Channel flow of a Maxwell fluid with chemical reaction

This work is concerned with the two-dimensional boundary layer flow of an upper-convected Maxwell (UCM) fluid in a channel with chemical reaction. The walls of the channel are porous. Employing similarity transformations the governing non-linear partial differential equations are reduced into non-linear ordinary differential equations. The resulting ordinary differential equations are solved analytically using homotopy analysis method (HAM). Expressions for series solutions are derived. The convergence of the obtained series solutions are shown explicitly. The effects of Reynold’s number Re, Deborah number De, Schmidt number Sc and chemical reaction parameter γ on the velocity and the concentration fields are shown through graphs and discussed.     

Numerical simulation of three-dimensional incompressible fluid in a box flow passage considering fluid–structure interaction by differential quadrature method

A numerical simulation scheme of 3D incompressible viscous fluid in a box flow passage is developed to solve Navier–Stokes (N–S) equations by firstly taking fluid–structure interaction (FSI) into account. This numerical scheme with FSI is based on the polynomial differential quadrature (PDQ) approximation technique, in which motions of both the fluid and the solid boundary structures are well described. The flow passage investigated consists of four rectangular plates, of which two are rigid, while another two are elastic. In the simulation the elastic plates are allowed to vibrate subjected to excitation of the time-dependent dynamical pressure induced by the unsteady flow in the passage. Meanwhile, the vibrating plates change the flow pattern by producing many transient sources and sinks on the plates. The effects of FSI on the flow are evaluated by running numerical examples with the incoming flow’s Reynolds numbers of 3000, 7000 and 10,000, respectively. Numerical computations show that FSI has significant influence on both the velocity and pressure fields, and the DQ method developed here is effective for modelling 3D incompressible viscous fluid with FSI.     

Peristaltic flow of viscoelastic fluid with fractional Maxwell model through a channel

The paper presents the transportation of viscoelastic fluid with fractional Maxwell model by peristalsis through a channel under long wavelength and low Reynolds number approximations. The propagation of wall of channel is taken as sinusoidal wave propagation (contraction and relaxation). Homotopy perturbation method (HPM) and Adomian decomposition method (ADM) are used to obtain the analytical approximate solutions of the problem. The expressions of axial velocity, volume flow rate and pressure gradient are obtained. The effects of fractional parameters (α), relaxation time (λ₁) and amplitude (?) on the pressure difference and friction force across one wavelength are calculated numerically for different particular cases and depicted through graphs.     

Unsteady flow of a Maxwell fluid over a stretching surface in presence of chemical reaction

An analysis is presented for unsteady two-dimensional flow of a Maxwell fluid over a stretching surface in presence of a first order constructive/destructive chemical reaction. Using suitable transformations, the governing partial differential equations are converted to ordinary one and are then solved numerically by shooting method. The flow fields and mass transfer are significantly influenced by the governing parameters. Fluid velocity initially decreases with increasing unsteadiness parameter and concentration decreases significantly due to unsteadiness. The effect of increasing values of the Maxwell parameter is to suppress the velocity field. But the concentration is enhanced with increasing Maxwell parameter.     

Effect of wall properties on the magnetohydrodynamic peristaltic flow of a Maxwell fluid with heat transfer and porous medium

The elastic effect of the flexible walls is analyzed on the peristaltic motion of Maxwell fluid in a channel with heat transfer. An incompressible and magnetohydrodynamic (MHD) fluid fills the porous space. The series solution of the modeled problem is derived by considering small wave number. The influence of pertinent parameters is shown and discussed with the help of graphs. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

MHD Falkner-Skan flow of Maxwell fluid by rational Chebyshev collocation method

The magnetohydrodynamics (MHD) Falkner-Skan flow of the Maxwell fluid is studied. Suitable transform reduces the partial differential equation into a nonlinear three order boundary value problem over a...     

Multiscale analysis and numerical algorithm for the Schrödinger equations in heterogeneous media

In solid state physics, the most widely used techniques to calculate the electronic levels in nanostructures are the effective masses approximation (EMA) and its extension the multiband k · p method (see [9]). They have been particularly successful in the case of heterostructures (see, e.g. [4], [9] and [11]). This paper discusses the multiscale analysis of the Schrödinger equation with rapidly oscillating coefficients. The new contributions obtained in this paper are the determination of the convergence rate for the approximate solutions, the definition of boundary layer solutions, and higher-order correctors. Consequently, a multiscale finite element method and some numerical results are presented. As one of the main results of this paper, we give a reasonable interpretation why the effective mass approximation is very accurate for calculating the band structures in semiconductor in the vicinity of Γ point, from the viewpoint of mathematics.     

Error estimation of prediction-correction legendre spectral approximation to incompressible fluid flow

1. IntroductionThere have been a lot of literatures concerning the existence, uniqueness, regularityof the solution of Navier-Stokes equation. Usually the primitive equation is considered,e.g.5 see 11,2]. Maily methods are used for its numerical simulation, e.g., see [2--7]. But wemeet several difficulties in calculation. For instance, if we use the finite difference method,then we have to evaluate the pressure at each time step. Some authors developed theartificial compressibility method or…     

Decay of potential vortex for a viscoelastic fluid with fractional Maxwell model

This paper is concerned with the exact analytic solutions for the velocity field and the associated tangential stress corresponding to a potential vortex for a fractional Maxwell fluid. The fractional calculus approach is taken into account in the constitutive relationship of a non-Newtonian fluid model. Exact analytic solutions are obtained by using the Hankel transform and the discrete Laplace transform of sequential fractional derivatives. The solutions for a Maxwell fluid appear as the limiting cases of our general solutions by setting α=1$\alpha =1$. The influence of fractional coefficient on the decay of vortex velocity is also analyzed by graphical illustrations.     

Linear and nonlinear stability analysis of binary viscoelastic fluid convection

The linear and weakly nonlinear stability analysis of the quiescent state in a viscoelastic fluid subject to vertical solute concentration and temperature gradients is investigated. The non-Newtonian behavior of the viscoelastic fluid is characterized using the Oldroyd model. Analytical expressions for the critical Rayleigh numbers and corresponding wave numbers for the onset of stationary or oscillatory convection subject to cross diffusion effects is determined. A stability diagram clearly demarcates non-overlapping regions of finger and diffusive instabilities. A Lorenz system is obtained in the case of the weakly nonlinear stability analysis. The effect of Dufour and Soret parameters on the heat and mass transports are determined and discussed. Due to consideration of dilute concentrations of the second diffusing component the route to chaos in binary viscoelastic fluid systems is similar to that of single-component (thermal) viscoelastic fluid systems.     

Analysis of a particle method for the one‐dimensional Vlasov‐Maxwell system

In this article we present a particle method for solving numerically the one‐dimensional Vlasov‐Maxwell equations. This method is based on the formulation by characteristics. We perform the error analysis and we investigate the properties of this scheme. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Cluster identification and characterization in the riser of a circulating fluidized bed from numerical simulation results

A methodology of identification and characterization of coherent structures mostly known as clusters is applied to hydrodynamic results of numerical simulation generated for the riser of a circulating fluidized bed. The numerical simulation is performed using the MICEFLOW code, which includes the two-fluids IIT’s hydrodynamic model B. The methodology for cluster characterization that is used is based in the determination of four characteristics, related to average life time, average volumetric fraction of solid, existing time fraction and frequency of occurrence. The identification of clusters is performed by applying a criterion related to the time average value of the volumetric solid fraction. A qualitative rather than quantitative analysis is performed mainly owing to the unavailability of operational data used in the considered experiments. Concerning qualitative analysis, the simulation results are in good agreement with literature. Some quantitative comparisons between predictions and experiment were also presented to emphasize the capability of the modeling procedure regarding the analysis of macroscopic scale coherent structures.     

Numerical stability analysis of the Taylor-Couette flow in the two-dimensional case

The stability of the laminar flow between two rotating cylinders (Taylor-Couette flow) is numerically studied. The simulation is based on the equations of motion of an inviscid fluid (Euler equations). The influence exerted on the flow stability by physical parameters of the problem (such as the gap width between the cylinders, the initial perturbation, and the velocity difference between the cylinders) is analyzed. It is shown that the onset of turbulence is accompanied by the formation of large vortices. The results are analyzed and compared with those of similar studies.     

Temporal decays and asymptotic behaviors for a Vlasov equation with a flocking term coupled to incompressible fluid flow

We are concerned with large-time behaviors of solutions for Vlasov–Navier–Stokes equations in two dimensions and Vlasov–Stokes system in three dimensions including the effect of velocity alignment/misalignment. We first revisit the large-time behavior estimate for our main system and refine assumptions on the dimensions and a communication weight function. In particular, this allows us to take into account the effect of the misalignment interactions between particles. We then use a sharp heat kernel estimate to obtain the exponential time decay of fluid velocity to its average in $L^{\infty }$-norm. For the kinetic part, by employing a certain type of Sobolev norm weighted by modulations of averaged particle velocity, we prove the exponential time decay of the particle distribution, provided that local particle distribution function is uniformly bounded. Moreover, we show that the support of particle distribution function in velocity shrinks to a point, which is the mean of averaged initial particle and fluid velocities, exponentially fast as time goes to infinity. This also provides that for any $p\in [1,\infty ]$, the $p$-Wasserstein distance between the particle distribution function and the tensor product of the local particle distributions and Dirac measure at that point in velocity converges exponentially fast to zero as time goes to infinity.     

On large Eddy simulation and variational multiscale methods in the numerical simulation of turbulent incompressible flows

Numerical simulation of turbulent flows is one of the great challenges in Computational Fluid Dynamics (CFD). In general, Direct Numerical Simulation (DNS) is not feasible due to limited computer resources (performance and memory), and the use of a turbulence model becomes necessary. The paper will discuss several aspects of two approaches of turbulent modeling—Large Eddy Simulation (LES) and Variational Multiscale (VMS) models. Topics which will be addressed are the detailed derivation of these models, the analysis of commutation errors in LES models as well as other results from mathematical analysis.     

Non-linear analysis of the consolidation of an elastic saturated soil with incompressible fluid and variable permeability by FEM

Research interest in the mechanical behaviour of soils is growing as a result of an increasing number of geomechanical problems involving consolidation effects. The main aim of this paper is to validate and to solve a model for consolidation of an elastic saturated soil with incompressible fluid and variable permeability. Firstly, we prove the existence and uniqueness of the solution of the variational problem corresponding to an initial and boundary value problem (IBVP): a special case of the Biot’s ‘consolidation of clay’ model (where the applied forces depend on time). Secondly, we prove the convergence of the method using a technique based on the proof of solution’s existence. Finally, we then solved this constitutive model by the finite element method (FEM) employing repeated fixed point techniques in order to obtain the results for displacement and pore water pressure. The pore fluid is considered incompressible. The results of the numerical experiments are compared with analytical solutions and, in cases where such solutions do not exist, with experimental data. Therefore, the model can be used for quantitative predictions of consolidation behaviour of soils with permeability dependent on the settlement.     

A low-Mach number method for the numerical simulation of complex flows

A new numerical procedure which considers a modification to the artificial acoustic stiffness correction method (AASCM) is here presented, to perform simulations of low Mach number flows with the compressible Navier–Stokes equations. An extra term is added to the energy fluxes instead of using an energy source correction term as in the original model. This new scheme re-scales the speed of sound to values similar to the flow velocity, enabling the use of larger time steps and leading to a more stable numerical method. The new method is validated performing Large Eddy Simulations on test problems. The effect of a crucial numerical parameter alpha is evaluated as well as the robustness of the method to variations of the Mach number. Numerical results are compared to the existing experimental data showing that the new method achieves good agreement increasing the time-step, and therefore accelerating the computation for low-Mach convective flows.