Accuracy of the Adomian decomposition method applied to the Lorenz system

In this paper, the Adomian decomposition method (ADM) is applied to the famous Lorenz system. The ADM yields an analytical solution in terms of a rapidly convergent infinite power series with easily computable terms. Comparisons between the decomposition solutions and the fourth-order Runge–Kutta (RK4) numerical solutions are made for various time steps. In particular we look at the accuracy of the ADM as the Lorenz system changes from a non-chaotic system to a chaotic one.     

Space Mapping Approach for Particle Control in Turbulent Flows

Controlling the motion of particles in turbulent flows, the paper at hand presents an efficient space–mapping approach that is based on a hierarchy of models. The approach reduces the highly complex optimization of the k-ε turbulence model for high Reynolds–number flows (fine model) to the cheaper one of the Navier–Stokes equations for smaller Reynolds–number (laminar) flows in direct numerical simulations on coarser grids (coarse model) by help of a space–map function that maps the respective coarse model control onto the desired fine model control. The numerical results are very convincing in terms of accuracy and computational effort. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analytical approximate solution of the cooling problem by Adomian decomposition method

The Adomian decomposition method (ADM) can provide analytical approximation or approximated solution to a rather wide class of nonlinear (and stochastic) equations without linearization, perturbation, closure approximation, or discretization methods. In the present work, ADM is employed to solve the momentum and energy equations for laminar boundary layer flow over flat plate at zero incidences with neglecting the frictional heating. A trial and error strategy has been used to obtain the constant coefficient in the approximated solution. ADM provides an analytical solution in the form of an infinite power series. The effect of Adomian polynomial terms is considered and shows that the accuracy of results is increased with the increasing of Adomian polynomial terms. The velocity and thermal profiles on the boundary layer are calculated. Also the effect of the Prandtl number on the thermal boundary layer is obtained. Results show ADM can solve the nonlinear differential equations with negligible error compared to the exact solution.     

A series solution of nonlinear injection–extraction well equation

In this paper, the groundwater flow will be investigated. The tracer concentration is calculated for the saturated–unsaturated aquifer. A nonlinear diffusion equation is derived in a single injection–extraction well. A numerical procedure based on Adomian-decomposition method (ADM) is proposed for solving this nonlinear diffusion equation and finally this method is examined for some test problems.     

Further accuracy tests on Adomian decomposition method for chaotic systems

The Adomian decomposition method (ADM) is treated as an algorithm for approximating the solutions of the Lorenz and Chen systems in a sequence of time intervals, i.e. the classical ADM is converted into a hybrid analytical–numerical method. Comparisons with the seventh- and eighth-order Runge–Kutta method (RK78) reconfirm the very high accuracy of the hybrid analytical–numerical ADM.     

Approximate analytical solution for MHD stagnation-point flow in porous media

In this paper, the steady two-dimensional laminar forced MHD Hiemenz flow against a flat plate with variable wall temperature in a porous medium which was solved numerically using the implicit finite-difference of Keller-box method [Yih KA. The effect of uniform suction/blowing on heat transfer of magnetohydrodynamic Hiemenz flow through porous media. Acta Mech 1998;130:147–58] is revisited. A simple analytic approach of the Adomian decomposition method (ADM) is employed to obtain an approximate analytical solution of the problem. The skin friction coefficient and the rate of heat transfer given by the ADM are in good agreement with the numerical solutions of the Keller-box method.     

伴有磁场和纳米固体颗粒时的Jeffery-Hamel流动解析研究——Adomian分解法

用一种强有力的解析方法,称为Adomian分解法(ADM),来研究磁场和纳米颗粒对Jeffery-Hamel流动的影响.将该问题模型的控制方程,即将传统的流体力学Navier-Stokes方程和Maxwell电磁方程,简化为非线性的常微分方程.该方法得到的结果与Runge-Kutta方法得到的数值结果相一致,结果用表格列出.不同α,Ha和Re数下的图形表明,本方法可以得到高精度的结果.首先对不同的Hartmann数和管壁倾角,研究喇叭形管道中的流场;最后在没有磁场作用时,研究纳米固体颗粒体积率的影响.     

Numerical modeling of the pressure coefficient of the circular cylinder

The article examines the possibilities of numerical solution of chimney load from the effect of wind. The shear-stress transport (SST) k-ω turbulence model in ANSYS Fluent software is used to evaluate the task of the flow around the circumference of the rough cylinder. Calculations are performed on two different meshes that lead to the solution using wall function and near wall modeling. These two solution approaches in terms of defining wall roughness are presented in the paper by evaluating of the time dependence of the mean pressure coefficient distribution at the circumference, drag coefficient, and lift coefficient. The accuracy of the calculations is verified with parameters determined according to valid standards.     

Numerical predictions of three-dimensional flow in a ventilated room using turbulence models

A three-dimensional recirculation flow in a ventilated room was predicted by the numerical methods in which the turbulence models are applied. The predicted results are compared with the experimental results obtained in a model room in order to estimate the practical utilities of such methods from the viewpoint of engineering. Taking account of the practicability of prediction method which the engineers regard as important, two turbulence models were selected and they were incorporated into the numerical prediction methods respectively. One is the two-equation model, in which transport equations of turbulence energy and its rate of dissipation are adopted. The other is the Deardoff's model, in which the subgrid scale eddy coefficient is utilized. The prediction was made by each numerical method. Consequently, no noticeable difference is recognized between both predicted results. Each result is compared with the experimental results. Generally speaking, each agreement is good with regard to the mean velocity. Thus we can conclude that the numerical method using the two-equation model has more practical utility than that using Deardoff's model, because it can give the solutions in a shorter computer time.     

Existence of solutions to nonlinear advection-diffusion equation applied to Burgers’ equation using Sinc methods

This paper has two objectives. First, we prove the existence of solutions to the general advection-diffusion equation subject to a reasonably smooth initial condition. We investigate the behavior of the solution of these problems for large values of time. Secondly, a numerical scheme using the Sinc-Galerkin method is developed to approximate the solution of a simple model of turbulence, which is a special case of the advection-diffusion equation, known as Burgers’ equation. The approximate solution is shown to converge to the exact solution at an exponential rate. A numerical example is given to illustrate the accuracy of the method.     

Numerical investigation of the effect of helix angle and leaf margin on the flow pattern and the performance of the axial flow cyclone separator

A two-stage turbulence model based on the RNG κ–ε model combined with the Reynolds stress model is developed in this paper to analyze the gas flow in an axial flow cyclone separator. Five representative simulation cases are obtained by changing the helix angle and leaf margins of the cyclone. The pressure field and velocity field of the five cases are simulated, and then the effects of helix angle and leaf margins on the internal flow field of the cyclone are analyzed. When the continuum fluid (air) flow is relatively convergent, the discrete particle phase is added into the continuous phase and the gas-solid two-phase flow is simulated. One-way coupling method is used to solve the two-phase flow and a stochastic trajectory model is implemented for simulation of the particle phase. Finally, the pressure drop and separation efficiency of one case are measured and compare quantitatively well with the numerical results, which validates the reliability and accuracy of the simulation method based on the two-stage turbulence model.     

Second-order,loosely coupled methods for fluid-poroelastic material interaction

This work focuses on modeling the interaction between an incompressible, viscous fluid and a poroviscoelastic material. The fluid flow is described using the time-dependent Stokes equations, and the poroelastic material using the Biot model. The viscoelasticity is incorporated in the equations using a linear Kelvin–Voigt model. We introduce two novel, noniterative, partitioned numerical schemes for the coupled problem. The first method uses the second-order backward differentiation formula (BDF2) for implicit integration, while treating the interface terms explicitly using a second-order extrapolation formula. The second method is the Crank–Nicolson and Leap-Frog (CNLF) method, where the Crank–Nicolson method is used to implicitly advance the solution in time, while the coupling terms are explicitly approximated by the Leap-Frog integration. We show that the BDF2 method is unconditionally stable and uniformly stable in time, while the CNLF method is stable under a CFL condition. Both schemes are validated using numerical simulations. Second-order convergence in time is observed for both methods. Simulations over a longer period of time show that the errors in the solution remain bounded. Cases when the structure is poroviscoelastic and poroelastic are included in numerical examples.     

3D numerical simulation of ambient discharge of buoyant water

Waste heat and wastewater are frequently discharged into ambient water and become intermittent sources of buoyancy. In order to control and reduce the environmental impact of these discharges, the mixing characteristics of such discharge in ambient flow should be determined. In this work the transport, mixing and turbulence characteristics of intermittent discharge of buoyant fluid in ambient flow are simulated by a 3D numerical model incorporating a buoyancy extended k–ε model for turbulence. In the numerical model the governing equations are split into three parts in the finite difference solution: advection, dispersion and propagation. The advection part is solved by a characteristics-based scheme. The dispersion part is solved by the central difference method and the propagation part is solved implicitly by using the Gauss–Seidel iteration method. The model has been applied to cases of instantaneous and continuous discharges of buoyancy in ambient water with or without current. Dimensional analysis is used to estimate the initial values. The estimated range of values are found not sensitive to the solution. Satisfactorily comparison between computed results and the experimental results is achieved for the trajectories and lateral widths of the buoyant discharge. The engineering applicability of the model is thus ascertained.     

Comparison of turbulence models in simulating swirling pipe flows

Swirling flow is a common phenomenon in engineering applications. A numerical study of the swirling flow inside a straight pipe was carried out in the present work with the aid of the commercial CFD code fluent. Two-dimensional simulations were performed, and two turbulence models were used, namely, the RNG k–ε model and the Reynolds stress model. Results at various swirl numbers were obtained and compared with available experimental data to determine if the numerical method is valid when modeling swirling flows. It has been shown that the RNG k–ε model is in better agreement with experimental velocity profiles for low swirl, while the Reynolds stress model becomes more appropriate as the swirl is increased. However, both turbulence models predict an unrealistic decay of the turbulence quantities for the flows considered here, indicating the inadequacy of such models in simulating developing pipe flows with swirl.     

A high accuracy minimally invasive regularization technique for navier–stokes equations at high reynolds number

A method is presented, that combines the defect and deferred correction approaches to approximate solutions of Navier–Stokes equations at high Reynolds number. The method is of high accuracy in both space and time, and it allows for the usage of legacy codes a frequent requirement in the simulation of turbulent flows in complex geometries. The two‐step method is considered here; to obtain a regularization that is second order accurate in space and time, the method computes a low‐order accurate, stable, and computationally inexpensive approximation (Backward Euler with artificial viscosity) twice. The results are readily extendable to the higher order accuracy cases by adding more correction steps. Both the theoretical results and the numerical tests provided demonstrate that the computed solution is stable and the accuracy in both space and time is improved after the correction step. We also perform a qualitative test to demonstrate that the method is capable of capturing qualitative features of a turbulent flow, even on a very coarse mesh. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 814–839, 2017     

An assessment of turbulence models applied to the simulation of a two-dimensional submerged jet

This paper is concerned with the investigation of the performance of different turbulence models in the numerical prediction of transient flow caused by a confined submerged jet. Several widely used models, i.e., the standard k–ε, RNG k–ε, low Reynolds number k–ε models and the differential Reynolds stress model, as included in CFD codes, were compared with each other for a two-dimensional, incompressible, turbulent jet flow and with reported experimental data. A flapping oscillation was predicted regardless of the model used. A chosen Strouhal (St) number definition brought the fundamental frequencies from both the experiments and computations into close proximity. However, different turbulence models have exhibited quite different behaviours in terms of the frequency and regularity of the oscillation and in terms of the scale and duration of the vortices generated. All versions of the k–ε model yielded regular oscillations, which agree with experimental observations. On the other hand, the Reynolds stress (RS) model produced a complex pattern but a slower dissipation of vortices. In addition, some aspects of gridding and inflow representation are also discussed.     

Nonstandard methods for the convective transport equation with nonlinear reactions

A new nonstandard Lagrangian method is constructed for the one-dimensional, transient convective transport equation with nonlinear reaction terms. An “exact” time-stepping scheme is developed with zero local truncation error with respect to time. The scheme is based on nonlocal treatment of nonlinear reactions, and when applied at each spatial grid point gives the new fully discrete numerical method. This approach leads to solutions free from the numerical instabilities that arise because of incorrect modeling of derivatives and nonlinear reaction terms. Algorithms are developed that preserve the properties of the numerical solution in the case of variable velocity fields by using nonuniform spatial grids. Effects of different interpolation techniques are examined and numerical results are presented to demonstrate the performance of the proposed new method. © 1998 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 14: 467–485, 1998     

Convergence acceleration by varying time‐step size using Bi‐CGSTAB method for turbulent flow computation

A design of varying step size approach both in time span and spatial coordinate systems to achieve fast convergence is demonstrated in this study. This method is based on the concept of minimization of residuals by the Bi‐CGSTAB algorithm, so that the convergence can be enforced by varying the time‐step size. The numerical results show that the time‐step size determined by the proposed method improves the convergence rate for turbulent computations using advanced turbulence models in low Reynolds‐number form, and the degree of improvement increases with the degree of the complexity of the turbulence models. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 454–474, 2001.     

Numerical solution of turbulent flow in a turbine cascade

The work deals with numerical modeling of subsonic and transonic flow through the SE1050 turbine cascade. AUSM and AUSMPW+ splitting is used for inviscid fluxes. The turbulence is modelled usind SST and EARSM turbulence model. The time integration method is backward Euler (implicit). Interaction of shock wave with turbulence models is observed. The results are compared with measurements. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)