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An uzawa-type algorithm for the coupled Stokes equations

Applied Mathematics and Mechanics(English Edition) 2020年第7期41卷 1095-1104页

作者： Pengzhan HUANG Yinnian HE College of Mathematics and System Sciences Xinjiang UniversityUrumqi 830046China School of Mathematics and Statistics Xi’an Jiaotong UniversityXi’an 710049China

An uzawa-type algorithm is designed for the coupled Stokes equations discretized by the mixed finite element *** velocity solved by the presented algorithm is weakly divergence-free,which is different from the one sol... 详细信息

关键词： coupled Stokes equation uzawa method optimal relaxation parameter weakly divergence-free

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An Implementation ofMAC Grid-Based IIM-Stokes Solver for Incompressible Two-Phase Flows

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Communications in Computational Physics 2011年第10期10卷 1333-1362页

作者： Zhijun Tan K.M.Lim B.C.Khoo Guangdong Province Key Laboratory of Computational Science and School of Mathematics and Computational Science Sun Yat-sen UniversityGuangzhou 510275China Singapore-MIT Alliance 4 Engineering Drive 3National University of SingaporeSingapore 117576Singapore Department ofMechanical Engineering National University of Singapore10 Kent Ridge CrescentSingapore 119260Singapore

*** this paper,a novel implementation of immersed interface method combined with Stokes solver on a MAC staggered grid for solving the steady two-fluid Stokes equations with *** velocity components along the interface are introduced as two augmented variables and the resulting augmented equation is then solved by the GMRES *** augmented variables and/or the forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity,and are interpolated using cubic splines and are then applied to the fluid through the jump *** Stokes equations are discretized on a staggered Cartesian grid via a second order finite difference method and solved by the conjugate gradient *** numerical results show that the overall scheme is second order *** major advantages of the present IIM-Stokes solver are the efficiency and flexibility in terms of types of fluid flow and different boundary *** proposed method avoids solution of the pressure Poisson equation,and comparisons are made to show the advantages of time savings by the present *** generalized two-phase Stokes solver with correction terms has also been applied to incompressible two-phase Navier-Stokes flow.

关键词： Incompressible two-phase Stokes equations two-phaseNavier-Stokes equations discontinuous viscosity singular force immersed interface method uzawa method front tracking method.

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