Implicit Finite-difference Algorithm Research Articles

Bifurcation Analysis and Numerical Study of Wave Solution for Initial-Boundary Value Problem of the KdV-BBM Equation

In this work, we study the bifurcation and the numerical analysis of the nonlinear Benjamin-Bona-Mahony-KdV equation. According to the bifurcation theory of a dynamic system, the various kinds of traveling wave profiles are obtained including the behavior of solitary and periodic waves. Additionally, a two-level linear implicit finite difference algorithm is implemented for investigating the Benjamin-Bona-Mahony-KdV model. The application of a priori estimation for the approximate solution also provides the convergence and stability analysis. It was demonstrated that the current approach is singularly solvable and that both time and space convergence are of second-order precision. To confirm the computational effectiveness, two numerical simulations are prepared. The findings show that the current technique performs admirably in terms of delivering second-order accuracy in both time and space with the maximum norm while outperforming prior schemes.

ANALISIS FREKUENSI DATA SEISMIK HASIL MIGRASI FINITE DIFFERENCE

Finite difference migration is one of the migration algorithms that uses the principle of downward continuation and upcoming waves which are solved numerically with finite difference. This migration in ProMAX software has various algorithms depending on the numerical solution used. From each finite difference migration algorithm this shows a significant difference in the frequency produced. Migration with the e xplicit f inite d ifference algorithm shows better frequency results than the Implicit Finite Difference algorithm.

Rotational impact on nanoscale particles Fe2O4, NiZnFe2O4, MnZnFe2O4 suspended in C2H6O2 confined between two stretchable disks: a computational study

This communication addresses the fluid and heat transfer flanked by two stretchable rotating disks influenced by the induced magnetic field. The fluid flows due to the rotation of the stretchable disks enclosing a nanofluid having nanoparticles of three distinct ferrite compounds. The mathematical formulation of the problem is performed in a cylindrical coordinate system. Similarity analysis is applied for the sake of simplification. The velocity, pressure, induced magnetic field, and temperature distributions accompanied by surface drag force and heat flux are computed numerically by employing implicit finite difference algorithm. Effects of important emerging parameters are addressed through graphs and tables. Some pivotal findings include that magnetic parameter and reciprocal magnetic Prandtl number contribute to increasing fluid pressure near the lower disk and the opposite trend is reported in the vicinity of the upper disk. The present investigation is a benchmark problem that has a promising future in geophysics, oil refinery, and the chemical processing industry.

Numerical modeling of the spray coating of spinning bodies

We derive the lubrication form of the fluid mechanical equations governing the motion of a thin liquid film on an arbitrarily curved, rotating, axisymmetric substrate. The resulting equations are discretized and then solved numerically using an efficient implicit finite difference algorithm. Non-Newtonian effects are included by incorporating an Ellis viscosity model. The primary application for this work is to model the spin coating of the interior of two-piece metal beverage cans, and we consider this problem in some depth. Specifically, we show how adjusting several parameters can eliminate one possible defect in the spin coating process: the tendency for droplets to detach from the substrate when the can is spun at high rotation rates.

Rancang Bangun Alat Pengukuran Suseptibilitas Dan Penampilan Karateristik Magnetik Batuan

Finite difference migration is one of the migration algorithms that uses the principle of downward continuation and upcoming waves which are solved numerically with finite difference. This migration in ProMAX software has various algorithms depending on the numerical solution used. From each finite difference migration algorithm this shows a significant difference in the frequency produced. Migration with the e xplicit f inite d ifference algorithm shows better frequency results than the Implicit Finite Difference algorithm.

3D Layer-Integrated Modelling of Morphodynamic Processes Near River Regulated Structures

Sedimentation and erosion can significantly affect the performance of river regulated reservoirs. In the vicinity of flow control structures, the interaction between the hydrodynamics and sediment transport often induces complex morphological processes. It is generally very challenging to accurately predict these morphological processes in real applications. Details are given of the refinement and application of a three-dimensional (3-D) layer integrated model to predict the morphological processes in a river regulated reservoir. The model employs an Alternating Direction Implicit finite difference algorithm to solve the mass, momentum and suspended sediment transport conservation equations, and an explicit finite difference scheme for the bed sediment mass conservation equation for calculating bed level changes. The model is verified against experimental data reported in the literature. It is then applied to a scaled physical model of a regulated reservoir, including the associated intakes and sluice gates, to predict the velocity distributions, sediment transport rates and bed level changes in the vicinity of the hydraulic structures. It is found that the velocity distribution near an intake is non-uniform, resulting in a reduction in the suspended sediment flux through the intake and the formation of a sedimentation zone inside the reservoir.

Variable-Permeability Well Test Model and Pressure Response of Non-Darcy Flow in Low-Permeability Reservoirs

Considering the variable-permeability effect of non-Darcy flow in low-permeability reservoirs, this work set up a two-dimensional model with boundaries. The implicit finite difference algorithm was employed to solve the well test model, and typical curves in log-log scale by considering the effects of variable-permeability and non-Darcy flow were obtained. The results show that, in reservoirs with impermeable boundary, the upturned part of the pressure derivative curve caused by boundary effect will be covered by that of non-Darcy effect, indicating boundary effect is postponed to appear. The more of the non-Darcy effects result in less obvious upturn of the typical curves. The upturn of typical curves and the effect of boundary are enhanced by increasing the numbers of impermeable boundaries or by decreasing the distance from the well to the boundary.

Group analysis and numerical computation of magneto-convective non-Newtonian nanofluid slip flow from a permeable stretching sheet

Two-dimensional magnetohydrodynamic bound- ary layer flow of non-Newtonian power-law nanofluids past a linearly stretching sheet with a linear hydrody- namic slip boundary condition is investigated numeri- cally. The non-Newtonian nanofluid model incorporates the effects of Brownian motion and thermophoresis. Similarity transformations and corresponding similarity equations of the transport equations are derived via a linear group of transformations. The transformed equa- tions are solved numerically using Runge-Kutta-Fehl- berg fourth-fifth order numerical method available in the Maple 14 software for the influence of power-law (rhe- ological) index, Lewis number, Prandtl number, thermo- phoresis parameter, Brownian motion parameter, magnetic field parameter and linear momentum slip parameter. Validation is achieved with an optimized Nakamura implicit finite difference algorithm (NANO- NAK). Representative results for the dimensionless axial velocity, temperature and concentration profiles have been presented graphically. The present results of skin friction factor and reduced heat transfer rate are also compared with the published results for several special cases of the model and found to be in close agreement. The study has applications in electromagnetic nano- materials processing.

A New Implicit Finite Difference Algorithm of Thermal Melt Flow in Filling Process Based on Projection Method

A New Implicit Finite Difference Algorithm of Thermal Melt Flow in Filling Process Based on Projection Method

Dual-code solution procedure for efficient computing equilibrium hypersonic axisymmetric transitional/turbulent flows

An appropriate combination of the thin-layer Navier–Stokes (TLNS) and parabolized Navier–Stokes (PNS) solvers is used to accurately and efficiently compute hypersonic transitional/turbulent flowfields of perfect gas and equilibrium air around blunt-body configurations. The TLNS equations are solved in the nose region to provide the initial data plane needed for the solution of the PNS equations. Then the PNS equations are employed to efficiently compute the flowfield for the afterbody region by using a space marching technique. Both the TLNS and the PNS equations are numerically solved by using the implicit non-iterative finite-difference algorithm of Beam and Warming. A shock fitting procedure is used in both the TLNS and PNS codes to obtain accurate solution in the vicinity of the shock. For turbulent flow simulations, both the Cebeci–Smith (CS) and the Baldwin–Lomax (BL) turbulence models are analyzed with the present technique for the case of long slender blunt bodies. The Baldwin–Lomax turbulence model, which does not need the determination of the edge of the boundary layer, is modified in the present work to include the effects of variable properties and damping factor to accurately calculate flowfield characteristics in turbulent regions. Detailed comparisons are made with other numerical and experimental results to assess the accuracy and efficiency of the present solution procedure for computing hypersonic transitional/turbulent flows over long slender blunt bodies. The results of these computations are found to be in good agreement with available data. The effects of real gas on the flowfield characteristics are also studied.

Dual-code solution procedure for efficient computing equilibrium hypersonic axisymmetric laminar flows

An appropriate combination of the thin-layer Navier–Stokes (TLNS) and parabolized Navier–Stokes (PNS) solvers is used to accurately and efficiently compute hypersonic flowfields of equilibrium air around blunt-body configurations. The TLNS equations are solved in the nose region to provide the initial data plane needed for the solution of the PNS equations. Then the PNS equations are employed to efficiently compute the flowfield for the afterbody region by using a space marching procedure. Both the TLNS and PNS equations are numerically solved by using the efficient implicit non-iterative finite-difference algorithm of Beam and Warming. A shock fitting technique is used in both the TLNS and PNS codes to obtain accurate solution in the vicinity of the shock. In the regions of the flowfield with upstream influences, the globally iterated PNS (IPNS) equations, which are computationally more efficient than the TLNS equations, can be used to improve the accuracy of the results. To validate the results of the developed TLNS code and study real gas effects on the flowfield, hypersonic laminar flow over a sphere at Mach number of 11.26 is computed. The computations are performed for hypersonic laminar flow over 5° long slender blunt cone at Mach number of 19.25 to demonstrate the accuracy and efficiency of using the present TLNS-PNS methodology. To show the capability and robustness of the present solution procedure, the comparisons are also made with the wall heat-transfer data on a 12.84 ° / 7 ° bicone at Mach number of 6.89 and freestream temperature of 1604 K. The results of these computations are found to be in good agreement with available numerical and experimental data. The results of the perfect gas for these cases are also presented and the effects of real gas on the flowfield characteristics are studied in both the TLNS and PNS solutions.

Formulation of the relativistic moment implicit particle-in-cell method

A new formulation is presented for the implicit moment method applied to the time-dependent relativistic Vlasov-Maxwell system. The new approach is based on a specific formulation of the implicit moment method that allows us to retain the same formalism that is valid in the classical case despite the formidable complication introduced by the nonlinear nature of the relativistic equations of motion. To demonstrate the validity of the new formulation, an implicit finite difference algorithm is developed to solve the Maxwell’s equations and equations of motion. A number of benchmark problems are run: two stream instability, ion acoustic wave damping, Weibel instability, and Poynting flux acceleration. The numerical results are all in agreement with analytical solutions.

Vibration of highly flexible free hanging pipe in calm water

The paper presents a numerical and experimental investigation on dynamic behaviors of a highly flexible free hanging pipe in calm water. In the numerical study, an implicit finite difference algorithm is employed for three-dimensional pipe equations. Fluid and geometric non-linearity and bending stiffness are considered and solved by Newton–Raphson iteration. In order to verify the numerical results and to see real physical phenomena, an experiment is carried out for a 6 m flexible free hanging pipe in a deep and long towing tank. In the experiment, the free hanging pipe is excited by top end oscillations and in-line displacements of the model are measured. The measured results are analyzed for the first vibration mode and found that the maximum response amplitude occurs at much smaller frequency than its natural frequency and the deviation is much larger than a usual damped vibration system. The large deviation is presumably due to high flexibility of the model where a structural wave speed is rather slow. The comparison between numerical and experimental results shows a good agreement for the upper mid part of the model but with some differences for the bottom part. The difference is due to the large interaction between in-line motion and vortex-induced transverse motion that is largest at the bottom part. In the case of slender marine structures with free end at bottom, the dynamic behavior of the bottom part is very important to safely operate the system but is difficult to analyze exactly in a numerical method due to large vortex shedding.

A numerical and experimental study on dynamics of a towed low tension cable

This paper presents a numerical and experimental investigation into the dynamic behaviour of a towed low tension cable applicable to a towed array sonar system for detecting submarines. In the numerical study, an implicit finite difference algorithm is employed for solving the three-dimensional cable equations. Bending stiffness is considered in order to cope with the low tension problem. Fluid and geometric non-linearities are solved by Newton-Raphson iteration. Block tri-diagonal matrix method is applied for the fast calculation of very large matrices. In order to verify the numerical results and to observe real physical phenomena, an experiment was carried out for a 6 m cable in a deep towing tank. In the experiment, the cable was towed in two different ways; one was towed at a constant speed and the other was towed at a constant speed with top end horizontal oscillations. Cable tension and shear forces were measured at the top end. Numerical results are compared with experimental data. Good agreements are only achieved by employing enhanced drag coefficients due to vortex induced vibrations. It is also found that in the numerical modelling, non-uniform element lengths are necessary to cope with the sharp variation of tension and shear forces near the top fixed end.

Zone partitioning computation technique during solidification simulation of sand casting process

According to the fact that the temperature distributions in the mould area around the casting vary faster than those in the outer area, a “transient surface area” concept was proposed and a zone partitioning technique for the computational area was developed to use different time steps in different calculation areas during the solidification simulation of sand casting process. As a prerequisite for the implementation of the concept, a fully implicit finite difference algorithm was developed according to the componentwise splitting finite difference method. Furthermore, an estimation method was proposed to determine the depth of the “transient surface area” of the mold in a sand casting process and was verified by temperature gradient analysis of the mold. Applications and verifications of zone partitioning computation technique show that the computational efficiency can be greatly improved without losing the accuracy of the simulation results.

Dispersion and asymmetry effects of ADI-FDTD

In this paper, a generalized derivation of the alternating direction implicit finite-difference time-domain algorithm based on operator splitting is proposed. The formulation follows the notation of the finite integration technique. A straightforward proof of stability is given and the numerical dispersion formula is presented and verified by numerical experiments. As an additional parasitic effect, the asymmetric behavior of the algorithm even for exactly symmetric setups is revealed. Both the dispersion error and the asymmetry error are discussed in terms of the applicability of ADI for low-frequency problems.

A Simplified Implicit Maxwell Solver

We apply the second-order formulation of Maxwell's equations proposed by Jiang et al. (1996, J. Comput. Phys. 125, 104) to the solution of the implicit formulation of the three-dimensional, time-dependent Vlasov–Maxwell's system. An implicit finite difference algorithm is developed to solve the Maxwell's equations in a bounded domain with physical boundary conditions comprising electrically conducting walls (perfect conductors) and constant magnetic flux walls. We formulate the boundary conditions for Maxwell's equations to satisfy Poisson's equation throughout the domain by solving it only on the boundary. This eliminates the need for a separate projection step. We compare numerical results with analytical solutions for electromagnetic waves in vacuo, and using the implicit particle-in-cell code CELESTE3D, we test the new solver on the geospace environment modeling magnetic reconnection challenge problem.

Three-dimensional nonlinear solitary waves in shallow water generated by an advancing disturbance

The nonlinear long waves generated by a disturbance moving at subcritical, critical and supercritical speed in unbounded shallow water are investigated. The problem is formulated by a new modified generalized Boussinesq equation and solved numerically by an implicit finite-difference algorithm. Three-dimensional upstream solitary waves with significant amplitude are generated with a periodicity by a pressure distribution or slender strut advancing on the free surface. The crestlines of these solitons are almost perfect parabolas with decreasing curvature with respect to time. Behind the disturbance, a complicated, divergent Kelvin-like wave pattern is formed. It is found that, unlike the wave breaking phenomena in a narrow channel at Fh [ges ] 1.2, the three- dimensional upstream solitons form several parabolic water humps and are blocked ahead of the disturbance at supercritical speed in an unbounded domain for large time.

Digital simulation of migrational voltammetry.: The effect of difference in diffusion coefficients of the reactant and the product of an electrode reaction

A simulation scheme, based on the fast implicit finite difference algorithm has been proposed for the modeling of steady-state voltammograms under conditions of mixed diffusion–migration transport in multi-ion systems. The scheme assumes the single-step reversible process taking place at a hemispherical electrode, and does not impose any limitations on the diffusion coefficients of the species present in the solution. Using this simulation tool the theoretical voltammograms for the charge neutralization-, charge decrease-, and charge increase systems were obtained for a broad range of diffusion coefficients of the reactant and the product, and for different concentrations of supporting electrolyte. For the charge decrease- and charge increase systems, the normalized limiting current plotted versus log( D R/ D P) gives a sigmoidal curve. The migrational component in the transport of the electroactive species varies significantly with log( D R/ D P), the largest variation being observed for log( D R/ D P) close to zero. A decrease in D P decreases the limiting current, while for a large D P the limiting current increases asymptotically to a limiting value. This value is identical to the limiting current observed in the analogous systems with a charge neutralization reaction, which shows that the charge of the product plays no role if the diffusion coefficient of the product approaches infinity. Approximate functions have been constructed to calculate the normalized limiting current (relative error <2%) and the shift of the normalized halfwave potential (error <2 mV) in the range of the D R/ D P ratio found in real experimental situations.

Gettering simulator: physical basis and algorithm

The basic physical principles and mechanisms ofgettering of metal impurities in silicon are well established.However, a predictive model of gettering that would enable oneto determine what fraction of contaminants will be gettered ina particular process and how the existing process should bemodified to optimize gettering is lacking. Predictive getteringof transition metals in silicon requires development of arobust algorithm to model diffusion and precipitation oftransition metals in silicon, and material parameters todescribe the kinetics of defect reactions and the stableequilibrium state of the formed complexes. This paperdescribes the algorithm of a gettering simulator, capable ofmodelling relaxation and segregation gettering of interstitially diffusingtransitionmetal impurities in silicon wafers. The basic physicalequations used to model gettering are differential equationsfor diffusion, precipitation and segregation. These equationsare solved using the implicit finite-difference algorithm,based on the underlying physics of the problem. The material parameters required as input for the getteringsimulator such as segregation coefficient, precipitation sitedensity and precipitation radius, which need to be obtainedexperimentally, are briefly discussed.