Far-Field Behavior of Waves in Non-Ideal Magnetogasdynamics

2020 ◽  
Author(s):  
Ankita Sharma ◽  
Rajan Arora
Keyword(s):  
Approximate Solution ◽  
Evolution Equation ◽  
Asymptotic Analysis ◽  
Asymptotic Method ◽  
Nonlinear Waves ◽  
Numerical Technique ◽  
Ideal Gas ◽  
Far Field ◽  
Field Behavior ◽  
Hyperbolic Quasilinear System

We have presented a study on the far-field behavior of weak nonlinear waves in magnetogasdynamics. An asymptotic analysis is carried out for the study. An evolution equation is obtained by using an asymptotic method which helps in learning the far-field behavior of a hyperbolic quasilinear system governing the propagation of nonlinear waves in a non-ideal gas. A numerical technique MVIM is employed to obtain the approximate solution of the evolution equation.

scholarly journals Smooth Approximations of Global in Time Solutions to Scalar Conservation Laws

2009 ◽  
Vol 2009 ◽  
pp. 1-26 ◽  
Author(s):  
V. G. Danilov ◽  
D. Mitrovic
Keyword(s):  
Approximate Solution ◽  
Initial Data ◽  
Conservation Laws ◽  
Asymptotic Method ◽  
Nonlinear Waves ◽  
Conservation Law ◽  
Scalar Conservation Laws ◽  
Scalar Conservation Law ◽  
Scalar Conservation ◽  
Smooth Approximations

We construct global smooth approximate solution to a scalar conservation law with arbitrary smooth monotonic initial data. Different kinds of singularities interactions which arise during the evolution of the initial data are described as well. In order to solve the problem, we use and further develop the weak asymptotic method, recently introduced technique for investigating nonlinear waves interactions.

Analysis of Structural and Non-Structural Problems by Coupling of Finite and Infinite Elements

2014 ◽  
Vol 578-579 ◽  
pp. 445-455
Author(s):  
Mustapha Demidem ◽  
Remdane Boutemeur ◽  
Abderrahim Bali ◽  
El-Hadi Benyoussef
Keyword(s):  
Numerical Technique ◽  
Near Field ◽  
Main Idea ◽  
Far Field ◽  
Mining Operations ◽  
Infinite Element ◽  
Infinite Elements ◽  
Structural Problems ◽  
Infinite Element Method ◽  
Element Method

The main idea of this paper is to present a smart numerical technique to solve structural and non-structural problems in which the domain of interest extends to large distance in one or more directions. The concerned typical problems may be the underground excavation (tunneling or mining operations) and some heat transfer problems (energy flow rate for construction panels). The proposed numerical technique is based on the coupling between the finite element method (M.E.F.) and the infinite element method (I.E.M.) in an attractive manner taking into consideration the advantages that both methods offer with respect to the near field and the far field (good accuracy and sensible reduction of equations to be solved). In this work, it should be noticed that the using of this numerical coupling technique, based on the infinite element ascent formulation, has introduced a more realistic and economic way to solve unbounded problems for which modeling and efficiency have been elegantly improved. The types of the iso-parametric finite elements used are respectively the eight-nodes (Q8) and the four-nodes (Q4) for the near field. However, for the far field the iso-parametric infinite elements used are the eight-nodes (Q8I) and the six-nodes (Q6I).

scholarly journals Error Estimates on Hybridizable Discontinuous Galerkin Methods for Parabolic Equations with Nonlinear Coefficients

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Minam Moon ◽  
Hyung Kyu Jun ◽  
Tay Suh
Keyword(s):  
Approximate Solution ◽  
Discontinuous Galerkin ◽  
Computer Simulations ◽  
Parabolic Equations ◽  
Discontinuous Galerkin Methods ◽  
Numerical Technique ◽  
Galerkin Methods ◽  
Hybridizable Discontinuous Galerkin ◽  
Hybridizable Discontinuous Galerkin Methods ◽  
Error Estimations

HDG method has been widely used as an effective numerical technique to obtain physically relevant solutions for PDE. In a practical setting, PDE comes with nonlinear coefficients. Hence, it is inevitable to consider how to obtain an approximate solution for PDE with nonlinear coefficients. Research on using HDG method for PDE with nonlinear coefficients has been conducted along with results obtained from computer simulations. However, error analysis on HDG method for such settings has been limited. In this research, we give error estimations of the hybridizable discontinuous Galerkin (HDG) method for parabolic equations with nonlinear coefficients. We first review the classical HDG method and define notions that will be used throughout the paper. Then, we will give bounds for our estimates when nonlinear coefficients obey “Lipschitz” condition. We will then prove our main result that the errors for our estimations are bounded.

scholarly journals Approximate Solution of Nonlinear System of BVP Arising in Fluid Flow Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
A. K. Alomari ◽  
N. Ratib Anakira ◽  
A. Sami Bataineh ◽  
I. Hashim
Keyword(s):  
Fluid Flow ◽  
Approximate Solution ◽  
Nonlinear System ◽  
Boundary Value Problems ◽  
Asymptotic Method ◽  
Series Solution ◽  
Flow Problem ◽  
Point Boundary ◽  
Optimal Homotopy Asymptotic Method ◽  
First Time

We extend for the first time the applicability of the Optimal Homotopy Asymptotic Method (OHAM) to find approximate solution of a system of two-point boundary-value problems (BVPs). The OHAM provides us with a very simple way to control and adjust the convergence of the series solution using the auxiliary constants which are optimally determined. Comparisons made show the effectiveness and reliability of the method.

Far Field Behavior of Bragg Reflection Waveguide Lasers

2011 ◽  
Author(s):  
Lijie Wang ◽  
Cunzhu Tong ◽  
Lijun Wang ◽  
Ye Yang ◽  
Yugang Zeng
Keyword(s):  
Bragg Reflection ◽  
Far Field ◽  
Waveguide Lasers ◽  
Field Behavior

scholarly journals Localized nonlinear waves in a semiconductor with charged dislocations

2021 ◽  
Vol 250 ◽  
pp. 03012
Author(s):  
Vladimir I. Erofeev ◽  
Anna V. Leonteva ◽  
Alexey O. Malkhanov ◽  
Ashot V. Shekoyan
Keyword(s):  
Electric Field ◽  
Evolution Equation ◽  
Ultrasonic Wave ◽  
Nonlinear Waves ◽  
Piezoelectric Properties ◽  
Exact Analytical Solution ◽  
Constant Electric Field ◽  
Ultrasonic Waves ◽  
Wave Dynamics ◽  
Piezoelectric Semiconductors

To describe a nonlinear ultrasonic wave in a semiconductor with charged dislocations, an evolution equation is obtained that generalizes the well-known equations of wave dynamics: Burgers and Korteweg de Vries. By the method of truncated decompositions, an exact analytical solution of the evolution equation with a kink profile has been found. The kind of kink (increasing, decreasing) and its polarity depend on the values of the parameters and their signs. An ultrasonic wave in a semiconductor containing numerous charged dislocations is considered. It is assumed that there is a constant electric field that creates an electric current. The situation is similar to the case of the propagation of ultrasonic waves in piezoelectric semiconductors, but in the problem under consideration, instead of the electric field due to the piezoelectric properties of the medium, the electric field of dislocations appears.

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