Search results for: navier equation

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

Abstract:

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: B. Tomczyk, R. Mania

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Thin linear-elastic cylindrical circular shells having a micro-periodic structure along two directions tangent to the shell midsurface (biperiodic shells) are object of considerations. The aim of this paper is twofold. First, we formulate an averaged nonasymptotic model for the analysis of parametric vibrations or dynamical stability of periodic shells under consideration, which has constant coefficients and takes into account the effect of a cell size on the overall shell behavior (a length-scale effect). This model is derived employing the tolerance modeling procedure. Second we apply the obtained model to derivation of frequency equation being a starting point in the analysis of parametric vibrations. The effect of the microstructure length oh this frequency equation is discussed.

Keywords: Micro-periodic shells, mathematical modeling, length-scale effect, parametric vibrations

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Authors: Alireza Rezaei, Fatemeh Baharifard, Kourosh Parand

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In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.

Keywords: Quasilinearization method, Barycentric lagrange interpolation, nonlinear ODE, fin problem, heat transfer.

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Authors: Rohit Suryawanshi

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In this study, the commercial Computational Fluid Dynamics (CFD), ANSYS-Fluent, has been used to optimize the marine propeller with the design of experiment (DOE) method. At the initial stage, different propeller parameters ware selected for the three different levels. The four characteristics factors are: no. of the blade, camber value, pitch delta & chord at the hub. Then, CAD modelling is performed by considering the selected factor and level. In this investigation, a total of 9 test models are simulated with the Reynolds-Averaged Navier-Stokes (RANS) equations. The standard, realizable

Keywords: Marine propeller, Computational Fluid Dynamics, optimization, DOE, propeller thrust.

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Authors: Hsian Ming Goo

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The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.

Keywords: Special approximate algorithm, square root, Pell’s equation, Newton’s method, error analysis.

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Authors: A. Soltani, M. Karimi Demneh

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In this paper, modeling of an acoustic enclosed vehicle cabin has been carried out by using boundary element method. Also, the second purpose of this study is analyzing of linear wave equation in an acoustic field. The resultants of this modeling consist of natural frequencies that have been compared with resultants derived from finite element method. By using numerical method (boundary element method) and after solution of wave equation inside an acoustic enclosed cabin, this method has been progressed to simulate noise inside a simple vehicle cabin.

Keywords: Boundary element method, natural frequency, noise, vehicle cabin.

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Authors: Navid Javidtash, Abdolmohamad Davodi, Mojtaba Hakimzadeh, Abdolreza Roozbeh

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Economic dispatch (ED) is considered to be one of the key functions in electric power system operation. This paper presents a new hybrid approach based genetic algorithm (GA) to economic dispatch problems. GA is most commonly used optimizing algorithm predicated on principal of natural evolution. Utilization of chaotic queue with GA generates several neighborhoods of near optimal solutions to keep solution variation. It could avoid the search process from becoming pre-mature. For the objective of chaotic queue generation, utilization of tent equation as opposed to logistic equation results in improvement of iterative speed. The results of the proposed approach were compared in terms of fuel cost, with existing differential evolution and other methods in literature.

Keywords: Economic Dispatch(ED), Optimization, Fuel Cost, Genetic Algorithm (GA).

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Authors: Simon Brown

Abstract:

Glomerular filtration rate (GFR) is a measure of kidney function. It is usually estimated from serum concentrations of cystatin C or creatinine although there has been considerable debate in the literature about (i) the best equation to use and (ii) the variability in the correlation between the concentrations of creatinine and cystatin C. The equations for GFR can be written in a general form and from these I calculate the error of the GFR estimates associated with analyte measurement error. These show that the error of the GFR estimates is such that it is not possible to distinguish between the equations over much of the concentration range of either analyte. The general forms of the equations are also used to derive an expression for the concentration of cystatin C as a function of the concentration of creatinine. This equation shows that these analyte concentrations are not linearly related. Clinical reports of cystatin C and creatinine concentration are consistent with the expression derived.

Keywords: creatinine, cystatin C, error analysis, glomerularfiltration rate, measurement error.

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Authors: Reza Mohammadi, Mahdieh Sahebi

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We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the derived method. Numerical comparison with other methods shows the superiority of presented scheme.

Keywords: Fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis.

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Authors: A.R. Ismail, M. R. A. Rani, Z. K. M. Makhbul, M. J. M. Nor, M. N. A. Rahman

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The environmental factors such as temperature and relative humidity are very contribute to the effect of comfort, health, performance and worker productivity. To ensure an ergonomics work environment, it is possible to require a specific attention especially in industries. The aim of this study is to show the effect of temperature and relative humidity on worker productivity in automotive industry by taking a workstation in an automotive plant as the location to conduct the study. From the analysis of the data, there were relationship between temperature and relative humidity on worker productivity. Mathematical equation to represent the relationship between temperatures and relative humidity on the production rate is modelled. From the equation model, the production rate for the workstation can be predicted base on the value of temperature and relative humidity.

Keywords: WBGT, Relative Humidity, Comfort, Productivity.

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Authors: Abdurrahim Dal, Tuncay Karaçay

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Dynamics of a rotor supported by air bearings is strongly depends on the pressure distribution between the rotor and the bearing. In this study, internal pressure in air bearings is numerical and experimental analyzed for different radial clearances. Firstly the pressure distribution between rotor and bearing is modeled using Reynold's equation and this model is solved numerically. The rotor-bearing system is also modeled in four degree of freedom and it is simulated for different radial clearances. Then, in order to validate numerical results, a test rig is designed and the rotor bearing system is run under the same operational conditions. Pressure signals of left and right bearings are recorded. Internal pressure variations are compared for numerical and experimental results for different radial clearances.

Keywords: Air bearing, internal pressure, Reynold’s equation, rotor.

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Authors: Mohammad M. Toufigh, Ahad Ouria

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This paper presents an analytical method to solve governing consolidation parabolic partial differential equation (PDE) for inelastic porous Medium (soil) with consideration of variation of equation coefficient under cyclic loading. Since under cyclic loads, soil skeleton parameters change, this would introduce variable coefficient of parabolic PDE. Classical theory would not rationalize consolidation phenomenon in such condition. In this research, a method based on time space mapping to a virtual time space along with superimposing rule is employed to solve consolidation of inelastic soils in cyclic condition. Changes of consolidation coefficient applied in solution by modification of loading and unloading duration by introducing virtual time. Mapping function is calculated based on consolidation partial differential equation results. Based on superimposing rule a set of continuous static loads in specified times used instead of cyclic load. A set of laboratory consolidation tests under cyclic load along with numerical calculations were performed in order to verify the presented method. Numerical solution and laboratory tests results showed accuracy of presented method.

Keywords: Mapping, Consolidation, Inelastic porous medium, Cyclic loading, Superimposing rule.

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Authors: Xin Luo, Jin Huang, Chuan-Long Wang

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The mechanical quadrature methods for solving the boundary integral equations of the anisotropic Darcy-s equations with Dirichlet conditions in smooth domains are presented. By applying the collectively compact theory, we prove the convergence and stability of approximate solutions. The asymptotic expansions for the error show that the methods converge with the order O (h3), where h is the mesh size. Based on these analysis, extrapolation methods can be introduced to achieve a higher convergence rate O (h5). An a posterior asymptotic error representation is derived in order to construct self-adaptive algorithms. Finally, the numerical experiments show the efficiency of our methods.

Keywords: Darcy's equation, anisotropic, mechanical quadrature methods, extrapolation methods, a posteriori error estimate.

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

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Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: Accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations.

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Authors: V. Ghadamyari, F. Samadi, F. Kowsary

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An inverse geometry problem is solved to predict an unknown irregular boundary profile. The aim is to minimize the objective function, which is the difference between real and computed temperatures, using three different versions of Conjugate Gradient Method. The gradient of the objective function, considered necessary in this method, obtained as a result of solving the adjoint equation. The abilities of three versions of Conjugate Gradient Method in predicting the boundary profile are compared using a numerical algorithm based on the method. The predicted shapes show that due to its convergence rate and accuracy of predicted values, the Powell-Beale version of the method is more effective than the Fletcher-Reeves and Polak –Ribiere versions.

Keywords: Boundary elements, Conjugate Gradient Method, Inverse Geometry Problem, Sensitivity equation.

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Authors: M. Akbari, S. Sadodin

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In this paper, the melting of a semi-infinite body as a result of a moving laser beam has been studied. Because the Fourier heat transfer equation at short times and large dimensions does not have sufficient accuracy; a non-Fourier form of heat transfer equation has been used. Due to the fact that the beam is moving in x direction, the temperature distribution and the melting pool shape are not asymmetric. As a result, the problem is a transient threedimensional problem. Therefore, thermophysical properties such as heat conductivity coefficient, density and heat capacity are functions of temperature and material states. The enthalpy technique, used for the solution of phase change problems, has been used in an explicit finite volume form for the hyperbolic heat transfer equation. This technique has been used to calculate the transient temperature distribution in the semi-infinite body and the growth rate of the melt pool. In order to validate the numerical results, comparisons were made with experimental data. Finally, the results of this paper were compared with similar problem that has used the Fourier theory. The comparison shows the influence of infinite speed of heat propagation in Fourier theory on the temperature distribution and the melt pool size.

Keywords: Non-Fourier, Enthalpy technique, Melt pool, Radiational boundary condition

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Authors: Mohammad R. Jalali, Mohammad M. Jalali

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The earliest theories of sloshing waves and solitary waves based on potential theory idealisations and irrotational flow have been extended to be applicable to more realistic domains. To this end, the computational fluid dynamics (CFD) methods are widely used. Three-dimensional CFD methods such as Navier-Stokes solvers with volume of fluid treatment of the free surface and Navier-Stokes solvers with mappings of the free surface inherently impose high computational expense; therefore, considerable effort has gone into developing depth-averaged approaches. Examples of such approaches include Green–Naghdi (GN) equations. In Cartesian system, GN velocity profile depends on horizontal directions, x-direction and y-direction. The effect of vertical direction (z-direction) is also taken into consideration by applying weighting function in approximation. GN theory considers the effect of vertical acceleration and the consequent non-hydrostatic pressure. Moreover, in GN theory, the flow is rotational. The present study illustrates the application of GN equations to propagation of sloshing waves and solitary waves. For this purpose, GN equations solver is verified for the benchmark tests of Gaussian hump sloshing and solitary wave propagation in shallow basins. Analysis of the free surface sloshing of even harmonic components of an initial Gaussian hump demonstrates that the GN model gives predictions in satisfactory agreement with the linear analytical solutions. Discrepancies between the GN predictions and the linear analytical solutions arise from the effect of wave nonlinearities arising from the wave amplitude itself and wave-wave interactions. Numerically predicted solitary wave propagation indicates that the GN model produces simulations in good agreement with the analytical solution of the linearised wave theory. Comparison between the GN model numerical prediction and the result from perturbation analysis confirms that nonlinear interaction between solitary wave and a solid wall is satisfactorilly modelled. Moreover, solitary wave propagation at an angle to the x-axis and the interaction of solitary waves with each other are conducted to validate the developed model.

Keywords: Even harmonic components of sloshing waves, Green–Naghdi equations, nonlinearity, solitary waves.

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Authors: Yiqin Lin, Liang Bao, Yimin Wei

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In this paper we study numerical methods for solving Sylvester matrix equations of the form AX +XBT +CDT = 0. A new projection method is proposed. The union of Krylov subspaces in A and its inverse and the union of Krylov subspaces in B and its inverse are used as the right and left projection subspaces, respectively. The Arnoldi-like process for constructing the orthonormal basis of the projection subspaces is outlined. We show that the approximate solution is an exact solution of a perturbed Sylvester matrix equation. Moreover, exact expression for the norm of residual is derived and results on finite termination and convergence are presented. Some numerical examples are presented to illustrate the effectiveness of the proposed method.

Keywords: Arnoldi process, Krylov subspace, Iterative method, Sylvester equation, Dissipative matrix.

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Authors: Arti Vaish, Harish Parthasarathy

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The scalar wave equation for a potential in a curved space time, i.e., the Laplace-Beltrami equation has been studied in this work. An action principle is used to derive a finite element algorithm for determining the modes of propagation inside a waveguide of arbitrary shape. Generalizing this idea, the Maxwell theory in a curved space time determines a set of linear partial differential equations for the four electromagnetic potentials given by the metric of space-time. Similar to the Einstein-s formulation of the field equations of gravitation, these equations are also derived from an action principle. In this paper, the expressions for the action functional of the electromagnetic field have been derived in the presence of gravitational field.

Keywords: General theory of relativity, electromagnetism, metric tensor, Maxwells equations, test functions, finite element method.

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Authors: M. Saeedi, R. Wuchner, K.-U. Bletzinger

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In order to study the aerodynamic performance of a semi-flexible membrane wing, Fluid-Structure Interaction simulations have been performed. The fluid problem has been modeled using two different approaches which are the vortex panel method and the numerical solution of the Navier-Stokes equations. Nonlinear analysis of the structural problem is performed using the Finite Element Method. Comparison between the two fluid solvers has been made. Aerodynamic performance of the wing is discussed regarding its lift and drag coefficients and they are compared with those of the equivalent rigid wing.

Keywords: CFD, FSI, Membrane wing, Vortex panel method.

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Authors: Djemai Bara, Mohamed Faouzi Mahboub, Djamila Bennaceur-Doumaz

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In this work, the role of the preformed plasma created on the front face of a target, irradiated by a high intensity short pulse laser, in the framework of ion acceleration process, modeled by Target Normal Sheath Acceleration (TNSA) mechanism, is studied. This plasma is composed of cold ions governed by fluid equations and non-thermal & trapped with densities represented by a "Cairns-Gurevich" equation. The self-similar solution of the equations shows that electronic trapping and the presence of non-thermal electrons in the pre-plasma are both responsible in ion acceleration as long as the proportion of energetic electrons is not too high. In the case where the majority of electrons are energetic, the electrons are accelerated directly by the ponderomotive force of the laser without the intermediate of an accelerating plasma wave.

Keywords: Cairns-Gurevich Equation, ion acceleration, plasma expansion, pre-plasma.

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Authors: Tan K. B., Norhashidah Hj. M. Ali

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In this article, we aim to discuss the formulation of two explicit group iterative finite difference methods for time-dependent two dimensional Burger-s problem on a variable mesh. For the non-linear problems, the discretization leads to a non-linear system whose Jacobian is a tridiagonal matrix. We discuss the Newton-s explicit group iterative methods for a general Burger-s equation. The proposed explicit group methods are derived from the standard point and rotated point Crank-Nicolson finite difference schemes. Their computational complexity analysis is discussed. Numerical results are given to justify the feasibility of these two proposed iterative methods.

Keywords: Standard point Crank-Nicolson (CN), Rotated point Crank-Nicolson (RCN), Explicit Group (EG), Explicit Decoupled Group (EDG).

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Authors: Zhenying Hong, Guangwei Yuan, Xuedong Fu, Shulin Yang

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In this paper, the typical exponential method, diamond difference and modified time discrete scheme is researched for self adaptive time step. The second-order time evolution scheme is applied to time-dependent spherical neutron transport equation by discrete ordinates method. The numerical results show that second-order time evolution scheme associated exponential method has some good properties. The time differential curve about neutron current is more smooth than that of exponential method and diamond difference and modified time discrete scheme.

Keywords: Exponential method, diamond difference, modified time discrete scheme, second-order time evolution scheme.

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Authors: Pranav Ravikumar, Arunabha Bera, Vijay K. Mehra, Anand Kumar

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This paper solves the Non Linear Schrodinger Equation using the Split Step Fourier method for modeling an optical fiber. The model generates a complex wave of optical pulses and using the results obtained two graphs namely Loss versus Wavelength and Dispersion versus Wavelength are generated. Taking Chromatic Dispersion and Polarization Mode Dispersion losses into account, the graphs generated are compared with the graphs formulated by JDS Uniphase Corporation which uses standard values of dispersion for optical fibers. The graphs generated when compared with the JDS Uniphase Corporation plots were found to be more or less similar thus verifying that the model proposed is right. MATLAB software was used for doing the modeling.

Keywords: Modulation, Non Linear Schrodinger Equation, Optical fiber, Split Step Fourier Method.

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Authors: Punit Kumar, Niraj Kumar

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The influence of transverse surface roughness on EHL characteristics has been investigated numerically using an extensive set of full EHL line contact simulations for shear-thinning lubricants under pure sliding condition. The shear-thinning behavior of lubricant is modeled using Carreau viscosity equation along with Doolittle-Tait equation for lubricant compressibility. The surface roughness is assumed to be sinusoidal and it is present on the stationary surface. It is found that surface roughness causes sharp pressure peaks along with reduction in central and minimum film thickness. With increasing amplitude of surface roughness, the minimum film thickness decreases much more rapidly as compared to the central film thickness.

Keywords: EHL, Carreau, Shear-thinning, Surface Roughness, Amplitude, Wavelength.

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Authors: Shafiq R. Qureshi, Syed Noman Danish, Muhammad Saeed Khalid

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Fossil fuels are the major source to meet the world energy requirements but its rapidly diminishing rate and adverse effects on our ecological system are of major concern. Renewable energy utilization is the need of time to meet the future challenges. Ocean energy is the one of these promising energy resources. Threefourths of the earth-s surface is covered by the oceans. This enormous energy resource is contained in the oceans- waters, the air above the oceans, and the land beneath them. The renewable energy source of ocean mainly is contained in waves, ocean current and offshore solar energy. Very fewer efforts have been made to harness this reliable and predictable resource. Harnessing of ocean energy needs detail knowledge of underlying mathematical governing equation and their analysis. With the advent of extra ordinary computational resources it is now possible to predict the wave climatology in lab simulation. Several techniques have been developed mostly stem from numerical analysis of Navier Stokes equations. This paper presents a brief over view of such mathematical model and tools to understand and analyze the wave climatology. Models of 1st, 2nd and 3rd generations have been developed to estimate the wave characteristics to assess the power potential. A brief overview of available wave energy technologies is also given. A novel concept of on-shore wave energy extraction method is also presented at the end. The concept is based upon total energy conservation, where energy of wave is transferred to the flexible converter to increase its kinetic energy. Squeezing action by the external pressure on the converter body results in increase velocities at discharge section. High velocity head then can be used for energy storage or for direct utility of power generation. This converter utilizes the both potential and kinetic energy of the waves and designed for on-shore or near-shore application. Increased wave height at the shore due to shoaling effects increases the potential energy of the waves which is converted to renewable energy. This approach will result in economic wave energy converter due to near shore installation and more dense waves due to shoaling. Method will be more efficient because of tapping both potential and kinetic energy of the waves.

Keywords: Energy Utilizing, Wave Shoaling Phenomenon

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Authors: Chien-Hua Lee, Cheng-Yi Chen

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The stability test problem for homogeneous large-scale perturbed bilinear time-delay systems subjected to constrained inputs is considered in this paper. Both nonlinear uncertainties and interval systems are discussed. By utilizing the Lyapunove equation approach associated with linear algebraic techniques, several delay-independent criteria are presented to guarantee the robust stability of the overall systems. The main feature of the presented results is that although the Lyapunov stability theorem is used, they do not involve any Lyapunov equation which may be unsolvable. Furthermore, it is seen the proposed schemes can be applied to solve the stability analysis problem of large-scale time-delay systems.

Keywords: homogeneous bilinear system, constrained input, time-delay, uncertainty, transient response, decay rate.

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Itô chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition method using the Wiener-Itô chaos expansion. Once the approximation of the solution is performed using the finite element method for example, the statistics of the numerical solution can be easily evaluated.

Keywords: Eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Itô chaos expansion.

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Authors: Stephen Kirkup

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This paper discusses the implementation of the boundary element method (BEM) on an Excel spreadsheet and how it can be used in teaching vector calculus and simulation. There are two separate spreadheets, within which Laplace equation is solved by the BEM in two dimensions (LIBEM2) and axisymmetric three dimensions (LBEMA). The main algorithms are implemented in the associated programming language within Excel, Visual Basic for Applications (VBA). The BEM only requires a boundary mesh and hence it is a relatively accessible method. The BEM in the open spreadsheet environment is demonstrated as being useful as an aid to teaching and learning. The application of the BEM implemented on a spreadsheet for educational purposes in introductory vector calculus and simulation is explored. The development of assignment work is discussed, and sample results from student work are given. The spreadsheets were found to be useful tools in developing the students’ understanding of vector calculus and in simulating heat conduction.

Keywords: Boundary element method, laplace equation, vector calculus, simulation, education.

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Authors: Karandeep Singh, Baibing Li

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Traffic density, an indicator of traffic conditions, is one of the most critical characteristics to Intelligent Transport Systems (ITS). This paper investigates recursive traffic density estimation using the information provided from inductive loop detectors. On the basis of the phenomenological relationship between speed and density, the existing studies incorporate a state space model and update the density estimate using vehicular speed observations via the extended Kalman filter, where an approximation is made because of the linearization of the nonlinear observation equation. In practice, this may lead to substantial estimation errors. This paper incorporates a suitable transformation to deal with the nonlinear observation equation so that the approximation is avoided when using Kalman filter to estimate the traffic density. A numerical study is conducted. It is shown that the developed method outperforms the existing methods for traffic density estimation.

Keywords: Density estimation, Kalman filter, speed-densityrelationship, Traffic surveillance.

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