Analysis of the diffusion influence on the bubble dynamics in an acoustic field

2012 ◽  
Vol 9 (1) ◽  
pp. 53-58
Author(s):  
E.V. Volkova ◽  
E.Sh. Nasibullaeva ◽  
I.Sh. Akhatov
Keyword(s):  
Numerical Method ◽  
Acoustic Field ◽  
Numerical Experiments ◽  
Bubble Dynamics ◽  
External Pressure ◽  
Diffusion Problem ◽  
Spherically Symmetric ◽  
Calculation Results ◽  
Cluster A ◽  
Parallelization Efficiency

A diffusion problem for a spherically symmetric gas bubble in a liquid in an isotropic acoustic field is considered. The problem is solved both for a single bubble and for a bubble in a monodisperse cluster. A numerical method for solving the diffusion problem is developed. For the oscillating part of the diffusion problem the numerical experiments have been carried out for different amplitudes of the external pressure. A comparison is made between the calculation results obtained by the approximation theory and the numerical method presented. The effect of taking into account the mass change on the bubble dynamics is studied. For extensive parametric research the algorithm is paralleled and the parallelization efficiency is evaluated.

scholarly journals A Numerical Method for a Singularly Perturbed Three-Point Boundary Value Problem

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
Author(s):  
Musa Çakır ◽  
Gabil M. Amiraliyev
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Numerical Method ◽  
Numerical Experiments ◽  
Diffusion Problem ◽  
Singularly Perturbed ◽  
Point Boundary ◽  
Convection Diffusion ◽  
First Order ◽  
Type Boundary

The purpose of this paper is to present a uniform finite difference method for numerical solution of nonlinear singularly perturbed convection-diffusion problem with nonlocal and third type boundary conditions. The numerical method is constructed on piecewise uniform Shishkin type mesh. The method is shown to be convergent, uniformly in the diffusion parameterε, of first order in the discrete maximum norm. Some numerical experiments illustrate in practice the result of convergence proved theoretically.

Nonlinear Oscillations of a Spherically Symmetric Single Bubble in an Acoustic Field

2011 ◽  
Vol 8 (1) ◽  
pp. 45-53
Author(s):  
E.V. Volkova ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Mass Transfer ◽  
Acoustic Field ◽  
Moving Boundary ◽  
Nonlinear Oscillations ◽  
Diffusion Problem ◽  
Spherically Symmetric ◽  
Lagrangian Coordinates ◽  
Gas Bubble ◽  
Bubble Wall ◽  
Convection Diffusion

In the present paper the dynamics of a single gas bubble under the influence of an acoustic field is studied, taking mass transfer through the moving bubble wall into account. Mass transfer is calculated separately in the diffusion problem. Due to changes in the pressure inside the bubble caused by oscillations of its volume, the concentration of the gas dissolved in the liquid undergoes oscillations of large amplitude near the bubble boundary. To eliminate the computational problems associated with the moving boundary, the convection-diffusion equations describing the transport of a gas dissolved in a liquid are written in Lagrangian coordinates.

Thermal Bubble Dynamics Under the Effect of Acoustic Vibration

2009 ◽  
Author(s):  
Xiaopeng Qu ◽  
Huihe Qiu
Keyword(s):  
Heat Transfer ◽  
Acoustic Field ◽  
Vapor Bubble ◽  
Boiling Heat Transfer ◽  
High Speed ◽  
Bubble Dynamics ◽  
Acoustic Vibration ◽  
Micro Electro Mechanical System ◽  
Mems Technology ◽  
Enhanced Boiling

The effect of acoustic field on the dynamics of micro thermal bubble is investigated in this paper. The micro thermal bubbles were generated by a micro heater which was fabricated by standard Micro-Electro-Mechanical-System (MEMS) technology and integrated into a mini chamber. The acoustic field formed in the mini chamber was generated by a piezoelectric plate which was adhered on the top side of the chamber’s wall. The dynamics and related heat transfer induced by the micro heater generated vapor bubble with and without the existing of acoustic field were characterized by a high speed photograph system and a micro temperature sensor. Through the experiments, it was found that in two different conditions, the temperature changing induced by the micro heater generated vapor bubble was significantly different. From the analysis of the high speed photograph results, the acoustic force induced micro thermal bubble movements, such as forcibly removing, collapsing and sweeping, were the main effects of acoustic enhanced boiling heat transfer. The experimental results and theoretical analysis were helpful for understanding of the mechanisms of acoustic enhanced boiling heat transfer and development of novel micro cooling devices.

scholarly journals Minimization of an energy error functional to solve a Cauchy problem arising in plasma physics: the reconstruction of the magnetic flux in the vacuum surrounding the plasma in a Tokamak

2012 ◽  
Vol Volume 15, 2012 ◽  
Author(s):  
Blaise Faugeras ◽  
Amel Ben Abda ◽  
Jacques Blum ◽  
Cedric Boulbe
Keyword(s):  
Cauchy Problem ◽  
Magnetic Flux ◽  
Plasma Physics ◽  
Numerical Method ◽  
Numerical Experiments ◽  
Energy Error ◽  
Error Functional ◽  
International Audience

International audience A numerical method for the computation of the magnetic flux in the vacuum surrounding the plasma in a Tokamak is investigated. It is based on the formulation of a Cauchy problem which is solved through the minimization of an energy error functional. Several numerical experiments are conducted which show the efficiency of the method.

scholarly journals Weak solvability of the unconditionally stable difference scheme for the coupled sine-Gordon system

2020 ◽  
Vol 25 (6) ◽  
pp. 997-1014
Author(s):  
Ozgur Yildirim ◽  
Meltem Uzun
Keyword(s):  
Difference Scheme ◽  
Numerical Method ◽  
Existence And Uniqueness ◽  
Numerical Experiments ◽  
Finite Difference Schemes ◽  
Order Of Accuracy ◽  
Unconditionally Stable ◽  
First Order ◽  
The Difference ◽  
Weak Solvability

In this paper, we study the existence and uniqueness of weak solution for the system of finite difference schemes for coupled sine-Gordon equations. A novel first order of accuracy unconditionally stable difference scheme is considered. The variational method also known as the energy method is applied to prove unique weak solvability.We also present a new unified numerical method for the approximate solution of this problem by combining the difference scheme and the fixed point iteration. A test problem is considered, and results of numerical experiments are presented with error analysis to verify the accuracy of the proposed numerical method.

scholarly journals A STABILIZING SUBGRID FOR CONVECTION–DIFFUSION PROBLEM

2006 ◽  
Vol 16 (02) ◽  
pp. 211-231 ◽  
Author(s):  
ALI I. NESLITURK
Keyword(s):  
Numerical Experiments ◽  
A Priori ◽  
Diffusion Problem ◽  
Triangular Element ◽  
Discrete Solution ◽  
Convergence Properties ◽  
Small Diffusion ◽  
Galerkin Finite Element ◽  
Convection Diffusion ◽  
Priori Error Estimates

A stabilizing subgrid which consists of a single additional node in each triangular element is analyzed by solving the convection–diffusion problem, especially in the case of small diffusion. The choice of the location of the subgrid node is based on minimizing the residual of a local problem inside each element. We study convergence properties of the method under consideration and its connection with previously suggested stabilizing subgrids. We prove that the standard Galerkin finite element solution on augmented grid produces a discrete solution that satisfy the same a priori error estimates that are typically obtained with SUPG and RFB methods. Some numerical experiments that confirm the theoretical findings are also presented.

KINEMATIC WAVE EQUATIONS FOR MOVABLE RIVERBEDS

2021 ◽  
pp. 43-54
Author(s):  
A. N. Krutov ◽  
◽  
S. Ya. Shkol’nikov ◽  
Keyword(s):  
Mathematical Model ◽  
Numerical Method ◽  
Wave Equations ◽  
Simple Wave ◽  
Kinematic Wave ◽  
Calculation Results ◽  
Self Similar ◽  
Similar Solutions ◽  
The Mathematical Model ◽  
Good Agreement

The mathematical model of kinematic wave, that is widely used in hydrological calculations, is generalized to compute processes in deformable channels. Self-similar solutions to the kinematic wave equations, namely, the discontinuous wave of increase and the “simple” wave of decrease are generalized. A numerical method is proposed for solving the kinematic wave equations for deformable channels. The comparison of calculation results with self-similar solutions revealed a good agreement.

scholarly journals A Novel and Efficient Numerical Algorithm for Solving 2D Fredholm Integral Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
H. Bin Jebreen
Keyword(s):  
Approximate Solution ◽  
Numerical Method ◽  
Convergence Analysis ◽  
Integral Equations ◽  
Numerical Algorithm ◽  
Numerical Experiments ◽  
Operational Matrix ◽  
Fredholm Integral Equations ◽  
Scaling Functions ◽  
Algebraic Equations

A novel and efficient numerical method is developed based on interpolating scaling functions to solve 2D Fredholm integral equations (FIE). Using the operational matrix of integral for interpolating scaling functions, FIE reduces to a set of algebraic equations that one can obtain an approximate solution by solving this system. The convergence analysis is investigated, and some numerical experiments confirm the accuracy and validity of the method. To show the ability of the proposed method, we compare it with others.

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