scholarly journals On Some Problems of the Numerical Implementation of Nonlinear Systems on Example of KPI Equation

2020 ◽  
Vol 226 ◽  
pp. 01003 ◽  
Author(s):  
Alexander V. Bogdanov ◽  
Vladimir V. Mareev
Keyword(s):  
Numerical Simulation ◽  
Wave Equations ◽  
Nonlinear Problems ◽  
Sufficient Accuracy ◽  
Numerical Implementation ◽  
Main Attention ◽  
Numerical Testing ◽  
Correct Representation ◽  
The Finite Difference Method ◽  
Calculated Region

Analytical and numerical peculiarities of solving nonlinear problems are considered on examples of wave equations like KdVB and Kadomtsev-Petviashvili-I equation (KPI). KPI is represented in integro-differential form. Main attention is paid to the problem of asymptotical behavior of solution and appearance of nonphysical artefacts. The numerical solution is carried out by the finite difference method. For a correct representation of the boundary condition along the y axis in numerical simulation a method is proposed for introducing small artificial convection into the original equation in the indicated direction. Along with the introduction of artificial convection, the procedure of trimming of the integral on the bands adjacent to the upper and lower boundaries of the calculated region is used. The results obtained by numerical testing, showed sufficient accuracy and validity of this procedure.

Numerical Simulation of Heat Transfer in a Closed Two-Phase Thermosiphon

2017 ◽  
Vol 743 ◽  
pp. 449-453
Author(s):  
Vladimir Arkhipov ◽  
Alexander Nee ◽  
Lily Valieva
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Phase Transitions ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Mathematical Modelling ◽  
Three Dimensional ◽  
Two Phase ◽  
One Dimensional ◽  
The Finite Difference Method

This paper presents the results of mathematical modelling of three–dimensional heat transfer in a closed two-phase thermosyphon taking into account phase transitions. Three-dimensional conduction equation was solved by means of the finite difference method (FDM). Locally one-dimensional scheme of Samarskiy was used to approximate the differential equations. The effect of the thermosyphon height and temperature of its bottom lid on the temperature difference in the vapor section was shown.

THE LANGEVIN OR KRAMERS APPROACH TO BIOLOGICAL MODELING

2004 ◽  
Vol 14 (10) ◽  
pp. 1561-1583 ◽  
Author(s):  
KARL P. HADELER ◽  
THOMAS HILLEN ◽  
FRITHJOF LUTSCHER
Keyword(s):  
Wave Equations ◽  
Space Variable ◽  
Linear Partial Differential Equation ◽  
Reaction Diffusion ◽  
Nonlinear Problems ◽  
Kramers Equation ◽  
Moment Approach ◽  
The Moment ◽  
Nonlinear Damped Wave Equations ◽  
And Diffusion

In the Langevin or Ornstein–Uhlenbeck approach to diffusion, stochastic increments are applied to the velocity rather than to the space variable. The density of this process satisfies a linear partial differential equation of the general form of a transport equation which is hyperbolic with respect to the space variable but parabolic with respect to the velocity variable, the Klein–Kramers or simply Kramers equation. This modeling approach allows for a more detailed description of individual movement and orientation dependent interaction than the frequently used reaction diffusion framework.For the Kramers equation, moments are computed, the infinite system of moment equations is closed at several levels, and telegraph and diffusion equations are derived as approximations. Then nonlinearities are introduced such that the semi-linear reaction Kramers equation describes particles which move and interact on the same time-scale. Also for these nonlinear problems a moment approach is feasible and yields nonlinear damped wave equations as limiting cases.We apply the moment method to the Kramers equation for chemotactic movement and obtain the classical Patlak–Keller–Segel model. We discuss similarities between chemotactic movement of bacteria and gravitational movement of physical particles.

scholarly journals Interaction of Solitons for Sine-Gordon-Type Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Georgii A. Omel’yanov ◽  
Israel Segundo-Caballero
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Analysis ◽  
Small Parameter ◽  
Wave Equations ◽  
Gordon Equation ◽  
Sine Gordon Equation ◽  
Semilinear Wave Equations ◽  
The Subject ◽  
Interaction Of Solitons

The subject of our consideration is a family of semilinear wave equations with a small parameter and nonlinearities which provide the existence of kink-type solutions (solitons). Using asymptotic analysis and numerical simulation, we demonstrate that solitons of the same type (kinks or antikinks) interact in the same manner as for the sine-Gordon equation. However, solitons of the different type preserve the shape after the interaction only in the case of two or three waves, and, moreover, under some additional conditions.

scholarly journals Numerical simulation of dynamic processes in transmission of vehicle

2021 ◽  
Vol 1 (1) ◽  
pp. 38-45
Author(s):  
S.I. Hoodorozhkov ◽  
◽  
A.А. Krasilnikov ◽  
Keyword(s):  
Numerical Simulation ◽  
Systematic Approach ◽  
Power Transmission ◽  
Combustion Engine ◽  
Dynamic Processes ◽  
Main Attention ◽  
Software Packages ◽  
Digital Modeling ◽  
Load Characteristics ◽  
Engine Friction

The article considers the issues of digital modeling of dynamic processes in the transmissions of vehicles. The purpose of this research was to develop an algorithm for numerical mathematical modeling of dynamic processes in the transmissions of transport vehicles using modern digital software packages. The method includes a systematic approach to the study of dynamic processes during switching, based on modeling the operation of the gearbox together with the internal com-bustion engine (taking into account its dynamic, speed and load characteristics). The order of appli-cation of the MATLab – Simulink, Simscape software for numerical simulation of dynamic pro-cesses is considered. Using the fundamental blocks of these applications, models of physical com-ponents are created: the internal combustion engine, friction clutches, gearboxes, elastic shafts, damping devices, and tractor power transmission control systems. A digital model of the tractor transmission is created, its design scheme is given, and the initial characteristics are set. It was used to simulate dynamic processes in the tractor gearbox. The main attention in this paper is paid to the application of the proposed method for calculating the dynamic processes in the gearbox during gear changes under load with forward and reverse switching, including the simultaneous use of several friction clutches.

scholarly journals Estimation of reliability of seismic and electromagnetic monitoring in seismic active areas by diffraction tomography

2001 ◽  
Vol 1 (1/2) ◽  
pp. 69-73 ◽  
Author(s):  
V. N. Troyan ◽  
Yu. V. Kiselev
Keyword(s):  
Numerical Simulation ◽  
Born Approximation ◽  
Maxwell Equations ◽  
Diffraction Tomography ◽  
Seismic Parameters ◽  
First Order ◽  
The Finite Difference Method ◽  
Tomography Method ◽  
Electromagnetic Monitoring ◽  
Direct Problems

Abstract. This paper presents the algorithms and results of the numerical simulation of the solution of a 2-D inverse problem on the restoration of seismic parameters and electrical conductivity of local inhomogeneities by the diffraction tomography method based upon the first order Born approximation. The direct problems for the Lame and Maxwell equations are solved by the finite difference method. Restoration of inhomogeneities which are not very weak is implemented with the use of a small number of receivers (source-receiver pairs).

scholarly journals COSICAF, a fission chamber simulation tool for academic purposes

2020 ◽  
Vol 225 ◽  
pp. 10003
Author(s):  
G. de Izarra ◽  
M. Lamotte ◽  
S. Bréaud ◽  
A. Pépino ◽  
P. Filliatre ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Proportional Counter ◽  
Empirical Models ◽  
Simulation Tool ◽  
Numerical Implementation ◽  
Fission Chamber ◽  
Semi Empirical ◽  
Simulation Codes

Since a few years, simulation codes were built at CEA Cadarache to predict the signal of ionisation chambers and taylor detectors for specific applications. It is proposed here to present COSICAF, a tool developed for mainly academic purpose and rapid fission chamber prototyping. This numerical simulation, mostly based on semi-empirical models and Monte-Carlo method will help students to understand how ionisation chambers work. Through the paper, models and their numerical implementation will be discussed. A focus is made on recently implemented features like charge multiplication and correlated source which make the simulation of proportional counter possible. To demonstrate the interest of the code, simulations of a planar fission chamber is proposed.

scholarly journals Determination of magnetic field intensity on open sample

2021 ◽  
Vol 72 (6) ◽  
pp. 419-422
Author(s):  
Karol Hilko ◽  
Vladimír Jančárik ◽  
Filip Kafka
Keyword(s):  
Magnetic Field ◽  
Numerical Simulation ◽  
Field Intensity ◽  
Magnetic Field Intensity ◽  
Sample Surface ◽  
Steel Sample ◽  
Sufficient Accuracy ◽  
The Magnetic Field

Abstract The work is focused on the refinement of the determination of the magnetic field intensity in a Charpy-shaped steel sample. When measuring on an open sample, the intensity of the magnetic field cannot be determined directly from the current by the magnetizing winding. The distribution of the magnetic field around the sample was determined by numerical simulation, the dependence of its intensity on the distance from the sample surface is fitted with sufficient accuracy by a polynomial of the 3rd degree. A system of sensors sensing the distribution of the field at selected points above the sample was designed; by extrapolation using said fitting function, the intensity of the magnetic field on the surface of the examined sample is determined.

scholarly journals Mass and Heat Transport Models for Analysis of the Drying Process in Porous Media: A Review and Numerical Implementation

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Hong Thai Vu ◽  
Evangelos Tsotsas
Keyword(s):  
Numerical Simulation ◽  
Porous Media ◽  
Heat Transport ◽  
Diffusion Theory ◽  
System Of Equations ◽  
Numerical Implementation ◽  
Drying Process ◽  
Transport Models ◽  
Moisture Migration ◽  
Drying Models

The modeling and numerical simulation of drying in porous media is discussed in this work by revisiting the different models of moisture migration during the drying process of porous media as well as their restrictions and applications. Among the models and theories, we consider those are ranging from simple ones like the diffusion theory to more complex ones like the receding front theory, the model of Philip and de Vries, Luikov’s theory, Krischer’s theory, and finally Whitaker’s model, in which all mass, heat transport, and phase change (evaporation) are taken into account. The review of drying models as such serves as the basis for the development of a framework for numerical simulation. In order to demonstrate this, the system of equations governing the drying process in porous media resulting from Whitaker’s model is presented and used in our numerical implementation. A numerical simulation of drying is presented and discussed to show the capability of the implementation.

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