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Chinese Journal of Aeronautics 2012年第3期25卷 297-310页

作者： JIANG Yongsong LIANG An SUN Xiaofeng JING Xiaodong School of Jet Propulsion Beihang University Beijing 100191 China Department of Compressor Design Shenyang Aeroengine Research Institute Shenyang 110015 China AVIC Commercial Aircrafl Engine Co. Ltd. Shanghai 200241 China

This paper presents the extension of the global description approach of a discontinuous function, which is proposed in the previous paper, to a spectral domain decomposition method. This multi-domain spectral immersed interlace method（IIM） divides the whole computation domain into the smooth and discontinuous parts. Fewer points on the smooth domains are used via taking advantage of the high accuracy property of the spectral method, but more points on the discontinuous domains are employed to enhance the resolution of the calculation. Two that the domain decomposition technique can placed around the discontinuity. The present reached, in spite of the enlarged computational discontinuous problems are tested to verify the present method. The results show reduce the error of the spectral IIM, especially when more collocation points are method is t：avorable for the reason that the same level of the accuracy can be domain.

关键词： computational aerodynamics immersed interface method immersed boundary method Chebyshev spectral method domain decomposition method

High Order Scheme for Schrödinger Equation with Discontinuous Potential I: immersed interface method

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Numerical Mathematics(Theory,methods and Applications) 2011年第4期4卷 576-597页

作者： Hao Wu Department of Mathematical Sciences Tsinghua UniversityBeijing10084China

The immersed interface method is modified to compute Schrödinger equation with discontinuous *** building the jump conditions of the solution into the finite difference approximation near the interface,this method can give at least second order convergence rate for the numerical solution on uniform cartesian *** accuracy of this algorithm is tested via several numerical examples.

关键词： Schrödinger equation discontinuous potential immersed interface method finite difference method

An immersed interface method for the Simulation of Inextensible interfaces in Viscous Fluids

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Communications in Computational Physics 2012年第3期11卷 925-950页

作者： Zhijun Tan D.V.Le K.M.Lim B.C.Khoo Guangdong Province Key Laboratory of Computational Science&School of Mathematics and Computational Science Sun Yat-senUniversityGuangzhou 510275China Institute of High Performance Computing 1 Fusionopolis Way#16-16 ConnexisSingapore 138632Singapore Singapore-MIT Alliance 4 Engineering Drive 3National University of SingaporeSingapore 117576Singapore Department of Mechanical Engineering National University of Singapore10 Kent Ridge CrescentSingapore 119260Singapore

In this paper,an immersed interface method is presented to simulate the dynamics of inextensible interfaces in an incompressible *** tension is introduced as an augmented variable to satisfy the constraint of interface inextensibility,and the resulting augmented system is solved by the GMRES *** this work,the arclength of the interface is locally and globally conserved as the enclosed region undergoes *** forces at the interface are calculated from the configuration of the interface and the computed augmented variable,and then applied to the fluid through the related jump *** governing equations are discretized on a MAC grid via a second-order finite difference scheme which incorporates jump contributions and solved by the conjugate gradient Uzawa-type *** proposed method is applied to several examples including the deformation of a liquid capsule with inextensible interfaces in a shear *** results reveal that both the area enclosed by interface and arclength of interface are conserved well *** provide further evidence on the capability of the present method to simulate incompressible flows involving inextensible interfaces.

关键词： Inextensible interface Stokes flows singular force immersed interface method CGUzawa method front tracking

The immersed interface method for Simulating Two-Fluid Flows

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Numerical Mathematics(Theory,methods and Applications) 2014年第4期7卷 447-472页

作者： Miguel Uh Sheng Xu Department of Mathematics Southern Methodist UniversityDallasTX 75275-0156USA

We develop the immersed interface method(IIM)to simulate a two-fluid flow of two immiscible fluids with different density and *** to the surface tension and the discontinuous fluid properties,the two-fluid flow has nonsmooth velocity and discontinuous pressure across the moving sharp interface separating the two *** IIM computes the flow on a fixed Cartesian grid by incorporating into numerical schemes the necessary jump conditions induced by the *** present how to compute these necessary jump conditions from the analytical principal jump conditions derived in[Xu,DCDS,Supplement 2009,pp.838-845].We test our method on some canonical two-fluid *** results demonstrate that the method can handle large density and viscosity ratios,is second-order accurate in the infinity norm,and conserves mass inside a closed interface.

关键词： immersed interface method two-fluid flows jump conditions augmented variable approach singular force Cartesian grid methods

The Algebraic immersed interface and Boundary method for Elliptic Equations with Jump Conditions

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Open Journal of Fluid Dynamics 2020年第3期10卷 239-269页

作者： Arthur Sarthou Stéphane Vincent Philippe Angot Jean-Paul Caltagirone Buf Compagnie Paris France Laboratoire MSME Université Gustave Eiffel Champs-sur-Marne France Institut de Mathématiques de Marseille Centrale Marseille Marseille France Institut Polytechnique de Bordeaux Université de Bordeaux Talence France

A new simple fictitious domain method, the algebraic immersed interface and boundary (AIIB) method, is presented for elliptic equations with immersed interface conditions. This method allows jump conditions on immersed interfaces to be discretized with a good accuracy on a compact stencil. Auxiliary unknowns are created at existing grid locations to increase the degrees of freedom of the initial problem. These auxiliary unknowns allow imposing various constraints to the system on interfaces of complex shapes. For instance, the method is able to deal with immersed interfaces for elliptic equations with jump conditions on the solution or discontinuous coefficients with a second order of spatial accuracy. As the AIIB method acts on an algebraic level and only changes the problem matrix, no particular attention to the initial discretization is required. The method can be easily implemented in any structured grid code and can deal with immersed boundary problems too. Several validation problems are presented to demonstrate the interest and accuracy of the method.

关键词： Fictitious Domain immersed interface method immersed Boundary method Penalty methods Finite Volumes Elliptic Equations Jump Embedded Conditions

Wave Propagation Across Acoustic/Biot’s Media:A Finite-Difference method

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Communications in Computational Physics 2013年第4期13卷 985-1012页

作者： Guillaume Chiavassa Bruno Lombard Centrale Marseille Laboratoire de Mecanique Modelisation et Procedes PropresUMR 7340 CNRSTechnopole de Chateau-Gombert38 rue Frederic Joliot-Curie13451 MarseilleFrance Laboratoire de Mecanique et d’Acoustique UPR 7051 CNRS31 chemin Joseph Aiguier13402 MarseilleFrance

Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid/poroelastic *** propagation is described by the usual acoustics equations(in the fluid medium)and by the low-frequency Biot’s equations(in the porous medium).interface conditions are introduced to model various hydraulic contacts between the two media:open pores,sealed pores,and imperfect ***-posedness of the initial-boundary value problem is *** grid numerical methods previously developed in porous heterogeneous media are adapted to the present context:a fourth-order ADER scheme with Strang splitting for timemarching;a space-time mesh-refinement to capture the slow compressional wave predicted by Biot’s theory;and an immersed interface method to discretize the interface conditions and to introduce a subcell *** experiments and comparisons with exact solutions are proposed for the three types of interface conditions,demonstrating the accuracy of the approach.

关键词： Biot’s model poroelastic waves jump conditions imperfect hydraulic contact highorder finite differences immersed interface method

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.

immersed interface CIP for One Dimensional Hyperbolic Equations

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Communications in Computational Physics 2014年第6期16卷 96-114页

作者： Kazufumi Ito Tomoya Takeuchi Department of Mathematics North Carolina State UniversityRaleighNC 27695USA. Collaborative Research Center for Innovative Mathematical Modelling Institute of Industrial ScienceUniversity of TokyoTokyoJapan. FIRST Aihara Innovative Mathematical Modelling ProjectJSTKawaguchiJapan.

The immersed interface technique is incorporated into CIP method to solve one-dimensional hyperbolic equations with piecewise constant *** proposed method achieves the third order of accuracy in time and space in the vicinity of the interface where the coefficients have jump discontinuities,which is the same order of accuracy of the standard CIP *** numerical tests are given to verify the accuracy of the proposed method.

关键词： CIP method immersed interface method hyperbolic equations in discontinuous media.

Numerical Study of Surfactant-Laden Drop-Drop Interactions

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Communications in Computational Physics 2011年第7期10卷 453-473页

作者： Jian-Jun Xu Zhilin Li John Lowengrub Hongkai Zhao School of Mathematical and Computational Sciences Xiangtan UniversityXiangtanHunan 411105China Department of Mathematics North Carolina State UniversityRaleighNC27695USA Department of Mathematics University of California IrvineIrvineCA92697USA

In this paper,we numerically investigate the effects of surfactant on dropdrop interactions in a 2D shear flow using a coupled level-set and immersed interface approach proposed in(Xu et al.,***.,212(2006),590–616).We find that surfactant plays a critical and nontrivial role in drop-drop *** particular,we find that the minimum distance between the drops is a non-monotone function of the surfactant coverage and Capillary *** non-monotonic behavior,which does not occur for clean drops,is found to be due to the presence of Marangoni forces along the drop *** suggests that there are non-monotonic conditions for coalescence of surfactant-laden drops,as observed in recent experiments of Leal and *** our study is two-dimensional,we believe that drop-drop interactions in three-dimensional flows should be qualitatively similar as the Maragoni forces in the near contact region in 3D should have a similar effect.

关键词： Surfactants drops coalescence surface tension Marangoni effect level-set method immersed interface method Stokes flow

The Sensitivity Analysis for the Flow Past Obstacles Problem with Respect to the Reynolds Number

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Advances in Applied Mathematics and Mechanics 2012年第1期4卷 21-35页

作者： Kazufumi Ito Zhilin Li Zhonghua Qiao Center for Research in Scientific Computation&Department of Mathematics North Carolina State UniversityRaleighNC 27695-8205USA School of Mathematical Sciences Nanjing Normal UniversityNo.1 Wenyuan RoadYadong New DistrictNanjing 210046China Department of Mathematics Hong Kong Baptist UniversityKowloon TongHong Kong

In this paper,numerical sensitivity analysis with respect to the Reynolds number for the flow past obstacle problem is *** carry out such analysis,at each time step,we need to solve the incompressible Navier-Stokes equations on irregular domains twice,one for the primary variables;the other is for the sensitivity variables with homogeneous boundary *** Navier-Stokes solver is the augmented immersed interface method for Navier-Stokes equations on irregular *** of the most important contribution of this paper is that our analysis can predict the critical Reynolds number at which the vortex shading begins to develop in the wake of the *** interesting experiments are shown to illustrate how the critical Reynolds number varies with different geometric settings.

关键词： Navier-Stokes equations sensitivity analysis flow past cylinder embedding technique immersed interface method irregular domain augmented system projection method fluid-solid interaction