SOLUTION OF TWO‐DIMENSIONAL MULTI‐INTERFACE STEFAN PROBLEM BY THE METHOD OF DYNAMIC ADAPTATION

2001 ◽  
Vol 6 (1) ◽  
pp. 129-137
Author(s):  
V. I. Mazhukin ◽  
M. M. Chuiko
Keyword(s):  
Coordinate System ◽  
Numerical Solution ◽  
Stefan Problem ◽  
Dynamic Adaptation ◽  
Arbitrary Form ◽  
Two Dimensional ◽  
System Transformation ◽  
Energy Fluxes ◽  
Stationary Coordinate System

In the present work a method of numerical solution of multi‐interface two-dimensional Stefan problem with explicit tracking of the interfaces in the domains of arbitrary form is considered. The method is based on the idea of dynamic adaptation of the calculated grid by means of transition to an arbitrary non-stationary coordinate system. The coordinate system transformation is controlled by the solution. The method is described by using the example of the problem that is typical for treatment of materials with concentrated energy fluxes.

Solution of the Multi-interface Stefan Problem by the Method of Dynamic Adaptation

2002 ◽  
Vol 2 (3) ◽  
pp. 283-294 ◽  
Author(s):  
Vladimir Mazhukin ◽  
Michail Chuiko
Keyword(s):  
Numerical Experiment ◽  
Coordinate System ◽  
Numerical Solution ◽  
Stefan Problem ◽  
High Energy ◽  
Dynamic Adaptation ◽  
Energy Fluxes ◽  
Stefan Problems ◽  
Stationary Coordinate System ◽  
Adaptation Method

AbstractThe application of the dynamic adaptation method to the numerical solution of multidimensional Stefan problems with explicit tracking of interfaces is considered. The dynamic adaptation method is based on the idea of transition to any non-stationary coordinate system. The results of the numerical experiment on modelling the pulsed action of high-energy fluxes on metals are presented.

scholarly journals DYNAMIC ADAPTATION METHOD FOR NUMERICAL SOLUTION OF AXISYMMETRIC STEFAN PROBLEMS

2003 ◽  
Vol 8 (4) ◽  
pp. 303-314
Author(s):  
V. I. Mazhukin ◽  
M. M. Chuiko ◽  
A. M. Lapanik
Keyword(s):  
Coordinate System ◽  
Numerical Solution ◽  
High Energy ◽  
Computational Experiments ◽  
Dynamic Adaptation ◽  
Energy Fluxes ◽  
Stefan Problems ◽  
Stationary Coordinate System ◽  
Adaptation Method

Application of the dynamic adaptation method for the numerical solution of multidimensional axisymmetric Stefan problems with explicit tracking of interfaces is presented. The dynamic adaptation method is based on the idea of transition of the physical coordinate system to the non‐stationary coordinate system. The results of computational experiments for modelling the action of high energy fluxes on metals are given.

scholarly journals ACCURATE MODELLING OP TWO-DIMENSIONAL MASS TRANSPORT

1984 ◽  
Vol 1 (19) ◽  
pp. 163
Author(s):  
Lance Bode ◽  
Rodney J. Sobey
Keyword(s):  
Exact Solution ◽  
Coordinate System ◽  
Numerical Solution ◽  
Transport Equation ◽  
Spatial Dimension ◽  
Convective Transport ◽  
Numerical Dispersion ◽  
Two Dimensional ◽  
Numerical Errors ◽  
Moving Coordinate

Any numerical solution of the convective transport equation in an Eulerian framework will exhibit inherent numerical dispersion and solution oscillations. The magnitude of such numerical errors is often so severe as to destroy the value of many computed solutions. A successful and economical algorithm for the convective transport equation in one spatial dimension has been published recently by one of the authors (RJS), in which an exact solution is achieved by means of a moving coordinate system. The present study describes the extension of this work to the more important and challenging two-dimensional case.

Numerical Solution to a Two-Dimensional Conduction Problem Using Rectangular and Cylindrical Body-Fitted Coordinate Systems

1981 ◽  
Vol 103 (4) ◽  
pp. 753-758 ◽  
Author(s):  
A. Goldman ◽  
Y. C. Kao
Keyword(s):  
Temperature Distribution ◽  
Coordinate System ◽  
Numerical Solution ◽  
Rectangular Plate ◽  
Three Dimensional ◽  
Cylindrical Body ◽  
Two Dimensional ◽  
Coordinate Systems

The temperature distribution in a rectangular plate with a circular void at the center was calculated using a body-fitted coordinate system. Three different transformed geometries were considered: rectangular-rectangular, cut-line, and cylindrical. Problems involving insulated outer surfaces could not be solved using the rectangular-rectangular transformation but could be solved with both the cut-line and cylindrical transformations. The cylindrical transformation also appears to have the capability of being extended to three-dimensional problems.

Simulation of Flow in a Rectangular Meandering Channel

2011 ◽  
Vol 130-134 ◽  
pp. 2688-2691
Author(s):  
K. Ma ◽  
W.L. Wei
Keyword(s):  
Experimental Data ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Coordinate System ◽  
Numerical Solution ◽  
Satisfactory Agreement ◽  
Two Dimensional ◽  
Complicated Shape ◽  
Partial Differential ◽  
Meandering Channel

This paper is concerned with the numerical solution of two-dimensional flows in a rectangular meandering channel. The technique of boundary-fitted coordinate system is used to overcome the difficulties resulting from the complicated shape of natural river boundaries; the method of physical fractional steps is used to solve the partial differential equations in the transformed plane. Comparison between computed and experimental data shows a satisfactory agreement.

Analysis and verification of harmonic interaction between DDWTs based on αβ stationary coordinate system

2020 ◽  
Vol 14 (10) ◽  
pp. 1893-1901
Author(s):  
Pingping Han ◽  
Longjian Wang ◽  
Sheng Dou ◽  
Lei Wang ◽  
Rui Bi ◽  
...  
Keyword(s):  
Coordinate System ◽  
Stationary Coordinate System ◽  
Harmonic Interaction

scholarly journals Numerical solution of the Stefan problem

2021 ◽  
Vol 1809 (1) ◽  
pp. 012002
Author(s):  
N G Burago ◽  
A I Fedyushkin
Keyword(s):  
Numerical Solution ◽  
Stefan Problem

The Best Perturbation Method for the Parameter Inversion of Two-Dimension Convection-Diffusion Equation

2013 ◽  
Vol 380-384 ◽  
pp. 1143-1146
Author(s):  
Xiang Guo Liu
Keyword(s):  
Inverse Problem ◽  
Diffusion Equation ◽  
Perturbation Method ◽  
Numerical Simulations ◽  
Numerical Solution ◽  
Two Dimensional ◽  
Convection Diffusion ◽  
Convection Diffusion Equation ◽  
Parameter Inversion ◽  
Parametric Inversion

The paper researches the parametric inversion of the two-dimensional convection-diffusion equation by means of best perturbation method, draw a Numerical Solution for such inverse problem. It is shown by numerical simulations that the method is feasible and effective.

Regularization of a two-dimensional two-phase inverse Stefan problem

1997 ◽  
Vol 13 (3) ◽  
pp. 607-619 ◽  
Author(s):  
D D Ang ◽  
A Pham Ngoc Dinh ◽  
D N Thanh
Keyword(s):  
Stefan Problem ◽  
Two Dimensional ◽  
Two Phase
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