers of Vanka-type are studied in the context of Computational Solid Mechanics(CSM).These smoothers were originally developed to solve saddle-point systems arising in the field of Computational Fluid Dynamics(CFD),particularly for incompressible flow problems.When treating(nearly)incompressible solids,similar equation systems arise so that it is reasonable to adopt the‘Vanka idea’for CSM.While there exist numerous studies about Vanka smoothers in the CFD literature,only few publications describe applications to solid mechanical problems.With this paper we want to contribute to close this gap.We depict and compare four different Vanka-like smoothers,two of them are oriented towards the stabilised equal-order Q_(1)/Q_(1)finite element pair.By means of different test configurations we assess how far the smoothers are able to handle the numerical difficulties that arise for nearly incompressible material and anisotropic meshes.On the one hand,we show that the efficiency of all Vanka-smoothers heavily depends on the proper parameter choice.On the other hand,we demonstrate that only some of them are able to robustly deal with more critical situations.Furthermore,we illustrate how the enclosure of the multigrid scheme by an outer Krylov space method influences the overall solver performance,and we extend all our examinations to the nonlinear finite deformation case.
