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A Simple 3D Immersed InterfaceMethod for Stokes Flow with Singular Forces on staggered grids

Communications in Computational Physics 2021年第6期30卷 227-254页

作者： Weiyi Wang Zhijun Tan School of Computer Science and Engineering Sun Yat-sen UniversityGuangzhou 510275China Guangdong Province Key Laboratory of Computational Science Sun Yat-sen Uni-versityGuangzhou 510275China

In this paper,a fairly simple 3D immersed interface method based on the CG-Uzawa type method and the level set representation of the interface is employed for solving three-dimensional Stokes flow with singular forces along the interface.The method is to apply the Taylor’s expansions only along the normal direction and incorporate the jump conditions up to the second normal derivatives into the finite difference schemes.A second order geometric iteration algorithm is employed for computing orthogonal projections on the surface with third-order accuracy.The Stokes equations are discretized involving the correction terms on staggered grids and then solved by the conjugate gradient Uzawa type method.The major advantages of the present method are the special simplicity,the ability in handling the Dirichlet boundary conditions,and no need of the pressure boundary condition.The method can also preserve the volume conservation and the discrete divergence free condition very well.The numerical results show that the proposed method is second order accurate and efficient.

关键词： 3D immersed interface method CG-Uzawa method Stokes flow level set method staggered grids singular forces

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A Multilevel Method for the Solution of Time Dependent Optimal Transport

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Numerical Mathematics(Theory,Methods and Applications) 2015年第1期8卷 97-111页

作者： Eldad Haber Raya Horesh Department of Mathematics&Department of Earth and Ocean Science The University of British ColumbiaVancouverBCCanada IBM research NYUSA

In this paper we present a new computationally efficientnumerical scheme for the minimizing flow for the computation of the optimal L 2 mass transport map-ping using the fluid approach.We review the method and discuss its numerical properties.We then derive a new scaleable,efficient discretization and a solution technique for the problem and show that the problem is equivalent to a mixed form formulation of a nonlinear fluid flow in porous media.We demonstrate the effec-tiveness of our approach using a number of numerical experiments.

关键词： Optimal mass transport inverse problems staggered grids

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A NUMERICAL METHOD OF MODELING ELASTIC WAVE PROPAGATION IN ANISOTROPIC MEDIA

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Acta Mechanica Solida Sinica 1995年第4期8卷 327-336页

作者： Liang Fei Yang Hueyju~★ Yang Guitong(Taiyuan University of Technology,Taiyuan 030024,P.R.China)(★Tsinghua University,Beijing 100084,P.R.China) Taiyuan University of Technology Taiyuan 030024 China Tsinghua University Beijing 100084 China

The velocity-stress finite-difference method is adopted to simulate the elastic wave propa- gation in azimuthal anisotropic media.The difference grids are completely staggered in the numerical im- plementation.To reduce the computational work,the absorbin8 boundary conditions for anisotropic media are introduced first and the corner points are specially treated.Examples show that more accurate results can be obtained from the modeling algorithm,which cost much less computational time than the conven- tional methods.Therefore,the algorithm has broad application prospects in engineering.

关键词： azimuthal anisotropy elastic wave finite-difference staggered grids

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