Papers by Keyword: Finite Difference

Abstract: This study addresses a numerical investigation of the bond behaviour exhibited by an FRCM system when subject to tensile and single direct shear tests. A reinforcement system, based on a polyparaphenylene benzobisoxazole (PBO) bi-directional fibre mesh and a mixed cement-pozzolanic mortar is selected. The system is characterized by the presence of coated glass-fibre yarns and dry polypropylene yarns alternated to the PBO yarns in the warp and weft directions, respectively. The mechanical characterization of composite constituent materials is carried out together with tensile and direct shear tests. Concerning mechanical interpretation of the tests, within a mode II fracture mechanics, and assuming a trilinear cohesive material law (CML), the stress transfer law between the fibre and the matrix is back calibrated from single direct shear test results. The CML obtained is employed into a finite-difference model developed for the purpose. Tensile tests are modelled providing adequate boundary conditions. Results satisfactorily agree with the tested behaviour of the FRCM system.

Abstract: In the present study, a numerical investigate the transport mechanism of laminar mixed convection in a vented enclosure. The walls of the cavity were kept adiabatic except the right vertical wall which was equipped with three fins dissipating the heat at a constant temperature. The equations of considered phenomenon were established and discretized by the finite difference method. The sweeping method line-by-line and the Thomas Algorithm (TDMA) were used for the resolution of the system of discretized equations. The results obtained showed that both the variations of the Prandtl and Richardson number have important effects on the flow structure and on the heat transfer.

Abstract: The problem of natural convection fluid flow and heat transfer of TiO₂-water nanofluid inside of two differentially-heated square ducts is analysed numerically by finite difference method. The outer duct is maintained at a constant temperature T_c, while the inner duct is kept at higher constant temperature T_h. The effect of the Rayleigh number, Ra and the nanoparticle volume fraction, φ on the heat transfer and Nusselt number, Nu are investigated and compared to previous study.

Abstract: The present study addresses the difficulties in heating thermoplastic sheets for ther-moforming applications. In industrial environments, the sheets are heated in a contact free method by means of convective hot air ovens and infrared radiation. In this study the temperature evolution at the outer surface as well as the core of thermoplastic sheets as a function of time is measured by means of thermocouples. These measurements reveal significant through thickness temperature dif-ferences which need to be resolved before high quality products can be made. The temperature dif-ferences can be decreased by decreasing the radiative power. This is however not acceptable in in-dustry since it lowers the number of produced parts per unit of time.In order to gain insight in the time-temperature relationship during the heating phase, a finite differ-ence model is developed. The model clearly shows the constantly changing through thickness tem-perature distribution and can be used as a tool by the thermoforming industry to optimize the pro-duction process.

Abstract: Recently the demand of sloshing analysis is rising for building FLNG (Floating Liquefied Natural Gas) vessel. This study considers the experimental and numerical observations on strongly nonlinear sloshing flows in ship motion. The FLNG (Floating Liquefied Natural Gas) vessel was considered to be rigid body supported by non-permanent pole with distributed spring damper. Based on the general equation of the ship motion in waves, and various wave amplitude, various heading, wave period and critical fluid level on the cargo tank period governing equation induced by sloshing were derived. Several physical issues are introduced in the analysis of sloshing flows, and the corresponding numerical models are described. To study the sloshing effects on ship motion, a ship motion program based on impulsive response function (IRF) is coupled with the developed numerical models for sloshing analysis. The results show that the nonlinearity of sloshing-induced forces and moments plays a critical role in the coupling effects.

Abstract: Two finite difference methods are presented and discussed, that are applied to the phase change process (freezing) occurring in plane and cylindrical geometries. The first one involves the use of a variable space step grid for each of the time steps of the procedure. An original technique based on Lagrange polynomials is used to determine the actual nodal temperature corresponding to the old temperature field. The second technique uses a fixed grid attached to the phase change material, and the finite difference equations of the nodes neighboring the solid-liquid interface are derived in a special form that involves fractions of the space step. Both techniques are applied to a plane and a cylindrical metallic wall respectively that represents the boundary of the phase change material domain. The numerical results obtained by running the computer codes that we have written for the two techniques show an excellent agreement, the values of the interface rate and of the solid phase fraction at every time step being practically the same.

Abstract: This paper uses the Hassan Carboniferous fractured reservoirs as the goal, firstly it analyses the reservoir characteristics of the cracks. On this basis, it uses two-dimensional random fractured media modeling method to build three different fracture models with different fracture parameters (fracture density, dip and speed). Then it uses finite difference wave equation forward and pre-stack depth migration processing of these models, and analyses seismic attribute of the migrated data, finally it finds a variety of seismic attributes sensitive to cracks, lays the foundation for fracture prediction with the seismic multi-attributes.

Abstract: Long-term analysis of timber-concrete composite (TCC) structures is a challenging task owing to the time-dependent behaviour of timber, concrete and connections which are highly nonlinear under variable environmental conditions (i.e. temperature, humidity). In this paper an efficient numerical method that takes advantage of a finite element-finite difference (FE-FD) scheme is presented. The differential equations governing the long-term behaviour of TCC section under variable humidity are solved using the FD scheme and the differential equations governing the mechanical behaviour of the composite beam are solved by a FE formulation recast in the framework of force-interpolation concept. The comparison between experimental data and numerical results shows the sufficient accuracy of the proposed FE-FD model for capturing long-term behaviour of TCC members.

Abstract: An investigation of the drying of spherical food particles was performed, using peas as the model material. In the development of a mathematical model for drying curves, moisture diffusion was modelled using Fick’s second law for mass transfer. The resulting partial differential equation was solved using a forward-time central-space finite difference approximation, with the assumption of variable effective diffusivity. In order to test the model, experimental data was collected for the drying of green peas in a fluidised bed at three drying temperatures. Through fitting three equation types for effective diffusivity to the data, it was found that a linear equation form, in which diffusivity increased with decreasing moisture content, was most appropriate. The final model accurately described the drying curves of the three experimental temperatures, with an R² value greater than 98.6% for all temperatures.

Abstract: Cloud computing, networking and other high-end computer data processing technology are the important contents of eleven-five development planning in China. They have developed rapidly in recent years in the field of engineering. In this paper, we combine parallel computing with the collaborative simulation principle, design a cloud computing platform, establish the mathematical model of cloud data processing and parallel computing algorithm, and verify the applicability of algorithm through the numerical simulation. Through numerical calculation, cloud computing platform can be divided into complex grids, and the transmission speed is fast, which is eight times than the finite difference method. The mesh is meticulous, which reaches millions. Convergence error is minimum, only 0.001. The calculation accuracy is up to 98.36%.