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| 1 | High-Order Accurate Entropy Stable Finite Difference Schemes for One- and Two-Dimensional Special Relativistic Hydrodynamics显示文摘This paper develops the high-order accurate entropy stable finite difference schemes for one-and two-dimensional special relativistic hydrodynamic equations.The schemes are built on the entropy conservative flux and the weighted essentially non-oscillatory(WENO)technique as well as explicit Runge-Kutta time discretization.The key is to technically construct the affordable entropy conservative flux of the semi-discrete second-order accurate entropy conservative schemes satisfying the semi-discrete entropy equality for the found convex entropy pair.As soon as the entropy conservative flux is derived,the dissipation term can be added to give the semidiscrete entropy stable schemes satisfying the semi-discrete entropy inequality with the given convex entropy function.The WENO reconstruction for the scaled entropy variables and the high-order explicit Runge-Kutta time discretization are implemented to obtain the fully-discrete high-order entropy stable schemes.Several numerical tests are conducted to validate the accuracy and the ability to capture discontinuities of our entropy stable schemes. | Junming Duan Huazhong Tang | 2020 | Advances in Applied Mathematics and Mechanics2020，12，1： | 4 |
| 2 | Investigation of Turbulent Transition in Plane Couette Flows Using Energy Gradient Method显示文摘The energy gradient method has been proposed with the aim of better understanding the mechanism of flow transition from laminar flow to turbulent flow.In this method,it is demonstrated that the transition to turbulence depends on the relative magnitudes of the transverse gradient of the total mechanical energy which amplifies the disturbance and the energy loss from viscous friction which damps the disturbance,for given imposed disturbance.For a given flow geometry and fluid properties,when the maximum of the function K(a function standing for the ratio of the gradient of total mechanical energy in the transverse direction to the rate of energy loss due to viscous friction in the streamwise direction)in the flow field is larger than a certain critical value,it is expected that instability would occur for some initial disturbances.In this paper,using the energy gradient analysis,the equation for calculating the energy gradient function K for plane Couette flow is derived.The result indicates that K reaches the maximum at the moving walls.Thus,the fluid layer near the moving wall is the most dangerous position to generate initial oscillation at sufficient high Re for given same level of normalized perturbation in the domain.The critical value of K at turbulent transition,which is observed from experiments,is about 370 for plane Couette flow when two walls move in opposite directions(anti-symmetry).This value is about the same as that for plane Poiseuille flow and pipe Poiseuille flow(385-389).Therefore,it is concluded that the critical value of K at turbulent transition is about 370-389 for wall-bounded parallel shear flows which include both pressure(symmetrical case)and shear driven flows(anti-symmetrical case). | Hua-Shu Dou Boo Cheong Khoo | 2011 | Advances in Applied Mathematics and Mechanics2011，3，2： | 3 |
| 3 | An Error Analysis for the Finite Element Approximation to the Steady-State Poisson-Nernst-Planck Equations显示文摘Poisson-Nernst-Planck equations are a coupled system of nonlinear partial differential equations consisting of the Nernst-Planck equation and the electrostatic Poisson equation with delta distribution sources,which describe the electrodiffusion of ions in a solvated biomolecular system.In this paper,some error bounds for a piecewise finite element approximation to this problem are derived.Several numerical examples including biomolecular problems are shown to support our analysis. | Ying Yang Benzhuo Lu | 2013 | Advances in Applied Mathematics and Mechanics2013，5，1： | 3 |
| 4 | Multiscale Basis Functions for Singular Perturbation on Adaptively Graded Meshes显示文摘We apply the multiscale basis functions for the singularly perturbed reaction-diffusion problem on adaptively graded meshes,which can provide a good balance between the numerical accuracy and computational cost.The multiscale space is built through standard finite element basis functions enriched with multiscale basis functions.The multiscale basis functions have abilities to capture originally perturbed information in the local problem,as a result our method is capable of reducing the boundary layer errors remarkably on graded meshes,where the layer-adapted meshes are generated by a given parameter.Through numerical experiments we demonstrate that the multiscale method can acquire second order convergence in the L^(2)norm and first order convergence in the energy norm on graded meshes,which is independent ofε.In contrast with the conventional methods,our method is much more accurate and effective. | Mei-Ling Sun Shan Jiang | 2014 | Advances in Applied Mathematics and Mechanics2014，6，5： | 2 |
| 5 | On the Full C_(1)-Q_(k) Finite Element Spaces on Rectangles and Cuboids显示文摘We study the extensions of the Bogner-Fox-Schmit element to the whole family of Q_(k) continuously differentiable finite elements on rectangular grids,for all k≥3,in 2D and 3D.We show that the newly defined C_(1) spaces are maximal in the sense that they contain all C_(1)-Q_(k) functions of piecewise polynomials.We give examples of other extensions of C_(1)-Q_(k) elements.The result is consistent with the Strang’s conjecture(restricted to the quadrilateral grids in 2D and 3D).Some numerical results are provided on the family of C_(1) elements solving the biharmonic equation. | Shangyou Zhang | 2010 | Advances in Applied Mathematics and Mechanics2010，2，6： | 2 |
| 6 | The Modified Ghost Fluid Method Applied to Fluid-Elastic Structure Interaction显示文摘In this work,the modified ghost fluid method is developed to deal with 2D compressible fluid interacting with elastic solid in an Euler-Lagrange coupled system.In applying the modified Ghost Fluid Method to treat the fluid-elastic solid coupling,the Navier equations for elastic solid are cast into a system similar to the Euler equations but in Lagrangian coordinates.Furthermore,to take into account the influence of material deformation and nonlinear wave interaction at the interface,an Euler-Lagrange Riemann problem is constructed and solved approximately along the normal direction of the interface to predict the interfacial status and then define the ghost fluid and ghost solid states.Numerical tests are presented to verify the resultant method. | Tiegang Liu A.W.Chowdhury Boo Cheong Khoo | 2011 | Advances in Applied Mathematics and Mechanics2011，3，5： | 2 |
| 7 | Localized Method of Fundamental Solutions for Three-Dimensional Elasticity Problems: Theory显示文摘A localized version of the method of fundamental solution(LMFS)is devised in this paper for the numerical solutions of three-dimensional(3D)elasticity problems.The present method combines the advantages of high computational efficiency of localized discretization schemes and the pseudo-spectral convergence rate of the classical MFS formulation.Such a combination will be an important improvement to the classical MFS for complicated and large-scale engineering simulations.Numerical examples with up to 100,000 unknowns can be solved without any difficulty on a personal computer using the developed methodologies.The advantages,disadvantages and potential applications of the proposed method,as compared with the classical MFS and boundary element method(BEM),are discussed. | Yan Gu Chia-Ming Fan Zhuojia Fu | 2021 | Advances in Applied Mathematics and Mechanics2021，13，6： | 2 |
| 8 | Convergence Analysis of the Spectral Methods for Weakly Singular Volterra Integro-Differential Equations with Smooth Solutions显示文摘The theory of a class of spectral methods is extended to Volterra integrodifferential equations which contain a weakly singular kernel(t−s)^(−μ) with 0<μ<1.In this work,we consider the case when the underlying solutions of weakly singular Volterra integro-differential equations are sufficiently smooth.We provide a rigorous error analysis for the spectral methods,which shows that both the errors of approximate solutions and the errors of approximate derivatives of the solutions decay exponentially in L^(∞)-norm and weighted L^(2)-norm.The numerical examples are given to illustrate the theoretical results. | Yunxia Wei Yanping Chen | 2012 | Advances in Applied Mathematics and Mechanics2012，4，1： | 2 |
| 9 | Compact Finite Difference Scheme for the Fourth-Order Fractional Subdiffusion System显示文摘In this paper,we study a high-order compact difference scheme for the fourth-order fractional subdiffusion system.We consider the situation in which the unknown function and its first-order derivative are given at the boundary.The scheme is shown to have high order convergence.Numerical examples are given to verify the theoretical results. | Seakweng Vong Zhibo Wang | 2014 | Advances in Applied Mathematics and Mechanics2014，6，4： | 2 |
| 10 | Development of Lattice Boltzmann Flux Solver for Simulation of Incompressible Flows显示文摘A lattice Boltzmann flux solver(LBFS)is presented in this work for simulation of incompressible viscous and inviscid flows.The new solver is based on Chapman-Enskog expansion analysis,which is the bridge to link Navier-Stokes(N-S)equations and lattice Boltzmann equation(LBE).The macroscopic differential equations are discretized by the finite volume method,where the flux at the cell interface is evaluated by local reconstruction of lattice Boltzmann solution from macroscopic flow variables at cell centers.The new solver removes the drawbacks of conventional lattice Boltzmann method such as limitation to uniform mesh,tie-up of mesh spacing and time interval,limitation to viscous flows.LBFS is validated by its application to simulate the viscous decaying vortex flow,the driven cavity flow,the viscous flow past a circular cylinder,and the inviscid flow past a circular cylinder.The obtained numerical results compare very well with available data in the literature,which show that LBFS has the second order of accuracy in space,and can be well applied to viscous and inviscid flow problems with non-uniform mesh and curved boundary. | C.Shu Y.Wang C.J.Teo J.Wu | 2014 | Advances in Applied Mathematics and Mechanics2014，6，4： | 2 |
| 11 | Convergence Analysis for the Chebyshev Collocation Methods to Volterra Integral Equations with a Weakly Singular Kernel显示文摘In this paper,a Chebyshev-collocation spectral method is developed for Volterra integral equations(VIEs)of second kind with weakly singular kernel.We first change the equation into an equivalent VIE so that the solution of the new equation possesses better regularity.The integral term in the resulting VIE is approximated by Gauss quadrature formulas using the Chebyshev collocation points.The convergence analysis of this method is based on the Lebesgue constant for the Lagrange interpolation polynomials,approximation theory for orthogonal polynomials,and the operator theory.The spectral rate of convergence for the proposed method is established in the L^(∞)-norm and weighted L^(2)-norm.Numerical results are presented to demonstrate the effectiveness of the proposed method. | Xiong Liu Yanping Chen | 2017 | Advances in Applied Mathematics and Mechanics2017，9，6： | 2 |
| 12 | Block substitutions using orthomorphic mappings 显示文摘 | Mittenthal L | 1995 | Advances in Applied Mathematics1995，16，： | 2 |
| 13 | A Posteriori Error Estimates of the Galerkin Spectral Methods for Space-Time Fractional Diffusion Equations显示文摘In this paper,an initial boundary value problem of the space-time fractional diffusion equation is studied.Both temporal and spatial directions for this equation are discreted by the Galerkin spectral methods.And then based on the discretization scheme,reliable a posteriori error estimates for the spectral approximation are derived.Some numerical examples are presented to verify the validity and applicability of the derived a posteriori error estimator. | Huasheng Wang Yanping Chen Yunqing Huang Wenting Mao | 2020 | Advances in Applied Mathematics and Mechanics2020，12，1： | 2 |
| 14 | Development and Comparative Studies of Three Non-free Parameter Lattice Boltzmann Models for Simulation of Compressible Flows显示文摘This paper at first shows the details of finite volume-based lattice Boltzmann method(FV-LBM)for simulation of compressible flows with shock waves.In the FV-LBM,the normal convective flux at the interface of a cell is evaluated by using one-dimensional compressible lattice Boltzmann model,while the tangential flux is calculated using the same way as used in the conventional Euler solvers.The paper then presents a platform to construct one-dimensional compressible lattice Boltzmann model for its use in FV-LBM.The platform is formed from the conservation forms of moments.Under the platform,both the equilibrium distribution functions and lattice velocities can be determined,and therefore,non-free parameter model can be developed.The paper particularly presents three typical non-free parameter models,D1Q3,D1Q4 and D1Q5.The performances of these three models for simulation of compressible flows are investigated by a brief analysis and their application to solve some one-dimensional and two-dimensional test problems.Numerical results showed that D1Q3 model costs the least computation time and D1Q4 and D1Q5 models have the wider application range of Mach number.From the results,it seems that D1Q4 model could be the best choice for the FVLBM simulation of hypersonic flows. | L.M.Yang C.Shu J.Wu | 2012 | Advances in Applied Mathematics and Mechanics2012，4，4： | 2 |
| 15 | An Improved Formulation of Singular Boundary Method显示文摘This study proposes a new formulation of singular boundary method(SBM)to solve the 2D potential problems,while retaining its original merits being free of integration and mesh,easy-to-program,accurate and mathematically simple without the requirement of a fictitious boundary as in the method of fundamental solutions(MFS).The key idea of the SBM is to introduce the concept of the origin intensity factor to isolate the singularity of fundamental solution so that the source points can be placed directly on the physical boundary.This paper presents a new approach to derive the analytical solution of the origin intensity factor based on the proposed subtracting and adding-back techniques.And the troublesome sample nodes in the ordinary SBM are avoided and the sample solution is also not necessary for the Neumann boundary condition.Three benchmark problems are tested to demonstrate the feasibility and accuracy of the new formulation through detailed comparisons with the boundary element method(BEM),MFS,regularized meshless method(RMM)and boundary distributed source(BDS)method. | Wen Chen Yan Gu | 2012 | Advances in Applied Mathematics and Mechanics2012，4，5： | 2 |
| 16 | A Hybrid Lattice Boltzmann Flux Solver for Simulation of Viscous Compressible Flows显示文摘In this paper,a hybrid lattice Boltzmann flux solver(LBFS)is proposed for simulation of viscous compressible flows.In the solver,the finite volume method is applied to solve the Navier-Stokes equations.Different from conventional Navier-Stokes solvers,in this work,the inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model,while the viscous flux is still approximated by conventional smooth function approximation.The present work overcomes the two major drawbacks of existing LBFS[28–31],which is used for simulation of inviscid flows.The first one is its ability to simulate viscous flows by including evaluation of viscous flux.The second one is its ability to effectively capture both strong shock waves and thin boundary layers through introduction of a switch function for evaluation of inviscid flux,which takes a value close to zero in the boundary layer and one around the strong shock wave.Numerical experiments demonstrate that the present solver can accurately and effectively simulate hypersonic viscous flows. | L.M.Yang C.Shu J.Wu | 2016 | Advances in Applied Mathematics and Mechanics2016，8，6： | 2 |
| 17 | Derivatives of the matrix exponential and their computation 显示文摘 | NAJFELD I HAVEL T F | 1995 | Advances in Applied Mathematics1995，16，3： | 1 |
| 18 | Shapiro,Some open problem questions about random walks,involutions,limiting distributions,and generating functions显示文摘 | | 2001 | Advances in Applied Mathematics2001，27，： | 1 |
| 19 | The extended analog computer显示文摘 | RUBEL L A | 1993 | Advances in Applied Mathematics1993，14，1： | 1 |
| 20 | Femtocell architec- tures with spectrum sharing for cellular radio networks 显示文摘 | Brett K Jorma L Behnaam A | 2013 | International Journal of Advances in Engineering Sciences and Applied Mathematics2013，5，1： | 1 |
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