Efficient Finite Element Scheme Research Articles

UNSTEADY MIXED CONVECTION HYDRO-MAGNETIC CASSON THERMO-DIFFUSION FLOW OF REACTING AND DISSIPATING FLUID WITH AN INCLINED MAGNETIC FIELD ALONG AN OSCILLATING SLANTED POROUS PLATE

A finite element numerical simulation is undertaken to explore the aspects of angled magnetic field and thermo-diffusion on an unsteady reacting mixed convection flow of hydro-magnetic Casson dissipating fluid with thermal radiation. The fluid streams across an oscillating tilted plate ingrained in a porous medium including time-altering temperature and concentration. The dimensionless flow, guiding partial differential equations along their associated initial and boundary conditions, are handled, enforcing an efficient finite element scheme. The key parameters affecting the velocity, temperature, and concentration profiles are comprehensively interpreted through graphical representations while the skin friction, heat transfer, and mass transfer rates are outlined via tables. The ultimate results of this study posted that the plate inclination angle, Casson parameter, and applied magnetic strengths are compelled to impede the fluid velocity and local skin friction, whereas the porosity parameter displays a reverse effect. The thermo-diffusion effect amplifies the fluid velocity and species concentration. It also supports that the Eckert number and heat source boost up the velocity and temperature profiles. Moreover, increasing radiation parameter and time crusade results in an upsurge in the Nusselt number. The chemical reaction quickens the Sherwood number, but it decays with the thermo-diffusion parameter. A comparative analysis between the current findings and existing research works in the literature demonstrates the results' precision and exactitude.

A mixed finite element discretisation of linear and nonlinear multivariate splines using the Laplacian penalty based on biorthogonal systems

We consider a mixed finite element method for a linear multivariate spline using the Laplacian penalty. Our discretisation is based on biorthogonal systems leading to a very simple and efficient finite element scheme. We also extend our approach to a nonlinear case and describe a split Bregman iteration scheme for the resulting nonlinear equations. We apply our numerical schemes to remove the mixture of Gaussian and impulsive noise for some test images.•This paper presents a method of discretising a multivariate spline using a finite element method.•The method uses a biorthogonal system to achieve an efficient finite element method.•The method is extended to cover a discretisation scheme for a nonlinear case, including an adaptation of the split Bregman method for the nonlinear case.

Finite element scheme for MHD forced convection flow near stagnation point and heat transfer by Newtonian heating, constant wall temperature and constant heat flux

Two dimensional, steady, forced convection magnetohydrodynamic flow of an incompressible, viscous electrically conducting fluid in a forward stagnation region of an infinite solid surface with Newtonian heating, constant wall temperature and constant heat flux has been investigated. Governing partial differential equations for the exploration have been formulated and converted to nonlinear ordinary differential equations by inserting convenient variables. An efficient finite element scheme along to Gauss elimination method has been introduced to find the numerical solutions of the resultant equations. Variation in velocity and temperature distributions against the pertinent parameters like magnetic parameter, Prandtl number and Eckert number have been displayed graphically while skin-friction coefficient and Nusselt number have been discussed quantitatively. A comparison of the computational results has been found in excellent agreement with open literature for limiting cases.

A B-spline finite element method for nonlinear differential equations describing crystal surface growth with variable coefficient

In this paper, an efficient finite element scheme is presented for a class of fourth-order nonlinear parabolic problems with variable coefficient. To deal with second-order term in weak formulation, we choose the cubic B-spline function as a trial function. Rigorous error estimates are derived for both semi-discrete and fully-discrete schemes. We provide a numerical example to confirm our theoretical results.

Segmentation of Three-Dimensional Images with Parametric Active Surfaces and Topology Changes

In this paper, we introduce a novel parametric finite element method for segmentation of three-dimensional images. We consider a piecewise constant version of the Mumford–Shah and the Chan–Vese functionals and perform a region-based segmentation of 3D image data. An evolution law is derived from energy minimization problems which push the surfaces to the boundaries of 3D objects in the image. We propose a parametric scheme which describes the evolution of parametric surfaces. An efficient finite element scheme is proposed for a numerical approximation of the evolution equations. Since standard parametric methods cannot handle topology changes automatically, an efficient method is presented to detect, identify and perform changes in the topology of the surfaces. One main focus of this paper are the algorithmic details to handle topology changes like splitting and merging of surfaces and change of the genus of a surface. Different artificial images are studied to demonstrate the ability to detect the different types of topology changes. Finally, the parametric method is applied to segmentation of medical 3D images.

Numerical simulation of nanocrystal synthesis in a microfluidic reactor

Modeling of continuous and controlled nanocrystal synthesis in a microfluidic reactor is presented. The population balance model that describes the nanocrystal synthesis consists of a population balance equation and a set of species concentration equations. In order to incorporate the effects of both reaction and diffusion limited growth conditions, a kinetic model with size-dependent growth and nucleation rate expressions are considered. An efficient finite element scheme based on Strang splitting that handles size-dependent particle diffusion and non-uniform growth expressions in the high dimensional population balance equation is proposed to solve the model equations. After the validation of the numerical scheme, an array of parametric studies is performed to study the effects of the flow condition and the growth environment on the nanocrystal synthesis in the microfluidic reactor. The computational results are consistent with the experimental observations. (C) 2016 Elsevier Ltd. All rights reserved.

Efficient solution of the non-linear Reynolds equation for compressible fluid using the finite element method

An efficient finite element scheme for solving the non-linear Reynolds equation for compressible fluid coupled to compliant structures is presented. The method is general and fast and can be used in the analysis of airfoil bearings with simplified or complex foil structure models. To illustrate the computational performance, it is applied to the analysis of a compliant foil bearing modelled using the simple elastic foundation model. The model is derived and perturbed using complex notation. Top foil sagging effect is added to the bump foil compliance in terms of a close-form periodic function. For a foil bearing utilized in an industrial turbo compressor, the influence of boundary conditions and sagging on the pressure profile, shaft equilibrium position and dynamic coefficients is numerically simulated. The proposed scheme is faster, leading to the conclusion that it is suitable, not only for steady-state analysis, but also for non-linear time domain analysis of rotors supported by airfoil bearings.

Numerical modelling of thermomechanical solids with highly conductive energetic interfaces

SUMMARYInterfaces within a solid can play a significant role in the overall response of a body. The influence of an interface increases as the scale of the problem decreases. Furthermore, the thermomechanical properties of the interface can differ significantly from those of the surrounding bulk. Such effects are described here using interface elasticity theory. The objective of this contribution is to detail the computational aspects of modelling thermomechanical solids with highly conductive energetic interfaces. The interface is termed energetic in the sense that it possesses its own energy, entropy, constitutive relations and dissipation. The equations governing the fully nonlinear, transient problem are given. They are then solved using an efficient finite element scheme. Full details of the consistent linearisation of the nonlinear governing equations are provided. Key features of highly conductive energetic interfaces are then elucidated via a series of three‐dimensional numerical examples. In particular and in contrast to highly conductive thermal interfaces, it is clearly shown that a jump in the heat flux across the interface is possible even in the absence of a heat flux along the interface. Copyright © 2012 John Wiley & Sons, Ltd.

Numerical modelling of thermomechanical solids with mechanically energetic (generalised) Kapitza interfaces

Interfaces within a solid can play a significant role in the overall response of the body. The influence of the interface increases as the scale of the problem decreases. Furthermore, the properties of the interface can differ significantly from those of the surrounding bulk. Such effects are described here using interface elasticity theory. The objective of this presentation is to detail the computational aspects of modelling thermomechanical solids with mechanically energetic interfaces. The interface is termed energetic in the sense that it possesses its own energy, entropy, constitutive relations, and dissipation. A mechanically energetic interface does not possess a thermal structure, and thus lacks its own heat capacity, heat conduction and heat expansion coefficient. For a mechanically energetic interface within a thermomechanical solid, the jump of the normal heat flux across the interface is zero while a temperature jump is allowed. In this sense, a mechanically energetic interface can be understood as a generalised Kapitza interface. Therefore the concept of Kapitza thermal resistance is used to control the temperature jump across the interface. The equations governing the fully-nonlinear, transient problem are given. They are then solved using an efficient finite element scheme. Key features of mechanically energetic interfaces are elucidated via a series of three-dimensional numerical examples.

Computer-aided design of clinical magnetic resonance imaging scanners by coupled magnetomechanical-acoustic modeling

This paper reports on an efficient finite-element scheme for computer-aided design of a clinical magnetic resonance imaging (MRI) scanner. The modeling scheme allows the full three-dimensional calculation of the electromagnetic, mechanical, and acoustic fields, including their mutual couplings. The validity of the computer simulations has been verified by appropriate measurements. Applications include the optimization of the gradient coil and the superconducting magnet with respect to eddy-current losses in the cryostat and the emitted noise.

An efficient finite element scheme for viscoelasticity with moving boundaries

An efficient finite element scheme is devised for problems in linear viscoelasticity of solids with a moving boundary. Such problems arise, for example, in the burning process of solid fuel (propellant). Since viscoelastic constitutive behavior is inherently associated with a “memory,” the potential need to store and operate on the entire history of the numerical solution has been a source of concern in computational viscoelasticity. A well-known “memory trick” overcomes this difficulty in the fixed-boundary case. Here the “memory trick” is extended to problems involving moving boundaries. The computational aspects of this extended scheme are discussed, and its performance is demonstrated via a numerical example. In addition, a special numerical integration rule is proposed for the viscoelastic integral, which is more accurate than the commonly-used trapezoidal rule and does not require additional computational effort.

An efficient finite element scheme for solving the three-dimensional poroelasticity problem in acoustics

In this paper, the finite element method (FEM) is used to solve the three-dimensional poroelasticity problem in acoustics based on the isotropic Biot–Allard theory. A displacement finite element model is derived using the Lagrangian approach together with an analogy with solid elements. From this model, it is seen that the “damping” and “stiffness” matrices of the poroelastic media are complex and frequency dependent. This leads to cumbersome calculations for large finite element models and spectral analyses. To overcome this difficulty, an efficient algorithm is proposed. It is based on low-frequency approximations of the frequency-dependent dissipation mechanisms in poroelastic media. This efficient algorithm allows the poroelastic materials to be modeled with classical FEM codes. Also, the acoustic–poroelastic and the poroelastic–poroelastic coupling conditions are presented. The proposed model is compared to existing literature for both two-dimensional and three-dimensional problems. Excellent comparisons prove both the accuracy and effectiveness of the proposed model and its coupling with acoustic elements. Finally, to show the usefulness of the proposed model, the edge effect on the absorption coefficient of a multilayered poroelastic material is presented. Results show that both analytical models based on laterally infinite poroelastic layers, and standing wave tube measurements may be misleading at low frequencies.

Effective probe response calculation using impedance boundary condition in eddy current NDE problems with massive conducting regions present

A 3-D finite element scheme is described for calculating probe responses in eddy current nondestructive evaluation (NDE) problems if massive conducting regions with small penetration depth are in the vicinity of the host specimen. These problems are related to the eddy current inspection of the tube support plate or tube sheet zones in PWR steam generator tubing. Recently, an efficient finite element scheme has been introduced to calculate the probe responses outside these zones. As a sequel to that work, the authors extend the technique for the tube support plate and the tube sheet zones. They use impedance boundary conditions (IBC) on the surface of the massive conductors and evaluate the probe responses due to these components by performing an integral over these IBC surfaces, thereby ensuring the same accuracy as in the previous work for the flaw signals. Benchmark problems-models of tube support plate zones with defects-have been measured and analyzed. The calculated probe responses show good agreement with the experimental data.

Approximate Optimal Trajectories for Flexible-Link Manipulator Slewing Using Recursive Quadratic Programming

The method of recursive quadratic programming, coupled with a homotopy method, has been used to generate approximate minimum-time and minimum tracking-error tip trajectories for two-link flexible manipulator movements in the horizontal plane. The manipulator is modeled with an efficient finite-element scheme for a multi-link, multi-joint system with bending only in the horizontal-plane. Constraints on the trajectory include boundary conditions on link tip position, final joint velocities, accelerations and torque inputs to complete a rest-to-rest maneuver, straight-line tip tracking between boundary positions, and motor torque limits. Trajectory comparisons demonstrate the impact of torque input smoothness on structural mode excitation. Applied torques retain much of the qualitative character of rigid-body slewing motion with alterations for energy dissipation.

Nonlinear Modeling of Kinematic and Flexibility Effects in Manipulator Design

This paper presents a finite-element-based, nonlinear model to predict the dynamic response of spatial manipulators with flexible links. The methodology takes into account the complete nonlinear coupling effects between the nonlinear gross motion of the links and their deformations due to distributed elasticity. The end-effector performance is predicted for commanded joint motion profiles, when the above nonlinear coupling is taken into account. A simple and efficient finite-element scheme has been developed using a Newton–Euler formulation and Timoshenko Beam Theory. In addition to the spatial manipulators, a particularized methodology is developed for the analysis of planar manipulators. Case studies of both planar and spatial manipulators are presented. Nonlinear kinematic coupling effects are observed to contribute significantly to end-effector positioning errors in flexible manipulator configurations.

A large-scale three-dimensional finite element analysis of incompressible viscous fluid flow

An efficient finite element scheme for large-scale three-dimensional flow analysis is proposed. Focus of attention is placed on the time integration algorithm and some techniques for the reduction of the storage requirement, including the one-point quadrature technique and an iterative matrix solver. Application to large-scale three-dimensional problems is given to demonstrate the feasibility of the proposed scheme.