Stability and accuracy of central difference method for real-time dynamic substructure testing considering mass participation coefficient

For real-time dynamic substructure testing(RTDST),the influence of the inertia force of fluid specimens on the stability and accuracy of the integration algorithms has never been investigated.Therefore,this study proposes to investigate the stability and accuracy of the central difference method(CDM)for RTDST considering the specimen mass participation coefficient.First,the theory of the CDM for RTDST is presented.Next,the stability and accuracy of the CDM for RTDST considering the specimen mass participation coefficient are investigated.Finally,numerical simulations and experimental tests are conducted for verifying the effectiveness of the method.The study indicates that the stability of the algorithm is affected by the mass participation coefficient of the specimen,and the stability limit first increases and then decreases as the mass participation coefficient increases.In most cases,the mass participation coefficient will increase the stability limit of the algorithm,but in specific circumstances,the algorithm may lose its stability.The stability and accuracy of the CDM considering the mass participation coefficient are verified by numerical simulations and experimental tests on a three-story frame structure with a tuned liquid damper.

Finite Difference-Peridynamic Differential Operator for Solving Transient Heat Conduction Problems

Transient heat conduction problems widely exist in engineering.In previous work on the peridynamic differential operator(PDDO)method for solving such problems,both time and spatial derivatives were discretized using the PDDO method,resulting in increased complexity and programming difficulty.In this work,the forward difference formula,the backward difference formula,and the centered difference formula are used to discretize the time derivative,while the PDDO method is used to discretize the spatial derivative.Three new schemes for solving transient heat conduction equations have been developed,namely,the forward-in-time and PDDO in space(FT-PDDO)scheme,the backward-in-time and PDDO in space(BT-PDDO)scheme,and the central-in-time and PDDO in space(CT-PDDO)scheme.The stability and convergence of these schemes are analyzed using the Fourier method and Taylor’s theorem.Results show that the FT-PDDO scheme is conditionally stable,whereas the BT-PDDO and CT-PDDO schemes are unconditionally stable.The stability conditions for the FT-PDDO scheme are less stringent than those of the explicit finite element method and explicit finite difference method.The convergence rate in space for these three methods is two.These constructed schemes are applied to solve one-dimensional and two-dimensional transient heat conduction problems.The accuracy and validity of the schemes are verified by comparison with analytical solutions.

High-Order Bound-Preserving Finite Difference Methods for Multispecies and Multireaction Detonations

In this paper,we apply high-order finite difference(FD)schemes for multispecies and multireaction detonations(MMD).In MMD,the density and pressure are positive and the mass fraction of the ith species in the chemical reaction,say zi,is between 0 and 1,withΣz_(i)=1.Due to the lack of maximum-principle,most of the previous bound-preserving technique cannot be applied directly.To preserve those bounds,we will use the positivity-preserving technique to all the zi'is and enforceΣz_(i)=1 by constructing conservative schemes,thanks to conservative time integrations and consistent numerical fluxes in the system.Moreover,detonation is an extreme singular mode of flame propagation in premixed gas,and the model contains a significant stiff source.It is well known that for hyperbolic equations with stiff source,the transition points in the numerical approximations near the shocks may trigger spurious shock speed,leading to wrong shock position.Intuitively,the high-order weighted essentially non-oscillatory(WENO)scheme,which can suppress oscillations near the discontinuities,would be a good choice for spatial discretization.However,with the nonlinear weights,the numerical fluxes are no longer“consistent”,leading to nonconservative numerical schemes and the bound-preserving technique does not work.Numerical experiments demonstrate that,without further numerical techniques such as subcell resolutions,the conservative FD method with linear weights can yield better numerical approximations than the nonconservative WENO scheme.

Efficient Finite Difference/Spectral Method for the Time Fractional Ito Equation Using Fast Fourier Transform Technic

A finite difference/spectral scheme is proposed for the time fractional Ito equation.The mass conservation and stability of the numerical solution are deduced by the energy method in the L^(2)norm form.To reduce the computation costs,the fast Fourier transform technic is applied to a pair of equivalent coupled differential equations.The effectiveness of the proposed algorithm is verified by the first numerical example.The mass conservation property and stability statement are confirmed by two other numerical examples.

Numerical Study by Imposing the Finite Difference Method for Unsteady Casson Fluid Flow with Heat Flux

This article presents an investigation into the flow and heat transfer characteristics of an impermeable stretching sheet subjected to Magnetohydrodynamic Casson fluid. The study considers the influence of slip velocity, thermal radiation conditions, and heat flux. The investigation is conducted employing a robust numerical method that accounts for the impact of thermal radiation. This category of fluid is apt for characterizing the movement of blood within an industrial artery, where the flow can be regulated by a material designed to manage it. The resolution of the ensuing system of ordinary differential equations (ODEs), representing the described problem, is accomplished through the application of the finite difference method. The examination of flow and heat transfer characteristics, including aspects such as unsteadiness, radiation parameter, slip velocity, Casson parameter, and Prandtl number, is explored and visually presented through tables and graphs to illustrate their impact. On the stretching sheet, calculations, and descriptions of the local skin-friction coefficient and the local Nusselt number are conducted. In conclusion, the findings indicate that the proposed method serves as a straightforward and efficient tool for exploring the solutions of fluid models of this kind.

Physicochemical properties and biological activities of polysaccharides from the peel of Dioscorea opposita Thunb.extracted by four different methods

Polysaccharides are the important biologically active components found in the peel of Dioscorea opposita Thunb.(DTTP).The influences of 4 extraction methods,namely hot water extraction(W),acidic extraction(HA),hot-compressed water extraction(HCW)and enzyme-assisted extraction(EAE),on the yields,physicochemical properties,hypoglycemic and antioxidant activities of polysaccharides from DTTP were studied and compared.Among these DTTP polysaccharides,DTTP-HA was outstanding in several respects.DTTP-HA was the most water soluble;it had the highest total carbohydrate content(85.08%),the highest uronic acid(13.20%)and the highest thermal stability.DTTP-HA and DTTP-W possessed a triple-helix structure.These 4 kinds of polysaccharides have the same types of monosaccharides,but in different molar percentages.Extraction method had a significant impact on the microstructures of the extracted polysaccharides.DTT-HA exhibited irregular structure with many holes.Among the 4 extracted methods,the DTTP-HA and DTTP-W initially exhibited higher hypoglycemic and antioxidant activities.The better bioactivities of DTTP-HA may be related to the above factors.The findings indicated that acid extraction is an effective method to extract polysaccharides with high biological activities from DTTP.

COMPACT FINITE DIFFERENCE-FOURIER SPECTRAL METHOD FOR THREE-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

A new compact finite difference-Fourier spectral hybrid method for solving the three dimensional incompressible Navier-Stokes equations is developed in the present paper. The fifth-order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth-order center compact schemes for the derivatives in spectral space are described, respectively. The fourth-order compact schemes in a single nine-point cell for solving the Helmholtz equations satisfied by the velocities and pressure in spectral space is derived and its preconditioned conjugate gradient iteration method is studied. The treatment of pressure boundary conditions and the three dimensional non-reflecting outflow boundary conditions are presented. Application to the vortex dislocation evolution in a three dimensional wake is also reported.

An explicit finite element－finite difference method for analyzing the effect of visco－elastic local topography on the earthquake motion

An explicit finite element-finite difference method for analyzing the effects of two-dimensional visco-elastic localtopography on earthquake ground motion is prOPosed in this paper. In the method, at first, the finite elementdiscrete model is formed by using the artificial boundary and finite element method, and the dynamic equationsof local nodes in the discrete model are obtained according to the theory of the special finite element method similar to the finite difference method, and then the explicit step-by-step integration formulas are presented by usingthe explicit difference method for solving the visco-elastic dynamic equation and Generalized Multi-transmittingBoundary. The method has the advantages of saving computing time and computer memory space, and it is suitable for any case of topography and has high computing accuracy and good computing stability.

A method of solving the stiffness problem in Biot＇s poroelastic equations using a staggered high-order finite-difference

In modelling elastic wave propagation in a porous medium, when the ratio between the fluid viscosity and the medium permeability is comparatively large, the stiffness problem of Blot＇s poroelastic equations will be encountered. In the paper, a partition method is developed to solve the stiffness problem with a staggered high-order finite-difference. The method splits the Biot equations into two systems. One is stiff, and solved analytically, the other is nonstiff, and solved numerically by using a high-order staggered-grid finite-difference scheme. The time step is determined by the staggered finite-difference algorithm in solving the nonstiff equations, thus a coarse time step may be employed. Therefore, the computation efficiency and computational stability are improved greatly. Also a perfect by matched layer technology is used in the split method as absorbing boundary conditions. The numerical results are compared with the analytical results and those obtained from the conventional staggered-grid finite-difference method in a homogeneous model, respectively. They are in good agreement with each other. Finally, a slightly more complex model is investigated and compared with related equivalent model to illustrate the good performance of the staggered-grid finite-difference scheme in the partition method.

Numerical storm surge model with higher order finite difference method of lines for the coast of Bangladesh

In this study, the method of lines (MOLs) with higher order central difference approximation method coupled with the classical fourth order Runge-Kutta (RK(4,4)) method is used in solving shallow water equations (SWEs) in Cartesian coordinates to foresee water levels associated with a storm accurately along the coast of Bangladesh. In doing so, the partial derivatives of the SWEs with respect to the space variables were discretized with 5-point central difference, as a test case, to obtain a system of ordinary differential equations with time as an independent variable for every spatial grid point, which with initial conditions were solved by the RK(4,4) method. The complex land-sea interface and bottom topographic details were incorporated closely using nested schemes. The coastal and island boundaries were rectangularized through proper stair step representation, and the storing positions of the scalar and momentum variables were specified according to the rules of structured C-grid. A stable tidal regime was made over the model domain considering the effect of the major tidal constituent, M2 along the southern open boundary of the outermost parent scheme. The Meghna River fresh water discharge was taken into account for the inner most child scheme. To take into account the dynamic interaction of tide and surge, the generated tidal regime was introduced as the initial state of the sea, and the surge was then made to come over it through computer simulation. Numerical experiments were performed with the cyclone April 1991 to simulate water levels due to tide, surge, and their interaction at different stations along the coast of Bangladesh. Our computed results were found to compare reasonable well with the limited observed data obtained from Bangladesh Inland Water Transport Authority (BIWTA) and were found to be better in comparison with the results obtained through the regular finite difference method and the 3-point central difference MOLs coupled with the RK(4,4) method with regard to the root mean square error values.

Implicit finite difference method for fractional percolation equation with Dirichlet and fractional boundary conditions

An implicit finite difference method is developed for a one-dimensional frac- tional percolation equation （FPE） with the Dirichlet and fractional boundary conditions. The stability and convergence are discussed for two special cases, i.e., a continued seep- age flow with a monotone percolation coefficient and a seepage flow with the fractional Neumann boundary condition. The accuracy and efficiency of the method are checked with two numerical examples.

SUPERCONVERGENCE OF GENERALIZED DIFFERENCE METHOD FOR ELLIPTIC BOUNDARY VALUE PROBLEM

Some superconvergence results of generalized difference solution for elliptic boundary value problem are given. It is shown that optimal points of the stresses for generalized difference method are the same as that for finite element method.

Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations

A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.

A Computational Study with Finite Element Method and Finite Difference Method for 2D Elliptic Partial Differential Equations

In this paper, we consider two methods, the Second order Central Difference Method (SCDM) and the Finite Element Method (FEM) with P1 triangular elements, for solving two dimensional general linear Elliptic Partial Differential Equations (PDE) with mixed derivatives along with Dirichlet and Neumann boundary conditions. These two methods have almost the same accuracy from theoretical aspect with regular boundaries, but generally Finite Element Method produces better approximations when the boundaries are irregular. In order to investigate which method produces better results from numerical aspect, we apply these methods into specific examples with regular boundaries with constant step-size for both of them. The results which obtained confirm, in most of the cases, the theoretical results.

Scientific connotation of “treating different diseases with the same method” from the perspective of metabolic-immune dysregulation in inflammation-mediated carcinogenesis of digestive organs

Inflammation-mediated carcinogenesis develops in the context of chronic inflammation and is a significant cause of cancer within the digestive system.In the chronic inflammation microenvironment,the metabolic activity of tissue cells undergoes extensive changes,which interfere with the normal function of immune cells.Dysregulation of cell metabolism and immune function has been identified as a key factor contributing to inflammation-mediated carcinogenesis within the major digestive organs,such as the stomach,liver,and colorectum.This metabolic-immune imbalance also corresponds to traditional Chinese medicine(TCM)theories of“yin-yang disharmony”and“disharmony between Ying-nutrients and Wei-defense.”The metabolic-immune imbalance has also been regarded as the key factor supporting“treatment of different diseases with the same method”,in which the same approach is adopted in the treatment of different conditions.In the TCM treatment process,it is necessary to first identify TCM patterns and then apply the corresponding TCM to correct the dysregulated metabolic and immune function,thereby blocking the progression from inflammation to malignancy.Our study findings deepen the TCM understanding of metabolic-immune dysregulation and the relationship between metabolic-immune dysregulation,pattern identification,and treatment method.They also provide new insights for the treatment of inflammation-mediated carcinogenesis in major digestive organs and help us further explore the scientific connotation of the TCM strategy of“treating different diseases with the same method”.

A SIMPLE PROOF OF STABILITY AND CONVERGENCE IN L＿2 FOR SOME DIFFERENCE SCHEMES AND THEIR EXTRAPOLATION METHOD FOR PARABOLIC EQUATIONS

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A Comparative Study of the Difference Method and the Enzyme-Hydrolyzed Casein Method for Determining True Amino Acid Digestibilities and Endogenous Amino Acid Losses in Duck Feed

In this study, we examined the varia- tions between the difference method and the enzyme- hydrolyzed casein method for determining endogenous amino acid loss and the true amino acid digestibility in ducks fed normal protein-containing diets. These methods were compared to the nitrogen-free （N-free） diet method. The difference method was based on soy- bean meal as the only protein source, with the experi- mental diets containing crude protein levels at 15% and 20%. The enzyme-hydrolyzed casein method was based on enzyme-hydrolyzed casein meal as the pro- tein source, with the experimental diet containing a crude protein level of 17.5%. The N-free diet was prepared with starches and paper fibers. In each meth- od,64 Tianfu meat drakes （7-weeks-old） with an av- erage body weight of 2.77±0.16 kg were used and divided into four groups, and fed four different diets. Each group contained four replicates of four drakes and they were force fed trial diets according to the Sirbald method for detecting their apparent amino aciddigestibility, endogenous amino acid loss and true a- mino acid digestibility. The results demonstrated that using the difference, enzyme-hydrolyzed casein and N-free diet methods, endogenous amino acid losses were 0. 9946,1. 2243 and 0. 9297 mg/g dry matter in- take （ DMI）, respectively. The true amino acid digest- ibility measured by the difference method was 88.93 %±4.43 %. Using the enzyme-hydrolyzed ca- sein method with two dietary crude protein levels of 15% and 20%, the digestibility was 91.15%±4.33% and 91.97%±4. 16%, respectively, and by the N-free diet methods with two dietary crude protein levels of 15% and 20% ,it was 88.55%±4.29% and 88.82 %±4.61%, respectively. The results suggested that when the dietary protein level was 15% to 20 %, the true amino acid digestibility and endogenous ami- no acid loss as determined by the difference method was more accurate than the values determined by the enzyme-hydrolyzed casein method.

Computing Bifurcation Diagrams of Steady State Kuramoto Sivashinsky Equation by Difference Method

Utilizing difference formulae, we obtained the discrete systems of steady state Kuramoto Sivashinsky (K S) equation. Applied Newton's method and continuation technology to the systems, the bifurcated solutions are derived, and the bifurcation diagrams are constructed. All the results are successful and satisfactory.

Solution precision of concrete temperature fields with finite difference method

With the finite difference method to calculate the temperature distribution in mass concrete structures, the solution precision will increase with a smaller step size, at the cost of computational time. In view of the basic characteristics of the finite difference method, a simple yet powerful improvement is introduced. By multiplying the adiabatic temperature function with a correction factor, the precision of the solution can be assured without an increase in the computation time. In addition, the correction rules for three types of commonly used concrete hydration formulas are investigated.

A Finite Difference Method for Determining Interdiffusivity of Aluminide Coating Formed on Superalloy

A numerical method has been developed to extract the composition-dependent interdiffusivity from the concentration profiles in the aluminide coating prepared by pack cementation. The procedure is based on the classic finite difference method (FDM). In order to simplify the model, effect of some alloying elements on interdiffusivity can be negligible. Calculated results indicate the interdiffusivity in aluminide coating strongly depends on the composition and give the formulas used to calculate interdiffusivity at 850, 950 and 1050癈. The effect on interdiffusivity is briefly discussed.