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| 1 | Numerical Methods for Fluid-Structure Interaction—A Review显示文摘The interactions between incompressible fluid flows and immersed structures are nonlinearmulti-physics phenomena that have applications to a wide range of scientific and engineering disciplines.In this article,we review representative numericalmethods based on conforming and non-conformingmeshes that are currently available for computing fluid-structure interaction problems,with an emphasis on some of the recent developments in the field.A goal is to categorize the selected methods and assess their accuracy and efficiency.We discuss challenges faced by researchers in this field,and we emphasize the importance of interdisciplinary effort for advancing the study in fluid-structure interactions. | Gene Hou Jin Wang Anita Layton | 2012 | Communications in Computational Physics2012，12，7： | 7 |
| 2 | Efficient Collocational Approach for Parametric Uncertainty Analysis显示文摘A numerical algorithm for effective incorporation of parametric uncertainty into mathematical models is presented.The uncertain parameters are modeled as random variables,and the governing equations are treated as stochastic.The solutions,or quantities of interests,are expressed as convergent series of orthogonal polynomial expansions in terms of the input random parameters.A high-order stochastic collocation method is employed to solve the solution statistics,and more importantly,to reconstruct the polynomial expansion.While retaining the high accuracy by polynomial expansion,the resulting“pseudo-spectral”type algorithm is straightforward to implement as it requires only repetitive deterministic simulations.An estimate on error bounded is presented,along with numerical examples for problems with relatively complicated forms of governing equations. | Dongbin Xiu | 2007 | Communications in Computational Physics2007，2，2： | 6 |
| 3 | Enabling Technologies in the Problem Solving Environment HEDP显示文摘Enabling technologies are those technologies preparing input data,analyzing output data and facilitating the whole processes for numerical simulations.This paper outlines current enabling technologies for large-scale multidisciplinary simulations used in the High End Digital Prototyping(HEDP)system,a problem solving environment equipped with capability of mesh generation and large-scale visualization.A problem solving environment is a computer system that provides all the computational facilities necessary to solve a target class of problems.Mesh generation continues to be the pacing technology for a practical numerical analysis,which is essential to yielding an accurate and efficient solution.Large-scale visualization maps the massive data to some kinds of scenes interactively,which can be realized through a tiled display wall system with distributed visualization capability.HEDP is designed for large-scale andmultidisciplinary simulations,and there are four categories of modules involved,namely pre-processing module,computing module,post-processing module,and platform control module.All these modules are coupled through a software bus,which makes the modules integrated seamlessly.Detailed design principles and applications of the HEDP environment are addressed in this paper. | Lijun Xie Yao Zheng Jianjun Chen Jianfeng Zou | 2008 | Communications in Computational Physics2008，4，10： | 6 |
| 4 | High-Order and High Accurate CFD Methods and Their Applications for Complex Grid Problems显示文摘The purpose of this article is to summarize our recent progress in high-order and high accurate CFD methods for flow problems with complex grids as well as to discuss the engineering prospects in using these methods.Despite the rapid development of high-order algorithms in CFD,the applications of high-order and high accurate methods on complex configurations are still limited.One of the main reasons which hinder the widely applications of thesemethods is the complexity of grids.Many aspects which can be neglected for low-order schemes must be treated carefully for high-order ones when the configurations are complex.In order to implement highorder finite difference schemes on complex multi-block grids,the geometric conservation lawand block-interface conditions are discussed.A conservativemetricmethod is applied to calculate the grid derivatives,and a characteristic-based interface condition is employed to fulfil high-order multi-block computing.The fifth-order WCNS-E-5 proposed by Deng[9,10]is applied to simulate flows with complex grids,including a double-delta wing,a transonic airplane configuration,and a hypersonic X-38 configuration.The results in this paper and the references show pleasant prospects in engineering-oriented applications of high-order schemes. | Xiaogang Deng Meiliang Mao Guohua Tu Hanxin Zhang Yifeng Zhang | 2012 | Communications in Computational Physics2012，11，4： | 6 |
| 5 | Spectral-Element andAdjointMethods in Seismology显示文摘We provide an introduction to the use of the spectral-elementmethod (SEM)in seismology. Following a brief review of the basic equations that govern seismicwave propagation, we discuss in some detail how these equations may be solved numericallybased upon the SEM to address the forward problem in seismology. Examplesof synthetic seismograms calculated based upon the SEM are compared to datarecorded by the Global Seismographic Network. Finally, we discuss the challenge ofusing the remaining differences between the data and the synthetic seismograms toconstrain better Earth models and source descriptions. This leads naturally to adjointmethods, which provide a practical approach to this formidable computational challengeand enables seismologists to tackle the inverse problem. | Jeroen Tromp Dimitri Komatitsch Qinya Liu | 2008 | Communications in Computational Physics2008，3，1： | 5 |
| 6 | A Stable Finite Difference Method for the Elastic Wave Equation on Complex Geometries with Free Surfaces显示文摘A stable and explicit second order accurate finite difference method for the elastic wave equation in curvilinear coordinates is presented.The discretization of the spatial operators in the method is shown to be self-adjoint for free-surface,Dirichlet and periodic boundary conditions.The fully discrete version of the method conserves a discrete energy to machine precision. | Daniel Appelo N.Anders Petersson | 2009 | Communications in Computational Physics2009，5，1： | 4 |
| 7 | Multiscale Modeling and Simulations of Flows in Naturally Fractured Karst Reservoirs显示文摘Modeling and numerical simulations of fractured,vuggy,porus media is a challenging problem which occurs frequently in reservoir engineering.The problem is especially relevant in flow simulations of karst reservoirs where vugs and caves are embedded in a porous rock and are connected via fracture networks at multiple scales.In this paper we propose a unified approach to this problem by using the StokesBrinkman equations at the fine scale.These equations are capable of representing porous media such as rock as well as free flow regions(fractures,vugs,caves)in a single system of equations.We then consider upscaling these equations to a coarser scale.The cell problems,needed to compute coarse-scale permeability of Representative Element of Volume(REV)are discussed.A mixed finite element method is then used to solve the Stokes-Brinkman equation at the fine scale for a number of flow problems,representative for different types of vuggy reservoirs.Upscaling is also performed by numerical solutions of Stokes-Brinkman cell problems in selected REVs.Both isolated vugs in porous matrix as well as vugs connected by fracture networks are analyzed by comparing fine-scale and coarse-scale flow fields.Several different types of fracture networks,representative of short-and long-range fractures are studied numerically.It is also shown that the Stokes-Brinkman equations can naturally be used to model additional physical effects pertaining to vugular media such as partial fracture with fill-in by some material and/or fluids with suspended solid particles. | Peter Popov Yalchin Efendiev Guan Qin | 2009 | Communications in Computational Physics2009，6，6： | 4 |
| 8 | Recent Progress in Symplectic Algorithms for Use in Quantum Systems显示文摘In this paper we survey recent progress in symplectic algorithms for use in quantum systems in the following topics:Symplectic schemes for solving Hamiltonian systems;Classical trajectories of diatomic systems,model molecule A2B,Hydrogen ion H+2 and elementary atmospheric reaction N(4S)+O2(X 3Σ−g)→NO(X 2Π)+O(3P)calculated by means of Runge-Kutta methods and symplectic methods;the classical dissociation of the HF molecule and classical dynamics of H+2 in an intense laser field;the symplectic form and symplectic-scheme shooting method for the time-independent Schr¨odinger equation;the computation of continuum eigenfunction of the Schr¨odinger equation;asymptotic boundary conditions for solving the time-dependent Schr¨odinger equation of an atom in an intense laser field;symplectic discretization based on asymptotic boundary condition and the numerical eigenfunction expansion;and applications in computing multi-photon ionization,above-threshold ionization,Rabbi oscillation and high-order harmonic generation of laser-atom interaction. | Xue-Shen Liu Yue-Ying Qi Jian-Feng He Pei-Zhu Ding | 2007 | Communications in Computational Physics2007，2，1： | 4 |
| 9 | Third Order WENO Scheme on Three Dimensional Tetrahedral Meshes显示文摘We extend the weighted essentially non-oscillatory(WENO)schemes on two dimensional triangular meshes developed in[7]to three dimensions,and construct a third order finite volume WENO scheme on three dimensional tetrahedral meshes.We use the Lax-Friedrichs monotone flux as building blocks,third order reconstructions made from combinations of linear polynomials which are constructed on diversified small stencils of a tetrahedral mesh,and non-linear weights using smoothness indicators based on the derivatives of these linear polynomials.Numerical examples are given to demonstrate stability and accuracy of the scheme. | Yong-Tao Zhang Chi-Wang Shu | 2009 | Communications in Computational Physics2009，5，2： | 4 |
| 10 | Heterogeneous Multiscale Methods: A Review显示文摘This paper gives a systematic introduction to HMM,the heterogeneous multiscale methods,including the fundamental design principles behind the HMM philosophy and the main obstacles that have to be overcome when using HMM for a particular problem.This is illustrated by examples from several application areas,including complex fluids,micro-fluidics,solids,interface problems,stochastic problems,and statistically self-similar problems.Emphasis is given to the technical tools,such as the various constrained molecular dynamics,that have been developed,in order to apply HMM to these problems.Examples of mathematical results on the error analysis of HMM are presented.The review ends with a discussion on some of the problems that have to be solved in order to make HMM a more powerful tool. | Weinan E Bjorn Engquist Xiantao Li Weiqing Ren Eric Vanden-Eijnden | 2007 | Communications in Computational Physics2007，2，3： | 4 |
| 11 | Simulations of Compressible Two-Medium Flow by Runge-Kutta Discontinuous Galerkin Methods with the Ghost Fluid Method显示文摘The original ghost fluid method (GFM) developed in [13] and the modifiedGFM (MGFM) in [26] have provided a simple and yet flexible way to treat twomediumflow problems. The original GFM and MGFM make the material interface'invisible' during computations and the calculations are carried out as for a singlemedium such that its extension to multi-dimensions becomes fairly straightforward.The Runge-Kutta discontinuous Galerkin (RKDG) method for solving hyperbolic conservationlaws is a high order accurate finite element method employing the usefulfeatures from high resolution finite volume schemes, such as the exact or approximateRiemann solvers, TVD Runge-Kutta time discretizations, and limiters. In this paper,we investigate using RKDG finite element methods for two-medium flow simulationsin one and two dimensions in which the moving material interfaces is treated via nonconservativemethods based on the original GFM and MGFM. Numerical results forboth gas-gas and gas-water flows are provided to show the characteristic behaviors ofthese combinations. | Jianxian Qiu Tiegang Liu Boo Cheong Khoo | 2008 | Communications in Computational Physics2008，3，2： | 4 |
| 12 | A LB-DF/FD Method for Particle Suspensions显示文摘In this paper, we propose a lattice Boltzmann (LB) method coupled with adirect-forcing fictitious domain (DF/FD) method for the simulation of particle suspensions. This method combines the good features of the LB and the DF/FD methodsby using two unrelated meshes, namely, an Eulerian mesh for the flow domain and aLagrangian mesh for the solid domain, which avoids the re-meshing procedure anddoes not need to calculate the hydrodynamic forces at each time step. The non-slipboundary condition is enforced by introducing a forcing term into the lattice Boltzmann equation, which preserves all remarkable advantages of the LBM in simulatingfluid flows. The present LB-DF/FD method has been validated by comparing its results with analytical results and previous numerical results for a single circular particleand two circular particles settling under gravity. The interaction between particle andwall, the process of drafting-kissing-tumbling (DKT) of two settling particles will bedemonstrated. As a manifestation of the efficiency of the present method, the settlingof a large number (128) of circular particles is simulated in an enclosure. | Deming Nie Jianzhong Lin | 2010 | Communications in Computational Physics2010，7，3： | 3 |
| 13 | Flow in Collapsible Tubes with Discontinuous Mechanical Properties:Mathematical Model and Exact Solutions显示文摘We formulate a one-dimensional time-dependent non-linear mathematical model for some types of physiological fluid flow in collapsible tubes with discontinuous material properties.The resulting 6×6 hyperbolic system is analysed and the associated Riemann problem is solved exactly.Although the solution algorithm deals with idealised cases,it is nonetheless uniquely well-suited for assessing the performance of numerical methods intended for simulating more general situations.Moreover,our model may be a useful starting point for numerical calculations of realistic flows involving rapid and discontinuous material property variations.One important example in mind is the simulation of blood flow in medium-to-large veins in humans.Finally,we also discuss some peculiarities of the model regarding the loss of strict hyperbolicity and uniqueness.In particular we show an example in which the solution of the Riemann problem is non unique. | Eleuterio F.Toro Annunziato Siviglia | 2013 | Communications in Computational Physics2013，13，2： | 3 |
| 14 | A Positivity-Preserving Scheme for the Simulation of Streamer Discharges in Non-Attaching and Attaching Gases显示文摘Assumed having axial symmetry,the streamer discharge is often described by a fluid model in cylindrical coordinate system,which consists of convection dominated(diffusion)equations with source terms,coupled with a Poisson’s equation.Without additional care for a stricter CFL condition or special treatment to the negative source term,popular methods used in streamer discharge simulations,e.g.,FEMFCT,FVM,cannot ensure the positivity of the particle densities for the cases in attaching gases.By introducing the positivity-preserving limiter proposed by Zhang and Shu[15]and Strang operator splitting,this paper proposes a finite difference scheme with a provable positivity-preserving property in cylindrical coordinate system,for the numerical simulation of streamer discharges in non-attaching and attaching gases.Numerical examples in non-attaching gas(N_(2))and attaching gas(SF_(6))are given to illustrate the effectiveness of the scheme. | Chijie Zhuang Rong Zeng | 2014 | Communications in Computational Physics2014，15，1： | 3 |
| 15 | Aerodynamic Analysis of a Localized Flexible Airfoil at Low Reynolds Numbers显示文摘A localized flexible airfoil at low Reynolds numbers is modeled and the aerodynamic performance is analyzed numerically.With characteristic based split scheme,a fluid solver for two dimensional incompressible Navier-Stokes equations is developed under the ALE framework,coupled with the theory of shallow arch,which is approximated by Galerkin method.Further,the interactions between the unsteady flow and the shallow arch are studied in detail.In particular,the effect of the selfexcited vibration of the structure on aerodynamic performance of the airfoil is investigated deeply at various angles of attack.The results show that the lift-to-drag ratio has been increased greatly compared with the rigid airfoil.Finally,the relationship between the self-excited vibration and the evolution of the flow is analyzed using FFT tools. | Wei Kang Jia-Zhong Zhang Pei-Hua Feng | 2012 | Communications in Computational Physics2012，11，4： | 3 |
| 16 | A High Order Adaptive Time-Stepping Strategy and Local Discontinuous Galerkin Method for the Modified Phase Field Crystal Equation显示文摘In this paper,we will develop a first order and a second order convex splitting,and a first order linear energy stable fully discrete local discontinuous Galerkin(LDG)methods for the modified phase field crystal(MPFC)equation.In which,the first order linear scheme is based on the invariant energy quadratization approach.The MPFC equation is a damped wave equation,and to preserve an energy stability,it is necessary to introduce a pseudo energy,which all increase the difficulty of constructing numerical methods comparing with the phase field crystal(PFC)equation.Due to the severe time step restriction of explicit timemarchingmethods,we introduce the first order and second order semi-implicit schemes,which are proved to be unconditionally energy stable.In order to improve the temporal accuracy,the semi-implicit spectral deferred correction(SDC)method combining with the first order convex splitting scheme is employed.Numerical simulations of the MPFC equation always need long time to reach steady state,and then adaptive time-stepping method is necessary and of paramount importance.The schemes at the implicit time level are linear or nonlinear and we solve them by multigrid solver.Numerical experiments of the accuracy and long time simulations are presented demonstrating the capability and efficiency of the proposed methods,and the effectiveness of the adaptive time-stepping strategy. | Ruihan Guo Yan Xu | 2018 | Communications in Computational Physics2018，24，6： | 3 |
| 17 | Numerical Simulation of an Aortic Flow Based on a HLLC Type Incompressible Flow Solver显示文摘In this study,a three-dimensional artificial compressibility solver based on the average-state Harten-Lax-van Leer-Contact(HLLC)[13]type Riemann solution is first proposed and developed to solve the time-dependent incompressible flow equations.To implement unsteady flow calculations,a dual time stepping strategy including the LU decomposition method is used in the pseudo-time iteration and the second-order accurate backward difference is adopted to discretize the unsteady flow term.Also a third-order accurate HLLC numerical flux is derived for approximating the inviscid terms.To verify numerical accuracy,flows over a lid-driven cavity and an oscillating flat plate are chosen as the benchmark tests.In addition,the current solver is extended to solve blood flows in a realistic human aorta measured from MRI(Magnetic Resonance Imaging).The simulation geometry was derived from a three-dimensional reconstruction of a series of two-dimensional slices obtained in vivo.Numerical results demonstrate wall stresses were highly dynamic,but were generally high along the outer wall in the vicinity of the branches and low along the inner wall,particularly in the descending aorta.The maximum wall stress distribution is presented on the aortic arch in the systole.In addition,extensive counter-clockwise secondary flows and three-dimensional helical vortex influenced considerably by the presence of vessel contraction,torsion and the branches were shown in the descending aorta in the late systole and early diastolic cycles. | Yang-Yao Niu Chih-Hung Chang Wen-Yih I.Tseng Hsu-Hsia Peng Hsi-Yu Yu | 2009 | Communications in Computational Physics2009，5，1： | 3 |
| 18 | The Construction of Simulation Algorithms for Laser Fusion显示文摘In this work,we will present a system of numerical simulations for inertial confinement fusion,which consists of a series of one-dimensional,two-dimensional and three-dimensional codes.Our efforts have been made to develop 2D and 3D computer simulation codes,forming a 2D simulation capability so with the key physics issues in laser fusion can be separately simulated mainly by a LARED family containing six different 2D(and partially 3D)code series.The models and the characteristics of the main codes will be described,and some simulation results using the LARED family will be presented. | Wenbing Pei | 2007 | Communications in Computational Physics2007，2，2： | 3 |
| 19 | A Hybrid Numerical Method to Cure Numerical Shock Instability显示文摘In this note,we propose a new method to cure numerical shock instability by hybriding different numerical fluxes in the two-dimensional Euler equations.The idea of this method is to combine a”full-wave”Riemann solver and a”less-wave”Riemann solver,which uses a special modified weight based on the difference in velocity vectors.It is also found that such blending does not need to be implemented in all equations of the Euler system.We point out that the proposed method is easily extended to other”full-wave”fluxes that suffer from shock instability.Some benchmark problems are presented to validate the proposed method. | Hao Wu Longjun Shen Zhijun Shen | 2010 | Communications in Computational Physics2010，8，10： | 3 |
| 20 | Stochastic Multi-Symplectic Integrator for Stochastic Nonlinear Schrodinger Equation显示文摘In this paper we propose stochastic multi-symplectic conservation law for stochastic Hamiltonian partial differential equations,and develop a stochastic multisymplectic method for numerically solving a kind of stochastic nonlinear Schrodinger equations.It is shown that the stochasticmulti-symplecticmethod preserves themultisymplectic structure,the discrete charge conservation law,and deduces the recurrence relation of the discrete energy.Numerical experiments are performed to verify the good behaviors of the stochastic multi-symplectic method in cases of both solitary wave and collision. | Shanshan Jiang Lijin Wang Jialin Hong | 2013 | Communications in Computational Physics2013，14，7： | 3 |
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