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Article
Publication date: 1 January 1996

Matthew Montgomery and Sanford Fleeter

The first compressible flow solution based solely on the locallyanalytical method is developed. This is accomplished by developing the flowmodel and locally analytical solution

Abstract

The first compressible flow solution based solely on the locally analytical method is developed. This is accomplished by developing the flow model and locally analytical solution for inviscid subsonic compressible flow. The stream function for irrotational, compressible flow without body forces was chosen as the governing differential equation. To demonstrate the modelling and locally analytical solution, this analysis is then applied to predict the flow in convergent nozzles, both planar and axially symmetric, for different back pressures. Results are presented which demonstrate the effectiveness of this technique.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 6 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 17 October 2019

J.I. Ramos

The purpose of this paper is to develop a new transversal method of lines for one-dimensional reactiondiffusion equations that is conservative and provides piecewise–analytical

Abstract

Purpose

The purpose of this paper is to develop a new transversal method of lines for one-dimensional reactiondiffusion equations that is conservative and provides piecewise–analytical solutions in space, analyze its truncation errors and linear stability, compare it with other finite-difference discretizations and assess the effects of the nonlinear diffusion coefficients, reaction rate terms and initial conditions on wave propagation and merging.

Design/methodology/approach

A conservative, transversal method of lines based on the discretization of time and piecewise analytical integration of the resulting two-point boundary-value problems subject to the continuity of the dependent variables and their fluxes at the control-volume boundaries, is presented. The method provides three-point finite difference expressions for the nodal values and continuous solutions in space, and its accuracy has been determined first analytically and then assessed in numerical experiments of reaction-diffusion problems, which exhibit interior and/or boundary layers.

Findings

The transversal method of lines presented here results in three-point finite difference equations for the nodal values, treats the diffusion terms implicitly and is unconditionally stable if the reaction terms are treated implicitly. The method is very accurate for problems with the interior and/or boundary layers. For a system of two nonlinearly-coupled, one-dimensional reactiondiffusion equations, the formation, propagation and merging of reactive fronts have been found to be strong function of the diffusion coefficients and reaction rates. For asymmetric ignition, it has been found that, after front merging, the temperature and concentration profiles are almost independent of the ignition conditions.

Originality/value

A new, conservative, transversal method of lines that treats the diffusion terms implicitly and provides piecewise exponential solutions in space without the need for interpolation is presented and applied to someone.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 29 no. 11
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 June 2000

A. Savini

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community…

1128

Abstract

Gives introductory remarks about chapter 1 of this group of 31 papers, from ISEF 1999 Proceedings, in the methodologies for field analysis, in the electromagnetic community. Observes that computer package implementation theory contributes to clarification. Discusses the areas covered by some of the papers ‐ such as artificial intelligence using fuzzy logic. Includes applications such as permanent magnets and looks at eddy current problems. States the finite element method is currently the most popular method used for field computation. Closes by pointing out the amalgam of topics.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 19 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 1 December 1997

J.I. Ramos and C.M. García‐López

Refers to Montgomery and Fleeter (1996) who employed the finite‐analytic method of Chen et al. (1980) to study steady, two‐dimensional, inviscid, compressible, subsonic flow in a…

170

Abstract

Refers to Montgomery and Fleeter (1996) who employed the finite‐analytic method of Chen et al. (1980) to study steady, two‐dimensional, inviscid, compressible, subsonic flow in a nozzle. Shows that, contrary to the statement made by Montgomery and Fleeter, their boundary conditions at the computational cell’s boundaries are not constructed from the particular solution to their equation (10). Deduces from a simple non‐linear second‐order ordinary differential equation that the finite or locally analytic method of Chen et al. (1980) only yields continuous but not differentiable solutions. Suggests a finite‐analytic method which provides continuous and differentiable solutions.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 7 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 7 August 2019

Muzaffer Metin, Arif Ulu, Ozgur Demir and Aytac Arikoglu

In this study, a railway superstructure is modeled with a new approach called locally continuous supporting, and its behavior under the effect of moving load is analyzed by using…

Abstract

Purpose

In this study, a railway superstructure is modeled with a new approach called locally continuous supporting, and its behavior under the effect of moving load is analyzed by using analytical and numerical techniques. The purpose of the study is to demonstrate the success of the new modeling technique.

Design/methodology/approach

In the railway superstructure, the support zones are not modeled with discrete spring-damping elements. Instead of this, it is considered to be a continuous viscoelastic structure in the local areas. To model this approach, the governing partial differential equations are derived by Hamilton’s principle and spatially discretized by the Galerkin’s method, and the time integration of the resulting ordinary differential equation system is carried out by the Newmark–Beta method.

Findings

Both the proposed model and the solution technique are verified against conventional one-dimensional and three-dimensional finite element models for a specific case, and a very good agreement between the results is observed. The effects of geometric, structural, and loading parameters such as rail-pad length, rail-pad stiffness, rail-pad damping ratio, the gap between rail pads and vehicle speed on the dynamic response of railway superstructure are investigated in detail.

Originality/value

There are mainly two approaches to the modeling of rail pads. The first approach considers them as a single spring-damper connected in parallel located at the centroid of the rail pad. The second one divides the rail pad into several parts, with each of part represented by an equivalent spring-damper system. To obtain realistic results with minimum CPU time for the dynamic response of railway superstructure, the rail pads are modeled as continuous linearly viscoelastic local supports. The mechanical model of viscoelastic material is considered as a spring and damper connected in parallel.

Article
Publication date: 8 March 2011

Jianhua Dai, Helder Pinheiro, Jonathan P. Webb and Igor Tsukerman

The purpose of this paper is to extend the generalized finite‐difference calculus of flexible local approximation methods (FLAME) to problems where local analytical solutions are…

Abstract

Purpose

The purpose of this paper is to extend the generalized finite‐difference calculus of flexible local approximation methods (FLAME) to problems where local analytical solutions are unavailable.

Design/methodology/approach

FLAME uses accurate local approximations of the solution to generate difference schemes with small consistency errors. When local analytical approximations are too complicated, semi‐analytical or numerical ones can be used instead. In the paper, this strategy is applied to electrostatic multi‐particle simulations and to electromagnetic wave propagation and scattering. The FLAME basis is constructed by solving small local finite‐element problems or, alternatively, by a local multipole‐multicenter expansion. As yet another alternative, adaptive FLAME is applied to problems of wave propagation in electromagnetic (photonic) crystals.

Findings

Numerical examples demonstrate the high rate of convergence of new five‐ and nine‐point schemes in 2D and seven‐ and 19‐point schemes in 3D. The accuracy of FLAME is much higher than that of the standard FD scheme. This paves the way for solving problems with a large number of particles on relatively coarse grids. FLAME with numerical bases has particular advantages for the multi‐particle model of a random or quasi‐random medium.

Research limitations/implications

Irregular stencils produced by local refinement may adversely affect the accuracy. This drawback could be rectified by least squares FLAME, where the number of stencil nodes can be much greater than the number of basis functions, making the method more robust and less sensitive to the irregularities of the stencils.

Originality/value

Previous applications of FLAME were limited to purely analytical basis functions. The present paper shows that numerical bases can be successfully used in FLAME when analytical ones are not available.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 30 no. 2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 7 August 2009

Karen L. Ricciardi and Stephen H. Brill

The Hermite collocation method of discretization can be used to determine highly accurate solutions to the steady‐state one‐dimensional convection‐diffusion equation (which can be…

Abstract

Purpose

The Hermite collocation method of discretization can be used to determine highly accurate solutions to the steady‐state one‐dimensional convection‐diffusion equation (which can be used to model the transport of contaminants dissolved in groundwater). This accuracy is dependent upon sufficient refinement of the finite‐element mesh as well as applying upstream or downstream weighting to the convective term through the determination of collocation locations which meet specified constraints. Owing to an increase in computational intensity of the application of the method of collocation associated with increases in the mesh refinement, minimal mesh refinement is sought. Very often this optimization problem is the one where the feasible region is not connected and as such requires a specialized optimization search technique. This paper aims to focus on this method.

Design/methodology/approach

An original hybrid method that utilizes a specialized adaptive genetic algorithm followed by a hill‐climbing approach is used to search for the optimal mesh refinement for a number of models differentiated by their velocity fields. The adaptive genetic algorithm is used to determine a mesh refinement that is close to a locally optimal mesh refinement. Following the adaptive genetic algorithm, a hill‐climbing approach is used to determine a local optimal feasible mesh refinement.

Findings

In all cases the optimal mesh refinements determined with this hybrid method are equally optimal to, or a significant improvement over, mesh refinements determined through direct search methods.

Research limitations

Further extensions of this work could include the application of the mesh refinement technique presented in this paper to non‐steady‐state problems with time‐dependent coefficients with multi‐dimensional velocity fields.

Originality/value

The present work applies an original hybrid optimization technique to obtain highly accurate solutions using the method of Hermite collocation with minimal mesh refinement.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 19 no. 7
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 June 2023

José Luis Díaz Palencia

The objective of this study is to model the propagating front in the interaction of gases in an aircraft fuel tank. To this end, we introduce a nonlinear parabolic operator, for…

Abstract

Purpose

The objective of this study is to model the propagating front in the interaction of gases in an aircraft fuel tank. To this end, we introduce a nonlinear parabolic operator, for which solutions are shown to be regular.

Design/methodology/approach

The authors provide an analytical expression for the propagating front, that shifts any combination of oxygen and nitrogen, in the tank airspace, into a safe condition to avoid potential explosions. The analytical exercise is validated with a real flight.

Findings

According to the flight test data, the safe condition, of maximum 7% of oxygen, is given for a time t = 45.2 min since the beginning of the flight, while according to our analysis, such a safe level is obtained for t = 41.42 min. For other safe levels of oxygen, the error between the analytical assessment and the flight data was observed to be below 10%.

Originality/value

The interaction of gases in a fuel tank has been little explored in the literature. Our value consists of introducing a set of nonlinear partial differential equations to increase the accuracy in modeling the interaction of gasses, which has been typically done via algebraic equations.

Details

Multidiscipline Modeling in Materials and Structures, vol. 19 no. 5
Type: Research Article
ISSN: 1573-6105

Keywords

Article
Publication date: 1 January 2014

Antoine Alexandre Journeaux, Nicolas Nemitz and Olivier Moreau

– This article presents a locally conservative projection method which aims to preserve the integral of a function and one operator among grad, div, or curl.

Abstract

Purpose

This article presents a locally conservative projection method which aims to preserve the integral of a function and one operator among grad, div, or curl.

Design/methodology/approach

After a theoretical description of the projection methods, the locally conservative projection is analytically tested and compared with the orthogonal method. In the second part, the implementation of the methods is described, and improvements are proposed. An industrial application of the present work, consisting in a magneto-thermal coupled problem, is then presented.

Findings

The implementation of the conservative method is simpler than the implementation of the orthogonal method while presenting similar behaviour in terms of accuracy and conservation.

Originality/value

The locally conservative method is extended to curl-conform and div-conform elements. Furthermore, three-dimensional studies are proposed.

Details

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering, vol. 33 no. 1/2
Type: Research Article
ISSN: 0332-1649

Keywords

Article
Publication date: 15 March 2013

Xiaoning Shi, Jifeng Guo, Naigang Cui and Rong Huang

The purpose of this paper is to design a solar sail heliocentric transfer orbit which can meet the requirements of control system and capture orbit, and to provide the change of…

Abstract

Purpose

The purpose of this paper is to design a solar sail heliocentric transfer orbit which can meet the requirements of control system and capture orbit, and to provide the change of angles for attitude control system.

Design/methodology/approach

Aiming at the problem of solar sail heliocentric transfer orbits design, this paper addresses the derivation of analytical optimal control law. The control laws can realize the combination of the control of each orbit element, but they can only give local optimal solution to meet the practical needs of mission. In order to solve this problem and meet the capture orbit and the attitude control system requirements, the modified genetic algorithm based on the analytical control law is introduced.

Findings

The algorithm addressed by this paper includes results closer to the global optimization, and also can meet the engineering constraints.

Practical implications

The analytical optimal control law can be applied to the future onboard sail control systems. The blending optimal algorithm is demonstrated to be suitable as a method of preliminary design for solar sail deep space exploration mission.

Originality/value

A blending optimal algorithm combining the analytical control law and genetic algorithm is proposed; the algorithm can search for global optimization based on the local optimal results of analytical control law.

Details

Aircraft Engineering and Aerospace Technology, vol. 85 no. 2
Type: Research Article
ISSN: 0002-2667

Keywords

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