Search for: runge-kutta-methods
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#### An improved progressive preconditioning method for steady non-cavitating and sheet-cavitating flows

, Article International Journal for Numerical Methods in Fluids ; Volume 68, Issue 2 , December , 2012 , Pages 210-232 ; 02712091 (ISSN) Esfahanian, V ; Akbarzadeh, P ; Hejranfar, K ; Sharif University of Technology
2012
Abstract
An improved progressive preconditioning method for analyzing steady inviscid and laminar flows around fully wetted and sheet-cavitating hydrofoils is presented. The preconditioning matrix is adapted automatically from the pressure and/or velocity flow-field by a power-law relation. The cavitating calculations are based on a single fluid approach. In this approach, the liquid/vapour mixture is treated as a homogeneous fluid whose density is controlled by a barotropic state law. This physical model is integrated with a numerical resolution derived from the cell-centered Jameson's finite volume algorithm. The stabilization is achieved via the second-and fourth-order artificial dissipation...

#### Desulfurization of liquid-phase Butane by zeolite molecular sieve 13X in a fixed bed: Modeling, simulation, and comparison with commercial-scale plant data

, Article Energy and Fuels ; Volume 22, Issue 1 , 2008 , Pages 570-575 ; 08870624 (ISSN) Shams, A ; Molaei Dehkordi, A ; Goodarznia, I ; Sharif University of Technology
2008
Abstract
This paper deals with the modeling and simulation of binary liquid-phase adsorption of methyl mercaptan and hydrogen sulfide from a liquid butane stream by zeolite molecular sieve 13X in a fixed bed. The model equations account for the effect of axial dispersion and the inter- and intraparticle, mass-transfer resistances at isothermal operating conditions. Orthogonal collocation and Gill's fourth-order Runge-Kutta methods were used to solve the dimensionless general forms of the 4N-eoupled ordinary differential equations for simultaneous adsorption of the solutes by the adsorbent in a fixed bed. The model predictions were compared to the commercial-scale plant data of an Iranian...

#### Large-eddy simulation of heavy-particle transport in turbulent channel flow

, Article Numerical Heat Transfer, Part B: Fundamentals ; Volume 50, Issue 4 , 2006 , Pages 285-313 ; 10407790 (ISSN) Elhami Amiri, A ; Kazemzadeh Hannani, S ; Mashayek, F ; Sharif University of Technology
2006
Abstract
Large-eddy simulations are carried out for a particle-laden vertical turbulent channel flow at Reynolds number of 180 based on friction velocity and channel half-width. To minimize the numerical and aliasing errors, a fourth-order compact finite-volume method in space and a fourth-order Runge-Kutta method in time along with a dynamic Smagorinsky model with explicit filter-grid size ratio 2 have been used to solve the filtered equations of the carrier flow. Heavy, small particle motion is governed by drag, gravitational, and Saffman lift forces in the Lagrangian frame. These particle equations are integrated in time using a second-order Adams-Bashforth method. The effect of subgrid-scale...

#### H2O based different nanofluids with unsteady condition and an external magnetic field on permeable channel heat transfer

, Article International Journal of Hydrogen Energy ; Volume 42, Issue 34 , 2017 , Pages 22005-22014 ; 03603199 (ISSN) Biglarian, M ; Rahimi Gorji, M ; Pourmehran, O ; Domairry, G ; Sharif University of Technology
Abstract
This paper investigates numerically the problem of unsteady magnetohydrodynamic nanofluid flow and heat transfer between parallel plates due to the normal motion of the porous upper plate. The governing equations are solved via the fourth-order Runge-Kutta method. Different kind of nanoparticles is examined. The effects of kind of nanoparticle, nanofluid volume fraction, expansion ratio, Hartmann number, Reynolds number on velocity and temperature profiles are considered. Also effect of different types of nanoparticles is examined. Results indicate that velocity decreases with increase of Hartmann number due to effect of Lorentz forces. Rate of heat transfer increase with increase of...

#### Dynamic pull-in instability and vibration analysis of a nonlinear microcantilever gyroscope under step voltage considering squeeze film damping

, Article International Journal of Applied Mechanics ; Volume 5, Issue 3 , September , 2013 ; 17588251 (ISSN) Mojahedi, M ; Ahmadian, M. T ; Firoozbakhsh, K ; Sharif University of Technology
2013
Abstract
In this paper, a nonlinear model is used to analyze the dynamic pull-in instability and vibrational behavior of a microcantilever gyroscope. The gyroscope has a proof mass at its end and is subjected to nonlinear squeeze film damping, step DC voltages as well as base rotation excitation. The electrostatically actuated and detected microgyroscopes are subjected to coupled flexural-flexural vibrations that are related by base rotation. In order to detune the stiffness and natural frequencies of the system, DC voltages are applied to the proof mass electrodes in drive and sense directions. Nonlinear integro differential equations of the system are derived using extended Hamilton principle...

#### Timoshenko versus Euler-Bernoulli beam theories for high speed two-link manipulator

, Article Scientia Iranica ; Volume 20, Issue 1 , 2013 , Pages 172-178 ; 10263098 (ISSN) Zohoor, H ; Kakavand, F ; Sharif University of Technology
2013
Abstract
In this paper, a two-link flexible manipulator is considered. For a prescribed motion, Timoshenko and Euler-Bernoulli beam models are considered. Using the Galerkin method, nonlinear equations of motion are solved. The Runge-Kutta method is employed for the time response integration method. A comparative study is made between the Euler-Bernoulli and Timoshenko beam models, with and without foreshortening effects. It is demonstrated that for two-link manipulators, both theories provide good models, and the results for both theories are very similar for all ranges of slenderness ratio. The findings suggest that for two-link manipulators with relatively high slenderness ratios, there is a...

#### Investigation on effects of the sleeper defects on rail vehicle vibration

, Article ASME 2012 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2012, Chicago, IL, 12 August 2012 through 12 August 2012 ; Volume 1, Issue parts A and B , 2012 , Pages 865-871 ; 9780791845004 (ISBN) Mortezaee, H ; Jalili, M. M ; Ahmadian, M. T ; Sharif University of Technology
2012
Abstract
In this article effects of sleepers defect on rail vehicle vibration have been investigated. Two parallel rails of the track have been modeled as Euler-Bernoulli beams on elastic points as rail pads. Also sleepers have been modeled as visco-elastic Euler-Bernoulli beams. It is assumed that, some sleepers under the rail track have been fractured and modeled by two beams. The wheelset has 5 DOF which are longitudinal, vertical and lateral movements plus roll and axial rotations. To determine normal contact force between wheel and rail, relative position of wheel and rail has been determined at each instant. Using the coordinate of each wheel points in rail coordinate system, the penetration of...

#### Nonlinear vibration analysis of a micro beam exposed to an external flow

, Article ASME 2011 International Mechanical Engineering Congress and Exposition, IMECE 2011 ; Volume 7, Issue PARTS A AND B , 2011 , Pages 643-646 ; 9780791854938 (ISBN) Mazaheri, H ; Hosseinzadeh, A ; Ahmadian, M. T ; Barari, A ; Sharif University of Technology
2011
Abstract
In this paper, nonlinear vibration of a micro cantilever exposed to a constant velocity flow is studied. In order to obtain vibration frequency and time response of the micro beam the variational iteration method is used as a novel tool for solving nonlinear differential equations. Results of the analytical solution are compared with those obtained by Runge-Kutta method which shows very good agreement between them. Results confirm that frequency of vibration depends on the flow velocity. Also, the high sensitivity of the vibration frequency to the flow velocity means that it can be an effective indicator of velocity

#### On application of high-order compact finite-difference schemes to compressible vorticity confinement method

, Article Aerospace Science and Technology ; Volume 46 , October–November , 2015 , Pages 398-411 ; 12709638 (ISSN) Sadri, M ; Hejranfar, K ; Ebrahimi, M ; Sharif University of Technology
Elsevier Masson SAS  2015
Abstract
The main goal of this study is to assess the application of high-order compact finite-difference schemes for the solution of the Euler equations in conjunction with the compressible vorticity confinement method on both uniform Cartesian and curvilinear grids. Here, the spatial discretization of the governing equations is performed by the fourth-order compact finite-difference scheme and the temporal term is discretized by the fourth-order Runge-Kutta method. To stabilize the numerical solution, appropriate dissipation terms are applied and a detail assessment is performed to study the effects of the values of confinement and dissipation coefficients on the solution to reasonably preserve the...

#### Stresses in thin-walled beams subjected to atraversing mass under a pulsating force

, Article Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science ; Volume 224, Issue 11 , April , 2010 , Pages 2363-2372 ; 09544062 (ISSN) Dehestani, M ; Vafai, A ; Mofid, M ; Sharif University of Technology
2010
Abstract
An analytical-numerical method to determine the dynamic response of beams with various boundary conditions subjected to a moving mass under a pulsating force is explained. Governing partial differential equations of the system are changed to a convenience type of ordinary differential equations to be solved through a Runge-Kutta scheme. Pulsating force specifications influenced the dynamic response of the beam depending on the moving mass properties. Results showed the significant effect of the boundary conditions on the dynamic response of the beam, which was considered rarely in the past. Stiffening the constraints reduces the maximum stresses in the beams. Results for identical...

#### A high-order nodal discontinuous galerkin method for solution of compressible non-cavitating and cavitating flows

, Article Computers and Fluids ; Volume 156 , 2017 , Pages 175-199 ; 00457930 (ISSN) Hejranfar, K ; Hajihassanpour, M ; Sharif University of Technology
Abstract
In this work, a high-order nodal discontinuous Galerkin method is applied and assessed for the simulation of compressible non-cavitating and cavitating flows. The one-fluid approach with the thermal effects is used to properly model the cavitation phenomenon. Here, the spatial and temporal derivatives in the system of governing equations are discretized using the nodal discontinuous Galerkin method and the third-order TVD Runge–Kutta method, respectively. Various numerical fluxes such as the Roe, Rusanov, HLL, HLLC and AUSM+-up and two discontinuity capturing methods, namely, the generalized MUSCL limiter and a generalized exponential filter are implemented in the solution algorithm. At...

#### Causal description of the interaction of a two-level atom with a classical field

, Article Physica Scripta ; Volume 78, Issue 3 , 28 August , 2008 ; 00318949 (ISSN) Mousavi, S. V ; Golshani, M ; Sharif University of Technology
2008
Abstract
We discuss the Bohmian paths of two-level atoms moving in a waveguide through an external resonance-producing field, perpendicular to the waveguide and localized in a region of finite diameter. The time spent by a particle in a potential region is not well-defined in standard quantum mechanics, but it is well defined in Bohmian mechanics. Bohm's theory is used for calculating the average time spent by a transmitted particle inside the field region and the arrival-time distributions at the edges of the field region. Using the Runge-Kutta method for the integration of the guidance law, some Bohmian trajectories were also calculated. Numerical results are presented for the special case of a...

#### Development and verification of a model to describe an immobilized glucose isomerase packed bed bioreactor

, Article Biochemical Engineering Journal ; Volume 40, Issue 2 , 2008 , Pages 328-336 ; 1369703X (ISSN) Khalilpour, R ; Roostaazad, R ; Sharif University of Technology
2008
Abstract
In this paper, the performance of immobilized packed bed glucose isomerase enzyme was mathematically modeled. A modified Michaelis-Menten type relation was used to describe the enzyme kinetics. Mass transfer inside the biocatalyst particle and through the bed column was analyzed simultaneously. Using measured data, physicochemical properties including diffusivity, viscosity and density of sugar solutions were correlated with its concentrations and were used to provide precision in solving the set of model equations. Model equations were solved using the Runge-Kutta and Gauss-Seidel algorithms and finite difference numerical method in MATLAB environment. Model output was used to demonstrate...

#### A higher-order Boussinesq-type model with moving bottom boundary: Applications to submarine landslide tsunami waves

, Article International Journal for Numerical Methods in Fluids ; Volume 53, Issue 6 , 2007 , Pages 1019-1048 ; 02712091 (ISSN) Ataie Ashtiani, B ; Najafi Jilani, A ; Sharif University of Technology
2007
Abstract
A two-dimensional depth-integrated numerical model is developed using a fourth-order Boussinesq approximation for an arbitrary time-variable bottom boundary and is applied for submarine-landslide-generated waves. The mathematical formulation of model is an extension of (4,4) Padé approximant for moving bottom boundary. The mathematical formulations are derived based on a higher-order perturbation analysis using the expanded form of velocity components. A sixth-order multi-step finite difference method is applied for spatial discretization and a sixth-order Runge-Kutta method is applied for temporal discretization of the higher-order depth-integrated governing equations and boundary...

#### Oscillating pipe flow: High-resolution simulation of nonlinear mechanisms

, Article 2006 ASME Joint U.S.- European Fluids Engineering Division Summer Meeting, FEDSM2006, Miami, FL, 17 July 2006 through 20 July 2006 ; Volume 1 SYMPOSIA , 2006 , Pages 1-10 ; 0791847500 (ISBN); 9780791847503 (ISBN) Ghasemi, A ; Sharif University of Technology
American Society of Mechanical Engineers  2006
Abstract
A new perspective suitable for understanding the details of nonlinear pumping (formation of traveling shocks) inside a pressurized cavity is constructed in this paper. Full compressible axisymmetric three-dimensional Navier-Stokes equations are used as the starting point to cover all complexities of the problem that exceedingly increase for particular ranges of Mach, Reynolds and Prandtl numbers. Then a very high-order numerical method is introduced to preserve the user-defined order of accuracy for practical simulations. For removal of spurious waves, higher-order compact filters are derived. All equations are marched in time using the classical Runge-Kutta algorithm which is appropriate...

#### Numerical study of shock-disturbances interaction in hypersonic inviscid flows with real gas effects using high-order WENO scheme

, Article Computers and Fluids ; Volume 229 , 2021 ; 00457930 (ISSN) Rahmani, S ; Hejranfar, K ; Sharif University of Technology
Elsevier Ltd  2021
Abstract
In the present study, the shock-disturbances interaction in hypersonic inviscid flows with real gas effects is studied by applying a high-order accurate numerical method with the shock capturing technique. To consider real gas effects, the equilibrium air model is utilized here. The strong conservative form of the unsteady compressible Euler equations in the 2D generalized curvilinear coordinates is formulated and the resulting system of equations for the equilibrium air model is discretized by using the fifth-order finite-difference WENO scheme in space and the explicit third-order TVD Runge–Kutta scheme in time to provide a highly accurate and robust equilibrium airflow solver. The...

#### A high-order compact finite-difference lattice Boltzmann method for simulation of steady and unsteady incompressible flows

, Article International Journal for Numerical Methods in Fluids ; Vol. 75, Issue. 10 , 2014 , Pages 713-746 ; ISSN: 02712091 Hejranfar, K ; Ezzatneshan, E ; Sharif University of Technology
Abstract
A high-order compact finite-difference lattice Boltzmann method (CFDLBM) is proposed and applied to accurately compute steady and unsteady incompressible flows. Herein, the spatial derivatives in the lattice Boltzmann equation are discretized by using the fourth-order compact FD scheme, and the temporal term is discretized with the fourth-order Runge-Kutta scheme to provide an accurate and efficient incompressible flow solver. A high-order spectral-type low-pass compact filter is used to stabilize the numerical solution. An iterative initialization procedure is presented and applied to generate consistent initial conditions for the simulation of unsteady flows. A sensitivity study is also...

#### Vibration analysis of a new type of compliant mechanism with flexible-link, using perturbation theory

, Article Mathematical Problems in Engineering ; Volume 2012 , February , 2012 ; 1024123X (ISSN) Viliani, N. S ; Zohoor, H ; Kargarnovin, M. H ; Sharif University of Technology
2012
Abstract
Vibration analysis of a new type of compliant parallel mechanism with flexible intermediate links is investigated. The application of the Timoshenko beam theory to the mathematical modeling of the intermediate flexible link is described, and the equations of motion of the flexible links are obtained by using Lagrange's equation of motion. The equations of motion are obtained in the form of a set of ordinary differential equations by using assumed mode method theory. The governing differential equations of motion are solved using perturbation method. The assumed mode shapes and frequencies are to be obtained based on clamped-clamped boundary conditions. Comparing perturbation method with...

#### Thermo-mechanical analysis of rotating disks with non-uniform thickness and material properties

, Article International Journal of Pressure Vessels and Piping ; Volume 98 , October , 2012 , Pages 95-101 ; 03080161 (ISSN) Hassani, A ; Hojjati, M. H ; Mahdavi, E ; Alashti, R. A ; Farrahi, G ; Sharif University of Technology
Elsevier  2012
Abstract
Theoretical and numerical analyses of rotating disks with non-uniform thickness and material properties subjected to thermo-mechanical loadings have been carried out by variable material properties (VMP), Runge-Kutta's (RK) and finite element (FE) methods. The material is assumed to be elastic-linear hardening. A power form function is used to describe the temperature gradient with the higher temperature at outer surface. Von-Mises theory has been used as failure criterion. The effects of geometry, material and thermal loading parameters as well as boundary conditions on radial, hoop and equivalent stress distributions which have not been studied in much detail in previous works have been...

#### Application of the variational iteration method for nonlinear free vibration of conservative oscillators

, Article Scientia Iranica ; Volume 19, Issue 3 , June , 2012 , Pages 513-518 ; 10263098 (ISSN) Baghani, M ; Fattahi, M ; Amjadian, A ; Sharif University of Technology
2012
Abstract
In this paper, an analytical solution for the nonlinear free vibration of a conservative oscillator is presented. The nonlinear governing equation is solved by employing the Variational Iteration Method (VIM). This method is based on the use of Lagrange multipliers for identification of optimal values of parameters in a function. Obtained results reveal that the proposed method is very effective, simple and exact. In the present investigation, the results of this method are compared with those of the Homotopy Analysis Method (HAM), as well as those predicted by the Runge-Kutta method. The excellent accuracy of the obtained results is demonstrated by comparing them with available analytical...
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