Search results for: finite element analysis.

Authors: K. Karuppasamy

Abstract:

In this paper, analysis of an infinite beam resting on multilayer tensionless extensible geosynthetic reinforced granular fill-poor soil system overlying soft soil strata under moving load with constant velocity is presented. The beam is subjected to a concentrated load moving with constant velocity. The upper reinforced granular bed is modeled by a rough membrane embedded in Pasternak shear layer overlying a series of compressible nonlinear winkler springs representing the underlying the very poor soil. The multilayer tensionless extensible geosynthetic layer has been assumed to deform such that at interface the geosynthetic and the soil have some deformation. Nonlinear behaviour of granular fill and the very poor soil has been considered in the analysis by means of hyperbolic constitutive relationships. Governing differential equations of the soil foundation system have been obtained and solved with the help of appropriate boundary conditions. The solution has been obtained by employing finite difference method by means of Gauss-Siedal iterative scheme. Detailed parametric study has been conducted to study the influence of various parameters on the response of soil–foundation system under consideration by means of deflection and bending moment in the beam and tension mobilized in the geosynthetic layer. These parameters include magnitude of applied load, velocity of load, damping, ultimate resistance of poor soil and granular fill layer. Range of values of parameters has been considered as per Indian Railway conditions. This study clearly observed that the comparisons of multilayer tensionless extensible geosynthetic reinforcement with poor foundation soil and magnitude of applied load, relative compressibility of granular fill and ultimate resistance of poor soil has significant influence on the response of soil–foundation system.

Keywords: Infinite beams, multilayer tensionless extensible geosynthetic, granular layer, moving load, nonlinear behavior of poor soil.

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Authors: Rafat Alshorman, Walter Hussak

Abstract:

Most of the concurrent transactional protocols consider serializability as a correctness criterion of the transactions execution. Usually, the proof of the serializability relies on mathematical proofs for a fixed finite number of transactions. In this paper, we introduce a protocol to deal with an infinite number of transactions which are iterated infinitely often. We specify serializability of the transactions and the protocol using a specification language based on temporal logics. It is worthwhile using temporal logics such as LTL (Lineartime Temporal Logic) to specify transactions, to gain full automatic verification by using model checkers.

Keywords: Multi-step transactions, LTL specifications, Model Checking.

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Authors: M. M. Toufigh, A. R. Ahangarasr, A. Ouria

Abstract:

Among many different methods that are used for optimizing different engineering problems mathematical (numerical) optimization techniques are very important because they can easily be used and are consistent with most of engineering problems. Many studies and researches are done on stability analysis of three dimensional (3D) slopes and the relating probable slip surfaces and determination of factors of safety, but in most of them force equilibrium equations, as in simplified 2D methods, are considered only in two directions. In other words for decreasing mathematical calculations and also for simplifying purposes the force equilibrium equation in 3rd direction is omitted. This point is considered in just a few numbers of previous studies and most of them have only given a factor of safety and they haven-t made enough effort to find the most probable slip surface. In this study shapes of the slip surfaces are modeled, and safety factors are calculated considering the force equilibrium equations in all three directions, and also the moment equilibrium equation is satisfied in the slip direction, and using nonlinear programming techniques the shape of the most probable slip surface is determined. The model which is used in this study is a 3D model that is composed of three upper surfaces which can cover all defined and probable slip surfaces. In this research the meshing process is done in a way that all elements are prismatic with quadrilateral cross sections, and the safety factor is defined on this quadrilateral surface in the base of the element which is a part of the whole slip surface. The method that is used in this study to find the most probable slip surface is the non-linear programming method in which the objective function that must get optimized is the factor of safety that is a function of the soil properties and the coordinates of the nodes on the probable slip surface. The main reason for using non-linear programming method in this research is its quick convergence to the desired responses. The final results show a good compatibility with the previously used classical and 2D methods and also show a reasonable convergence speed.

Keywords: Non-linear programming, numerical optimization, slope stability, 3D analysis.

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Authors: Yasir M. Alyazichi, Brian G. Jones, Errol McLean, Hamd N. Altalyan, Ali K. M. Al-Nasrawi

Abstract:

The main purpose of this study is to assess the sediment quality and potential ecological risk in marine sediments in Gymea Bay located in south Sydney, Australia. A total of 32 surface sediment samples were collected from the bay. Current track trajectories and velocities have also been measured in the bay. The resultant trace elements were compared with the adverse biological effect values Effect Range Low (ERL) and Effect Range Median (ERM) classifications. The results indicate that the average values of chromium, arsenic, copper, zinc, and lead in surface sediments all reveal low pollution levels and are below ERL and ERM values. The highest concentrations of trace elements were found close to discharge points and in the inner bay, and were linked with high percentages of clay minerals, pyrite and organic matter, which can play a significant role in trapping and accumulating these elements. The lowest concentrations of trace elements were found to be on the shoreline of the bay, which contained high percentages of sand fractions. It is postulated that the fine particles and trace elements are disturbed by currents and tides, then transported and deposited in deeper areas. The current track velocities recorded in Gymea Bay had the capability to transport fine particles and trace element pollution within the bay. As a result, hydrodynamic measurements were able to provide useful information and to help explain the distribution of sedimentary particles and geochemical properties. This may lead to knowledge transfer to other bay systems, including those in remote areas. These activities can be conducted at a low cost, and are therefore also transferrable to developing countries. The advent of portable instruments to measure trace elements in the field has also contributed to the development of these lower cost and easily applied methodologies available for use in remote locations and low-cost economies.

Keywords: Current track velocities, Gymea Bay, surface sediments, trace elements.

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Authors: M. Ghorbany

Abstract:

A square matrix over the complex field with non- negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful representation of G by quasi-permutation matrices over the rationals and the complex numbers are denoted by q(G) and c(G) respectively. Finally r (G) denotes the minimal degree of a faithful rational valued complex character of C. The purpose of this paper is to calculate q(G), c(G) and r(G) for the group S L(2, q) when extended by a certain group of order two.

Keywords: General linear group, Quasi-permutation

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Authors: Ahmet Tekcan

Abstract:

Let F(x, y) = ax2 + bxy + cy2 be a positive definite binary quadratic form with discriminant Δ whose base points lie on the line x = -1/m for an integer m ≥ 2, let p be a prime number and let Fp be a finite field. Let EF : y2 = ax3 + bx2 + cx be an elliptic curve over Fp and let CF : ax3 + bx2 + cx ≡ 0(mod p) be the cubic congruence corresponding to F. In this work we consider some properties of positive definite quadratic forms, elliptic curves and cubic congruences.

Keywords: Binary quadratic form, elliptic curves, cubic congruence.

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Authors: Chothmal, Basant Agarwal

Abstract:

Sentiment analysis means to classify a given review document into positive or negative polar document. Sentiment analysis research has been increased tremendously in recent times due to its large number of applications in the industry and academia. Sentiment analysis models can be used to determine the opinion of the user towards any entity or product. E-commerce companies can use sentiment analysis model to improve their products on the basis of users’ opinion. In this paper, we propose a new One-class Support Vector Machine (One-class SVM) based sentiment analysis model for movie review documents. In the proposed approach, we initially extract features from one class of documents, and further test the given documents with the one-class SVM model if a given new test document lies in the model or it is an outlier. Experimental results show the effectiveness of the proposed sentiment analysis model.

Keywords: Feature selection methods, Machine learning, NB, One-class SVM, Sentiment Analysis, Support Vector Machine.

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Authors: Abhijit Mitra

Abstract:

The paper provides an in-depth tutorial of mathematical construction of maximal length sequences (m-sequences) via primitive polynomials and how to map the same when implemented in shift registers. It is equally important to check whether a polynomial is primitive or not so as to get proper m-sequences. A fast method to identify primitive polynomials over binary fields is proposed where the complexity is considerably less in comparison with the standard procedures for the same purpose.

Keywords: Finite field, irreducible polynomial, primitive polynomial, maximal length sequence, additive shift register, multiplicative shift register.

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Authors: M. H. M. Rashid

Abstract:

A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.

Keywords: Weyl’s theorem, Weyl spectrum, polaroid operators, property (gm), property (m).

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Authors: Jeong Hye Moon, Byung Hoon Kang, PooGyeon Park

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In this paper, we proposed the direct method for converting Finite-Impulse Response (FIR) filter with low nonzero tap into Infinite-Impulse Response (IIR) filter using the pre-determined table. The prony method is used by ghost cancellator which is IIR approximation to FIR filter which is better performance than IIR and have much larger calculation difference. The direct method for many ghost combination with low nonzero tap of NTSC(National Television System Committee) TV signal in Korea is described. The proposed method is illustrated with an example.

Keywords: NTSC, Ghost cancellation, FIR, IIR, Prony method.

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Authors: Z. Altawallbeh

Abstract:

In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra, by providing certain homotopic function.

Keywords: Exterior algebra, free resolution, free and projective modules, Hochschild homology, homotopic function, symmetric algebra.

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Authors: Guang Zeng, Jin Huang, Zicai Li

Abstract:

In this paper, we research the standard 13-point difference schemes for solving the biharmonic equation. Heuristic method is applied to judging the stability of multi-level difference schemes of the biharmonic equation. It is showed that the standard 13-point difference schemes are stable.

Keywords: Finite-difference equation, computational stability, hirt method.

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Authors: M. N. Nwodo, Y. P. Cheng, N. H. Minh

Abstract:

In the process of recovering oil in weak sandstone formations, the strength of sandstones around the wellbore is weakened due to the increase of effective stress/load from the completion activities around the cavity. The weakened and de-bonded sandstone may be eroded away by the produced fluid, which is termed sand production. It is one of the major trending subjects in the petroleum industry because of its significant negative impacts, as well as some observed positive impacts. For efficient sand management therefore, there has been need for a reliable study tool to understand the mechanism of sanding. One method of studying sand production is the use of the widely recognized Discrete Element Method (DEM), Particle Flow Code (PFC^3D) which represents sands as granular individual elements bonded together at contact points. However, there is limited knowledge of the particle-scale behavior of the weak sandstone, and the parameters that affect sanding. This paper aims to investigate the reliability of using PFC^3D and a simple Darcy flow in understanding the sand production behavior of a weak sandstone. An isotropic tri-axial test on a weak oil sandstone sample was first simulated at a confining stress of 1MPa to calibrate and validate the parallel bond models of PFC^3D using a 10m height and 10m diameter solid cylindrical model. The effect of the confining stress on the number of bonds failure was studied using this cylindrical model. With the calibrated data and sample material properties obtained from the tri-axial test, simulations without and with fluid flow were carried out to check on the effect of Darcy flow on bonds failure using the same model geometry. The fluid flow network comprised of every four particles connected with tetrahedral flow pipes with a central pore or flow domain. Parametric studies included the effects of confining stress, and fluid pressure; as well as validating flow rate – permeability relationship to verify Darcy’s fluid flow law. The effect of model size scaling on sanding was also investigated using 4m height, 2m diameter model. The parallel bond model successfully calibrated the sample’s strength of 4.4MPa, showing a sharp peak strength before strain-softening, similar to the behavior of real cemented sandstones. There seems to be an exponential increasing relationship for the bigger model, but a curvilinear shape for the smaller model. The presence of the Darcy flow induced tensile forces and increased the number of broken bonds. For the parametric studies, flow rate has a linear relationship with permeability at constant pressure head. The higher the fluid flow pressure, the higher the number of broken bonds/sanding. The DEM PFC^3D is a promising tool to studying the micromechanical behavior of cemented sandstones.

Keywords: Discrete Element Method, fluid flow, parametric study, sand production/bonds failure.

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Authors: Marcelo Hayashi, João Lima, Bruno Chieregatti, Ernani Volpe

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The adjoint method has been used as a successful tool to obtain sensitivity gradients in aerodynamic design and optimisation for many years. This work presents an alternative approach to the continuous adjoint formulation that enables one to compute gradients of a given measure of merit with respect to control parameters other than those pertaining to geometry. The procedure is then applied to the steady 2–D compressible Euler and incompressible Navier–Stokes flow equations. Finally, the results are compared with sensitivities obtained by finite differences and theoretical values for validation.

Keywords: Adjoint method, optimisation, non–geometric sensitivities, boundary conditions.

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Authors: Mehrdad Mahdavi Boroujerdi, Soheil Nazem

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Cloud Computing is a new technology that helps us to use the Cloud for compliance our computation needs. Cloud refers to a scalable network of computers that work together like Internet. An important element in Cloud Computing is that we shift processing, managing, storing and implementing our data from, locality into the Cloud; So it helps us to improve the efficiency. Because of it is new technology, it has both advantages and disadvantages that are scrutinized in this article. Then some vanguards of this technology are studied. Afterwards we find out that Cloud Computing will have important roles in our tomorrow life!

Keywords: Cloud Computing, Grid Computing, Internet as a Platform, On-demand Computing, Software as a Service.

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Authors: Basudev Ghosh, Sailendranath Paul, Sreyasi Banerjee

Abstract:

Using quantum hydrodynamical (QHD) model the linear dispersion relation for the electron plasma waves propagating in a cylindrical waveguide filled with a dense plasma containing streaming electron, hole and stationary charged dust particles has been derived. It is shown that the effect of finite boundary and stream velocity of electrons and holes make some of the possible modes of propagation linearly unstable. The growth rate of this instability is shown to depend significantly on different plasma parameters.

Keywords: Electron Plasma wave, Quantum plasma, Quantum Hydrodynamical model.

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Authors: R. Bhargava, Sonam Singh

Abstract:

In the present study, a numerical analysis is carried out to investigate unsteady MHD (magneto-hydrodynamic) flow and heat transfer of a non-Newtonian second grade viscoelastic fluid over an oscillatory stretching sheet. The flow is induced due to an infinite elastic sheet which is stretched oscillatory (back and forth) in its own plane. Effect of viscous dissipation and joule heating are taken into account. The non-linear differential equations governing the problem are transformed into system of non-dimensional differential equations using similarity transformations. A newly developed meshfree numerical technique Element free Galerkin method (EFGM) is employed to solve the coupled non linear differential equations. The results illustrating the effect of various parameters like viscoelastic parameter, Hartman number, relative frequency amplitude of the oscillatory sheet to the stretching rate and Eckert number on velocity and temperature field are reported in terms of graphs and tables. The present model finds its application in polymer extrusion, drawing of plastic films and wires, glass, fiber and paper production etc.

Keywords: EFGM, MHD, Oscillatory stretching sheet, Unsteady, Viscoelastic

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Authors: Jianmin Xing Wei Shao

Abstract:

We introduce the notion of strongly ω -Gorenstein modules, where ω is a faithfully balanced self-orthogonal module. This gives a common generalization of both Gorenstein projective (injective) modules and ω-Gorenstein modules. We investigate some characterizations of strongly ω -Gorenstein modules. Consequently, some properties under change of rings are obtained.

Keywords: Faithfully balanced self-orthogonal module, ω-Gorenstein module, strongly ω-Gorenstein module, finite generated.

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Authors: B. Chetti

Abstract:

Dynamic characteristics of a four-lobe journal bearing of micropolar fluids are presented. Lubricating oil containing additives and contaminants is modelled as micropolar fluid. The modified Reynolds equation is obtained using the micropolar lubrication theory and solving it by using finite difference technique. The dynamic characteristics in terms of stiffness, damping coefficients, the critical mass and whirl ratio are determined for various values of size of material characteristic length and the coupling number. The results show compared with Newtonian fluids, that micropolar fluid exhibits better stability.

Keywords: Four-lobe bearings, dynamic characteristics, stabilityanalysis, micropolar fluid

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Authors: A.R Alesaadi, M. Nafar, A.H. Gheisari

Abstract:

In this paper sensitivity analysis is performed for reliability evaluation of power systems. When examining the reliability of a system, it is useful to recognize how results change as component parameters are varied. This knowledge helps engineers to understand the impact of poor data, and gives insight on how reliability can be improved. For these reasons, a sensitivity analysis can be performed. Finally, a real network was used for testing the presented method.

Keywords: sensitivity analysis, reliability evaluation, powersystems.

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Authors: N. Mohamad, W. Samiati Andriana Wan Mohd Daud, M. Suhaimi Tohid, M. Fazli Othman, M. Rizal Salleh

Abstract:

This is a collaborative project of the mural art between The Department of Fine Art from Universiti Teknologi MARA (UiTM) and Petronas Dagangan Berhad (PDB), the most leading retailer and marketer of downstream oil and gas products in Malaysia. Five different states have been identified in showcasing the National Identity of Malaysia at each Petronas gas station; the Air Keroh in Melaka, Pasir Pekan in Kelantan, Pontian in Johor, Simpang Pulai in Perak and also Wakaf Bharu in Terengganu. This project is to analyze the element of national identity that has been demonstrated at the Petronas's Mural. The ultimate aim of the mural is to let the community and local people to be aware about what Malaysians are consists and proud of and how everyone is able to connect with the idea through art. The method that is being explained in this research is by using visual data through research and also self-experience in collecting the visual data in identifying what images are considered as the national identity and idea development and visual analysis is being transferred based upon the visual data collection. In this stage elements and principle of design will be the key in highlighting what is necessary in a work of art. In conclusion, image of the National Identity of Malaysia is able to connect to the audience from local and also to the people from outside the country to learn and understand the beauty and diversity of Malaysia as a unique country with art, through the wall of five Petronas gas stations.

Keywords: Mural art, fine art, national identity, community.

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Authors: André Trudel, Haiyi Zhang

Abstract:

Over the years, many implementations have been proposed for solving IA networks. These implementations are concerned with finding a solution efficiently. The primary goal of our implementation is simplicity and ease of use. We present an IA network implementation based on finite domain non-binary CSPs, and constraint logic programming. The implementation has a GUI which permits the drawing of arbitrary IA networks. We then show how the implementation can be extended to find all the solutions to an IA network. One application of finding all the solutions, is solving probabilistic IA networks.

Keywords: Constraint logic programming, CSP, logic, temporalreasoning.

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Authors: Aso Rahimzadegan, Seyyed Poorya Hosseini, Kamran Qaderi

Abstract:

In this paper, we have proposed two novel plasmonic demultiplexing structures based on metal-insulator-metal surfaces which, beside their compact size, have a very good transmission spectrum. The impact of the key internal parameters on the transmission spectrum is numerically analyzed by using the twodimensional (2D) finite difference time domain (FDTD) method. The proposed structures could be used to develop ultra-compact photonic wavelength demultiplexing devices for large-scale photonic integration.

Keywords: Photonic integrated devices, Plasmonics, Metalinsulator- metal (MIM) waveguide, Demultiplexers.

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Authors: R. Haoui

Abstract:

The aim of this work is to determine the supersonic nozzle profiles used in propulsion, for the launchers or embarked with the satellites. This design has as a role firstly, to give a important propulsion, i.e. with uniform and parallel flow at exit, secondly to find a short length profiles without modification of the flow in the nozzle. The first elaborate program is used to determine the profile of divergent by using the characteristics method for an axisymmetric flow. The second program is conceived by using the finite volume method to determine and test the profile found connected to a convergent.

Keywords: Characteristic method, nozzles, supersonic flow, propellers.

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Authors: P. G. Siddheshwar, R. K. Vanishree, C. Kanchana

Abstract:

A local nonlinear stability analysis using a eight-mode expansion is performed in arriving at the coupled amplitude equations for Rayleigh-Bénard-Brinkman convection (RBBC) in the presence of LTNE effects. Streamlines and isotherms are obtained in the two-dimensional unsteady finite-amplitude convection regime. The parameters’ influence on heat transport is found to be more pronounced at small time than at long times. Results of the Rayleigh-Bénard convection is obtained as a particular case of the present study. Additional modes are shown not to significantly influence the heat transport thus leading us to infer that five minimal modes are sufficient to make a study of RBBC. The present problem that uses rolls as a pattern of manifestation of instability is a needed first step in the direction of making a very general non-local study of two-dimensional unsteady convection. The results may be useful in determining the preferred range of parameters’ values while making rheometric measurements in fluids to ascertain fluid properties such as viscosity. The results of LTE are obtained as a limiting case of the results of LTNE obtained in the paper.

Keywords: Rayleigh-Bénard convection, heat transport, porous media, generalized Lorenz model, coupled Ginzburg-Landau model.

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Authors: Young-Seok Choi

Abstract:

We present a new framework of the data-reusing (DR) adaptive algorithms by incorporating a constraint on noise, referred to as a noise constraint. The motivation behind this work is that the use of the statistical knowledge of the channel noise can contribute toward improving the convergence performance of an adaptive filter in identifying a noisy linear finite impulse response (FIR) channel. By incorporating the noise constraint into the cost function of the DR adaptive algorithms, the noise constrained DR (NC-DR) adaptive algorithms are derived. Experimental results clearly indicate their superior performance over the conventional DR ones.

Keywords: Adaptive filter, data-reusing, least-mean square (LMS), affine projection (AP), noise constraint.

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Authors: G. Bhushan, S. S. Rattan, N. P. Mehta

Abstract:

A four-lobe pressure dam bearing which is produced by cutting two pressure dams on the upper two lobes and two relief-tracks on the lower two lobes of an ordinary four-lobe bearing is found to be more stable than a conventional four-lobe bearing. In this paper a four-lobe pressure dam bearing supporting rigid and flexible rotors is analytically investigated to determine its performance when L/D ratio is varied in the range 0.75 to 1.5. The static and dynamic characteristics are studied at various L/D ratios. The results show that the stability of a four-lobe pressure dam bearing increases with decrease in L/D ratios both for rigid as well as flexible rotors.

Keywords: Four-lobe pressure dam bearing, finite-elementmethod, L/D ratio.

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Authors: Muritala Babatunde Hassan

Abstract:

In the contemporary global political economy, foreign direct investment (FDI) is gaining currency on daily basis. Notably, the end of the Cold War has brought about the dominance of neoliberal ideology with its mantra of private-sector-led economy. As such, nation-states now see FDI attraction as an important element in their approach to national development. Governments and policy makers are preoccupying themselves with unraveling the best strategies to not only attract more FDI but also to attain the desired socio-economic development status. In Nigeria, the perceived development potentials of FDI have brought about aggressive hunt for foreign investors, most especially since transition to civilian rule in May 1999. Series of liberal and market oriented strategies are being adopted not only to attract foreign investors but largely to stimulate private sector participation in the economy. It is on this premise that this study interrogates the politics of FDI attraction for domestic development in Nigeria between 1999 and 2014, with the ultimate aim of examining the nexus between regime type and the ability of a state to attract and benefit from FDI. Building its analysis within the framework of institutional utilitarianism, the study posits that the essential FDI strategies for achieving the greatest happiness for the greatest number of Nigerians are political not economic. Both content analysis and descriptive survey methodology were employed in carrying out the study. Content analysis involves desk review of literatures that culminated in the development of the study’s conceptual and theoretical framework of analysis. The study finds no significant relationship between transition to democracy and FDI inflows in Nigeria, as most of the attracted investments during the period of the study were market and resource seeking as was the case during the military regime, thereby contributing minimally to the socio-economic development of the country. It is also found that the country placed much emphasis on liberalization and incentives for FDI attraction at the neglect of improving the domestic investment environment. Consequently, poor state of infrastructure, weak institutional capability and insecurity were identified as the major factors seriously hindering the success of Nigeria in exploiting FDI for domestic development. Given the reality of the currency of FDI as a vector of economic globalization and that Nigeria is trailing the line of private-sector-led approach to development, it is recommended that emphasis should be placed on those measures aimed at improving the infrastructural facilities, building solid institutional framework, enhancing skill and technological transfer and coordinating FDI promotion activities by different agencies and at different levels of government.

Keywords: Foreign capital, politics, socio-economic development, FDI attraction strategies, Redemocratization.

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Authors: Appanah Rao Appadu, Muhammad Zaid Dauhoo

Abstract:

In this paper, we have combined some spatial derivatives with the optimised time derivative proposed by Tam and Webb in order to approximate the linear advection equation which is given by = 0. Ôêé Ôêé + Ôêé Ôêé x f t u These spatial derivatives are as follows: a standard 7-point 6 th -order central difference scheme (ST7), a standard 9-point 8 th -order central difference scheme (ST9) and optimised schemes designed by Tam and Webb, Lockard et al., Zingg et al., Zhuang and Chen, Bogey and Bailly. Thus, these seven different spatial derivatives have been coupled with the optimised time derivative to obtain seven different finite-difference schemes to approximate the linear advection equation. We have analysed the variation of the modified wavenumber and group velocity, both with respect to the exact wavenumber for each spatial derivative. The problems considered are the 1-D propagation of a Boxcar function, propagation of an initial disturbance consisting of a sine and Gaussian function and the propagation of a Gaussian profile. It is known that the choice of the cfl number affects the quality of results in terms of dissipation and dispersion characteristics. Based on the numerical experiments solved and numerical methods used to approximate the linear advection equation, it is observed in this work, that the quality of results is dependent on the choice of the cfl number, even for optimised numerical methods. The errors from the numerical results have been quantified into dispersion and dissipation using a technique devised by Takacs. Also, the quantity, Exponential Error for Low Dispersion and Low Dissipation, eeldld has been computed from the numerical results. Moreover, based on this work, it has been found that when the quantity, eeldld can be used as a measure of the total error. In particular, the total error is a minimum when the eeldld is a minimum.

Keywords: Optimised time derivative, dissipation, dispersion, cfl number, Nomenclature: k : time step, h : spatial step, β :advection velocity, r: cfl/Courant number, hkrβ= , w =θ, h : exact wave number, n :time level, RPE : Relative phase error per unit time step, AFM :modulus of amplification factor

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Authors: Joan Goh, Ahmad Abd. Majid, Ahmad Izani Md. Ismail

Abstract:

In this paper, collocation based cubic B-spline and extended cubic uniform B-spline method are considered for solving one-dimensional heat equation with a nonlocal initial condition. Finite difference and θ-weighted scheme is used for time and space discretization respectively. The stability of the method is analyzed by the Von Neumann method. Accuracy of the methods is illustrated with an example. The numerical results are obtained and compared with the analytical solutions.

Keywords: Heat equation, Collocation based, Cubic Bspline, Extended cubic uniform B-spline.

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