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Article

Soucheng OuYang and Yi Lin

While still arguing whether a quasi‐linear equation has a “stability” problem in integration, comparative analyses are made by numerical experimentations using…

Abstract

While still arguing whether a quasi‐linear equation has a “stability” problem in integration, comparative analyses are made by numerical experimentations using conservation with smoothing and non‐conservation schemes as well as a time‐moving treatment scheme proposed by the first author respectively. The results show that the solution seeking method of the quasi‐linear model should not be considered as a “stability” problem. The traditional well‐posed computational model needs to be improved. The Lorenz’s “butterfly effect” should be in nature a Richardson’s explosive increase in time evolution of moving fluid.

Details

Kybernetes, vol. 27 no. 6/7
Type: Research Article
ISSN: 0368-492X

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Article

M. Rezaiee‐Pajand and J. Alamatian

This paper aims to provide a simple and accurate higher order predictor‐corrector integration which can be used in dynamic analysis and to compare it with the previous works.

Abstract

Purpose

This paper aims to provide a simple and accurate higher order predictor‐corrector integration which can be used in dynamic analysis and to compare it with the previous works.

Design/methodology/approach

The predictor‐corrector integration is defined by combining the higher order explicit and implicit integrations in which displacement and velocity are assumed to be functions of accelerations of several previous time steps. By studying the accuracy and stability conditions, the weighted factors and acceptable time step are determined.

Findings

Simplicity and vector operations plus accuracy and stability are the main specifications of the new predictor‐corrector method. This procedure can be used in linear and nonlinear dynamic analysis.

Research limitations/implications

In the proposed integration, time step is assumed to be constant.

Practical implications

The numerical integration is the heart of a dynamic analysis. The result's accuracy is strongly influenced by the accuracy and stability of the numerical integration.

Originality/value

This paper presents simple and accurate predictor‐corrector integration based on accelerations of several previous time steps. This may be used as a routine in any dynamic analysis software to enhance accuracy and reduce computational time.

Details

Engineering Computations, vol. 25 no. 6
Type: Research Article
ISSN: 0264-4401

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Article

Alper Korkmaz and İdris Dağ

The purpose of this paper is to simulate numerical solutions of nonlinear Burgers' equation with two well‐known problems in order to verify the accuracy of the cubic…

Abstract

Purpose

The purpose of this paper is to simulate numerical solutions of nonlinear Burgers' equation with two well‐known problems in order to verify the accuracy of the cubic B‐spline differential quadrature methods.

Design/methodology/approach

Cubic B‐spline differential quadrature methods have been used to discretize the Burgers' equation in space and the resultant ordinary equation system is integrated via Runge‐Kutta method of order four in time. Numerical results are compared with each other and some former results by calculating discrete root mean square and maximum error norms in each case. A matrix stability analysis is also performed by determining eigenvalues of the coefficient matrices numerically.

Findings

Numerical results show that differential quadrature methods based on cubic B‐splines generate acceptable solutions of nonlinear Burgers' equation. Constructing hybrid algorithms containing various basis to determine the weighting coefficients for higher order derivative approximations is also possible.

Originality/value

Nonlinear Burgers' equation is solved by cubic B‐spline differential quadrature methods.

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Article

Muhammad Azim bin Azizi, Ahmad Kamal Ariffin bin Mohd Ihsan and Nik Abdullah bin Nik Mohamed

The purpose of this paper is to establish a peridynamic method in predicting viscoelastic creep behaviour with recovery stage and to find the suitable numerical parameters…

Abstract

Purpose

The purpose of this paper is to establish a peridynamic method in predicting viscoelastic creep behaviour with recovery stage and to find the suitable numerical parameters of peridynamic method.

Design/methodology/approach

A rheological viscoelastic creep constitutive equation including recovery and an elastic peridynamic equation (with integral basis) are examined and used. The elasticity equation within the peridynamic equation is replaced by the viscoelastic equation. A new peridynamic method with two time parameters, i.e. numerical time and viscoelastic real time is designed. The two parameters of peridynamic method, horizon radius and number of nodes per unit volume are studied to get their optimal values. In validating this peridynamic method, comparisons are made between numerical and analytical result and between numerical and experimental data.

Findings

The new peridynamic method for viscoelastic creep behaviour is approved by the good matching in numerical-analytical data comparison with difference of < 0.1 per cent and in numerical-experimental data comparison with difference of 4-6 per cent. It can be used for further creep test which may include non-linear viscoelastic behaviour and creep rupture. From this paper, the variation of constants in Burger’s viscoelastic model is also studied and groups of constants values that can simulate solid, fluid and solid-fluid viscoelastic behaviours were obtained. In addition, the numerical peridynamic parameters were also manipulated and examined to achieve the optimal values of the parameters.

Research limitations/implications

The peridynamic model of viscoelastic creep behaviour preferably should have only one time parameter. This can only be done by solving the unstable fluctuation of dynamic results, which is not discussed in this paper. Another limitation is the tertiary region and creep rupture are not included in this paper.

Practical implications

The viscoelastic peridynamic model in this paper can serve as an alternative for conventional numerical simulations in viscoelastic area. This model also is the initial step of developing peridynamic model of viscoelastic creep rupture properties (crack initiation, crack propagation, crack branching, etc.), where this future model has high potential in predicting failure behaviours of any components, tools or structures, and hence increase safety and reduce loss.

Originality/value

The application of viscoelastic creep constitutive model on peridynamic formulation, effect of peridynamic parameters manipulation on numerical result, and optimization of constants of viscoelastic model in simulating three types of viscoelastic creep behaviours.

Details

Multidiscipline Modeling in Materials and Structures, vol. 11 no. 4
Type: Research Article
ISSN: 1573-6105

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Article

Boris Trogrlic and Ante Mihanovic

This paper aims to present a new numerical model for the stability and load‐bearing capacity computation of space reinforced‐concrete (R/C) frame structures. Both material…

Abstract

Purpose

This paper aims to present a new numerical model for the stability and load‐bearing capacity computation of space reinforced‐concrete (R/C) frame structures. Both material and geometric nonlinearities are taken into account. The R/C cross‐sections are assumed to undergo limited distortion under torsional action.

Design/methodology/approach

A simple, global discretization using beam‐column finite elements is preferred to a full, global discretization using 3D elements. This is more acceptable from a practical point of view. The composite cross‐section is discretized using 2D elements to apply the fiber decomposition procedure to solve the material and geometrical nonlinear behavior of the cross‐section under biaxial moments and axial forces. A local discretization of each beam element based on the comparative body model (i.e. a prismatic body discretized using brick elements, element by element, during the incremental‐iterative procedure) allows determining the torsional constant of the cross‐section under limited warping. The classical global iterative‐incremental procedure is then used to solve the resulting material and geometric nonlinear problem.

Findings

It has been noticed that, in case of a limited distortion of the cross‐section, the torsional constant of homogeneous (linear elastic) materials is greater than the one obtained from the Saint‐Venant theory. However, due to low‐tensile strength of concrete materials, the torsional constant decreases significantly after an early loading phase, primarily due to the lack of reinforcing flanges.

Research limitations/implications

The current study does not cover the torsion analysis of R/C cross‐section with stirrups. Besides, the bond‐slip effect between concrete and steel reinforcement is not taken into account, nor is the local buckling of the beam flanges and rebar.

Practical implications

This new numerical model has been implemented in a computer program for effectively computing the nonlinear stability and load bearing capacity of space R/C frames.

Originality/value

The authors believe that the comparative body model should bring a new approach to the solution of torsion problems with limited distortion of cross‐sections in material and geometric nonlinear analysis of space R/C frames.

Details

Engineering Computations, vol. 25 no. 2
Type: Research Article
ISSN: 0264-4401

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Article

Alper Korkmaz and İdris Dağ

This paper aims to present a numerical solution of non‐linear Burger's equation using differential quadrature method based on sinc functions.

Abstract

Purpose

This paper aims to present a numerical solution of non‐linear Burger's equation using differential quadrature method based on sinc functions.

Design/methodology/approach

Sinc Differential Quadrature Method is used for space discretization and four stage Runge‐Kutta algorithm is used for time discretization. A rate of convergency analysis is also performed for shock‐like solution. Numerical stability analysis is performed.

Findings

Sinc Differential Quadrature Method generates more accurate solutions of Burgers' equation when compared with the other methods.

Originality/value

This combination, Sinc Differential Quadrature and Runge‐Kutta of order four, has not been used to obtain numerical solutions of Burgers' equation.

Details

Engineering Computations, vol. 28 no. 6
Type: Research Article
ISSN: 0264-4401

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Article

Ioannis St Doltsinis

Addresses problems in mechanics and physics involving two or more coupled variables of different nature, or a number of distinct domains which interact. For these kinds of…

Abstract

Addresses problems in mechanics and physics involving two or more coupled variables of different nature, or a number of distinct domains which interact. For these kinds of problems, considers numerical solution by the coupling of operators appertaining to the individual participating phenomena, or defined in the domains. Reviews the co‐operation of distinct discretized operators in connection with the integration of temporal evolution processes, and the iterative treatment of stationary equations of state. The specification of subtasks complies with the demand for an independent treatment on different processing units arising in parallel computation. Physical subtasks refer to problems of different field variables interacting on the continuum level; their number is usually small. Fine granularity may be achieved by separating the problem region into subdomains which communicate via the boundaries. In multiphysics simulations operators are preferably combined such that subdomains are processed in parallel on different units, while physical phenomena are processed sequentially in the subdomain.

Details

Engineering Computations, vol. 14 no. 8
Type: Research Article
ISSN: 0264-4401

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Article

Ramesh Chand Mittal and Sumita Dahiya

In this study, a second-order standard wave equation extended to a two-dimensional viscous wave equation with timely differentiated advection-diffusion terms has been…

Abstract

Purpose

In this study, a second-order standard wave equation extended to a two-dimensional viscous wave equation with timely differentiated advection-diffusion terms has been solved by differential quadrature methods (DQM) using a modification of cubic B-spline functions. Two numerical schemes are proposed and compared to achieve numerical approximations for the solutions of nonlinear viscous wave equations.

Design/methodology/approach

Two schemes are adopted to reduce the given system into two systems of nonlinear first-order partial differential equations (PDE). For each scheme, modified cubic B-spline (MCB)-DQM is used for calculating the spatial variables and their derivatives that reduces the system of PDEs into a system of nonlinear ODEs. The solutions of these systems of ODEs are determined by SSP-RK43 scheme. The CPU time is also calculated and compared. Matrix stability analysis has been performed for each scheme and both are found to be unconditionally stable. The results of both schemes have been extensively discussed and compared. The accuracy and reliability of the methods have been successfully tested on several examples.

Findings

A comparative study has been carried out for two different schemes. Results from both schemes are also compared with analytical solutions and the results available in literature. Experiments show that MCB-DQM with Scheme II yield more accurate and reliable results in solving viscous wave equations. But Scheme I is comparatively less expensive in terms of CPU time. For MCB-DQM, less depository requirements lead to less aggregation of approximation errors which in turn enhances the correctness and readiness of the numerical techniques. Approximate solutions to the two-dimensional nonlinear viscous wave equation have been found without linearizing the equation. Ease of implementation and low computation cost are the strengths of the method.

Originality/value

For the first time, a comparative study has been carried out for the solution of nonlinear viscous wave equation. Comparisons are done in terms of accuracy and CPU time. It is concluded that Scheme II is more suitable.

Details

Engineering Computations, vol. 35 no. 1
Type: Research Article
ISSN: 0264-4401

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Article

Carlos A. Felippa and Thomas L. Geers

Partitioned analysis is a method by which sets of time‐dependent ordinary differential equations for coupled systems may be numerically integrated in tandem, thereby…

Abstract

Partitioned analysis is a method by which sets of time‐dependent ordinary differential equations for coupled systems may be numerically integrated in tandem, thereby avoiding brute‐force simultaneous solution. The coupled systems addressed pertain to fluid—structure, fluid—soil, soil—structure, or even structure—structure interaction. The paper describes the partitioning process for certain discrete‐element equations of motion, as well as the associated computer implementation. It then delineates the procedure for designing a partitioned analysis method in a given application. Finally, examples are presented to illustrate the concepts. It is seen that a key element in the implementation of partitioned analysis is the use of integrated, as opposed to monolithic software.

Details

Engineering Computations, vol. 5 no. 2
Type: Research Article
ISSN: 0264-4401

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Article

J.M. Zhan and Y.S. Li

A numerical scheme is proposed to solve double‐diffusive problems using a boundary‐fitted coordinate system to introduce finer grids in the boundary layer regions and an…

Abstract

A numerical scheme is proposed to solve double‐diffusive problems using a boundary‐fitted coordinate system to introduce finer grids in the boundary layer regions and an accurate high‐order difference method. Numerical stability is improved by using fourth‐order accurate upwind‐biased differences to approximate the convection terms. The other terms in the governing differential equations are discretized using fourth‐order central difference. To demonstrate the versatility of the boundary‐fitted coordinate system, natural convection in an eccentric annulus is first simulated. The numerical results are consistent with the experimental results by Kuehn and Goldstein and better than the numerical results by Projahn et al. for eccentric cases. Secondly, the symmetry breaking and overturning states in thermohaline‐driven flows in a two‐dimensional rectangular cavity are simulated first to validate the numerical scheme. The numerical results agree well with those by Dijkstra and Molemaker and Quon and Ghil. Finally, the effect of the Lewis number on the flow system is investigated in detail. Depending on the value of the Lewis number, the flow pattern is either stable and symmetric, periodic and oscillatory, or unsymmetric and random.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 13 no. 8
Type: Research Article
ISSN: 0961-5539

Keywords

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