Numerical Simulation of Thermocapillary-Buoyancy Convection in Encapsulated Liquid Column With Deformable Interfaces

2009 ◽  
Author(s):  
Lan Peng ◽  
Juan-Fang Liu ◽  
You-Rong Li ◽  
Yan Wang
Keyword(s):  
Numerical Simulation ◽  
Liquid Bridge ◽  
Immiscible Liquid ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Buoyancy Convection ◽  
Valuable Method ◽  
Dimensional Parameters ◽  
Physical And Mathematical Models ◽  
Volume Method

The physical and mathematical models of thermocapillary-buoyancy convection in two immiscible liquid layers are established. In order to capture the free surface and the liquid-liquid interface deformation, Runge-Kutta method is adopted to solve the Young-Laplace equation. Numerical simulation of thermocapillary-buoyancy convection in encapsulated liquid bridge is performed by employing primitive valuable method and finite volume method. The fluids of liquid bridge and liquid encapsulation are FC-70 and KF-96, respectively. Furthermore, the profiles of temperature and velocity in encapsulated liquid bridge are obtained. Meanwhile, the effects of a series of non-dimensional parameters on the thermocapillary-buoyancy convection are analyzed.

Research on Numerical Simulation of Quad Bundle Conductor on Galloping

2013 ◽  
Vol 457-458 ◽  
pp. 23-27
Author(s):  
Xue Ping Zhan ◽  
Kuan Jun Zhu ◽  
Cao Lan Liu ◽  
Bin Liu ◽  
Jun Zhang ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Numerical Results ◽  
Kutta Method ◽  
Aerodynamic Parameter ◽  
Runge Kutta Method ◽  
Simulation Results ◽  
Runge Kutta ◽  
Element Method

The models of the multi-bundled conductors are constructed by finite element method in this paper. The numerical results are given by using the 4th order Runge-Kutta method considering aerodynamic parameter of sub-conductor. The simulation results are obtained on galloping of quad bundle conductors with the different span. Thus some effective numerical results of quad twin bundle conductor can provide a useful reference for anti-galloping design.

Symmetric and symplectic methods for gyrocenter dynamics in time-independent magnetic fields

2016 ◽  
Vol 07 (02) ◽  
pp. 1650008 ◽  
Author(s):  
Beibei Zhu ◽  
Zhenxuan Hu ◽  
Yifa Tang ◽  
Ruili Zhang
Keyword(s):  
Numerical Simulation ◽  
Hamiltonian System ◽  
Second Order ◽  
Symplectic Methods ◽  
Kutta Method ◽  
Numerical Accuracy ◽  
Runge Kutta Method ◽  
Simulation Results ◽  
Runge Kutta

We apply a second-order symmetric Runge–Kutta method and a second-order symplectic Runge–Kutta method directly to the gyrocenter dynamics which can be expressed as a noncanonical Hamiltonian system. The numerical simulation results show the overwhelming superiorities of the two methods over a higher order nonsymmetric nonsymplectic Runge–Kutta method in long-term numerical accuracy and near energy conservation. Furthermore, they are much faster than the midpoint rule applied to the canonicalized system to reach given precision.

scholarly journals Comparison of Numerical Simulation of Epidemiological Model between Euler Method with 4th Order Runge Kutta Method

2021 ◽  
Vol 2 (1) ◽  
pp. 37-44
Author(s):  
Rizky Ashgi
Keyword(s):  
Numerical Simulation ◽  
Numerical Methods ◽  
Sir Model ◽  
Euler Method ◽  
Kutta Method ◽  
System Of Differential Equations ◽  
Runge Kutta Method ◽  
Global Pandemic ◽  
The World ◽  
Runge Kutta

Coronavirus Disease 2019 has become global pandemic in the world. Since its appearance, many researchers in world try to understand the disease, including mathematics researchers. In mathematics, many approaches are developed to study the disease. One of them is to understand the spreading of the disease by constructing an epidemiology model. In this approach, a system of differential equations is formed to understand the spread of the disease from a population. This is achieved by using the SIR model to solve the system, two numerical methods are used, namely Euler Method and 4th order Runge-Kutta. In this paper, we study the performance and comparison of both methods in solving the model. The result in this paper that in the running process of solving it turns out that using the euler method is faster than using the 4th order Runge-Kutta method and the differences of solutions between the two methods are large.

Applications of Numerical Simulation of Solar Cooker Type Box With Multi-Step Inner Reflector

Solar Energy ◽  
2003 ◽  
Author(s):  
H. Terre´s-Pen˜a ◽  
P. Quinto-Diez
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Thermal Conversion ◽  
Numerical Results ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Energetic Analysis ◽  
The Mathematical Model ◽  
Solar Rays

It is shown a mathematical model of a solar box cooker with multi-step inner reflector and the numerical results for two applications has been analyzed. These applications are 1. Numerical simulation of operation of solar box cooker with multi-step inner reflector in Tanta, Egypt and 2. Numerical simulation of solar box cooker with multi-step inner reflector for 10 hours of operation. In the case 1, is analyzed a solar box cooker constructed and evaluated in Tanta, Egypt [1]. The experimental results that was obtained are compared with the numerical results that was obtained for the mathematical model. The case 2, is an evaluation of numerical results that was obtained for the operation of 10 hours for solar box cooker constructed in the Laboratorio de Ingenieri´a Te´rmica e Hidra´ulica Aplicada (LABINTHAP) in Me´xico City. [4] The solar box cooker is integrated by a covert that was made with double glass, this is use with two purposes, reduce the loss heat convection with outer and to generated the greenhouse effect with inner of cooker. In the inner of cooker there are a mirrors arrangement in inclined position (inner reflectors) placed in angles of 30°, 45° and 75°, these helped to reflex the solar rays in direction to the cook recipient. The recipient also received the solar rays in the upper part (lid). The mathematical model that was obtained from energetic analysis, is formed for five differential equations system no linear and the fourth Runge-Kutta method is used to resolve it. The numerical solution of the equations system is obtained with a computational software in C++. This work is a contribution to the application of numerical methods and computational for development of the solar energy used in thermal conversion equipments. The use of these techniques to solve the mathematical model is important to contribute in the evaluation and design of solar box cookers with multi-step inner reflector.

A Numerical Study of Effect of Liquid Encapsulation on Thermocapillary Convection in Liquid Bridge

2004 ◽  
Author(s):  
Lan Peng ◽  
Dan-Ling Zeng ◽  
You-Rong Li
Keyword(s):  
Numerical Simulation ◽  
Crystal Growth ◽  
Liquid Bridge ◽  
Function Method ◽  
Thermocapillary Convection ◽  
Numerical Study ◽  
Flow Profile ◽  
Float Zone ◽  
Physical And Mathematical Models

The physical and mathematical models of the thermocapillary convection in liquid bridge with liquid encapsulation are established in the present paper. A numerical simulation of the thermocapillary convection in liquid bridge with liquid encapsulation is performed by employed vorticity-stream function method and the Alternative Direction Implicit scheme in finite difference. The distribution of temperature and flow in liquid columns is then obtained. It is verified that liquid encapsulation can reduce the thermocapillary convection in liquid bridge and can improve the quality of crystal growth in float zone. The influence law of the thickness of liquid encapsulation on the thermocapillary convection in liquid bridge is obtained, the more thickness of liquid encapsulation decreases, the more the thermocapillary convection in the inner liquid and the outer liquid diminishes. It is found that the flow profile of two liquid columns is much more complex than that of single liquid column.

A Modification of Pragmatical Generalized Synchronization of Chaotic Systems with Uncertain Parameters by Adaptive Control

2012 ◽  
Vol 442 ◽  
pp. 375-378 ◽  
Author(s):  
Wen Guang Zhang ◽  
Jun Wei Lei ◽  
Guo Qiang Liang
Keyword(s):  
Numerical Simulation ◽  
Adaptive Control ◽  
Chaotic Systems ◽  
Uncertain Parameters ◽  
Generalized Synchronization ◽  
Kutta Method ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Runge Kutta Method

A modification to the synchronization law in [Zheng-Ming Ge, Pragmatical generalized synchronization of chaotic systems with uncertain parameters by adaptive control, Physica D (2007) 87-94] is proposed. To verify and demonstrate the effectiveness of the proposed method, a numerical simulation is done and the fourth-order Runge-Kutta method is used to solve the system with time step size 0.001.

scholarly journals Numerical Investigation on Heat and Mass transfer through a porous medium in the presence of MHD and Chemical Reaction

2021 ◽  
Vol 12 (2) ◽  
pp. 1178-1182
Author(s):  
R.Kavitha, Et. al.
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Heat And Mass Transfer ◽  
Chemical Reaction ◽  
Schmidt Number ◽  
Magnetic Parameter ◽  
Kutta Method ◽  
Governing Equations ◽  
Runge Kutta Method ◽  
Dimensional Parameters

An attempt has been made to investigate the heat and mass transfer through a porous medium in the presence of Magnetohydrodynamic flow and chemical reaction. On the basis of certain assumptions, the momentum, energy and concentration equations are obtained. These governing equations are transformed into ordinary differential equations using self-suitable transformations and these resulting equations are solved numerically using shooting procedure with fourth order Runge-Kutta Method. The effect of various non- dimensional parameters like magnetic parameter (M), Schmidt number (Sc), Chemical reaction (Kr) are discussed with the help of graphs.

scholarly journals Numerical Investigation of Fuzzy Predator-Prey Model with a Functional Response of the Form Arctan(ax)

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1919
Author(s):  
Saed Mallak ◽  
Doa’a Farekh ◽  
Basem Attili
Keyword(s):  
Numerical Simulation ◽  
Numerical Investigation ◽  
Functional Response ◽  
Kutta Method ◽  
Predator Prey ◽  
Generalized Hukuhara Derivative ◽  
Predator Prey Model ◽  
Runge Kutta Method ◽  
Prey Model ◽  
Over Time

In this paper we study a fuzzy predator-prey model with functional response arctan(ax). The fuzzy derivatives are approximated using the generalized Hukuhara derivative. To execute the numerical simulation, we use the fuzzy Runge-Kutta method. The results obtained over time for the evolution and the population are presented numerically and graphically with some conclusions.

Sign in / Sign up

Export Citation Format

Share Document