Nuclear Energy for New Europe 2009

(This is a HTML version of the abstract for information only. It can differ from the original, submitted by the author(s). Special characters, formulas and figures are not properly reproduced here. Please, contact the author(s) or refer to the printed Book of Abstracts for the correct version.)

No: 909

Conference: Nuclear Energy for New Europe 2009

Title: Solving Moving-Boundary Problems with Multiquadric Function, Level Set Method and Adaptive Greedy Algorithm

Theme: Radioactive Waste Management

Author(s): Leopold Vrankar, Goran Turk, Franc Runovc

Contact : Leopold Vrankar

E-mail: Leopold.Vrankar@gov.si

Address: Uprava Republike Slovenije za jedrsko varnost
1001 Ljubljana

Country: Slovenia

Moving-boundary problems are often called Stefan problems, with reference to the early work of J. Stefan, around 1890, when he was interested in the melting of the polar ice cap. In this frame we can include a large number of important physical processes involving heat conduction and materials undergoing a change of phase. One of these is a heat transfer problem involving a phase change due to solidification or melting which is important in many industrial applications such as the drilling of high ice-content soil, the storage of thermal energy, the safety studies of nuclear reactors and fire studies.
Moving boundaries are also associated with time-dependent problems and the position of the boundary has to be determined as a function of time and space, but depends also on basis variables of the problems.
Various numerical methods are known to solve Stefan problems, e.g. front-tracking, front-fixing, and fixed-domain methods. The finite-difference methods and finite-element techniques have been used extensively for numerical solution of moving boundary problems.
Recent research on the numerical method has focused on the idea of using a meshless methodology for the numerical solution of partial differential equations (PDEs). One of the common characteristics of all mesh-free methods is their ability to construct functional approximation or interpolation entirely from the information at a set of scattered nodes, among which there is no relationship. During the past decade, increasing attention has been given to the development of meshless methods using radial basis functions (e.g. multiquadric -MQ) for the numerical solution of PDEs.
The usual method of solving PDEs with RBFs is similar to standard mesh based methods by constructing a uniform grid that is consecutively refined, yielding progressively to more ill-conditioned systems of equations. To overcome the problems of ill-conditioned matrices many efforts have been made to find a new computational method that is capable of circumventing the ill-conditioning problems using linear solvers. In the literature the following methods are reported: pre-conditioning the coefficient matrix, the greedy algorithm, etc.
Level set methods have become an attractive design tool for tracking, modelling and simulating the motion of free boundaries in fluid mechanics, combustion, computer animation and image processing.
The goal is to include MQ RBFs into level set methods to construct a more efficient approach and stabilize the solution process with the adaptive greedy algorithm.

No:	909
Conference:	Nuclear Energy for New Europe 2009
Title:	Solving Moving-Boundary Problems with Multiquadric Function, Level Set Method and Adaptive Greedy Algorithm
Theme:	Radioactive Waste Management
Author(s):	Leopold Vrankar, Goran Turk, Franc Runovc
Contact :	Leopold Vrankar
E-mail:	Leopold.Vrankar@gov.si
Address:	Uprava Republike Slovenije za jedrsko varnost 1001 Ljubljana
Country:	Slovenia

Moving-boundary problems are often called Stefan problems, with reference to the early work of J. Stefan, around 1890, when he was interested in the melting of the polar ice cap. In this frame we can include a large number of important physical processes involving heat conduction and materials undergoing a change of phase. One of these is a heat transfer problem involving a phase change due to solidification or melting which is important in many industrial applications such as the drilling of high ice-content soil, the storage of thermal energy, the safety studies of nuclear reactors and fire studies. Moving boundaries are also associated with time-dependent problems and the position of the boundary has to be determined as a function of time and space, but depends also on basis variables of the problems. Various numerical methods are known to solve Stefan problems, e.g. front-tracking, front-fixing, and fixed-domain methods. The finite-difference methods and finite-element techniques have been used extensively for numerical solution of moving boundary problems. Recent research on the numerical method has focused on the idea of using a meshless methodology for the numerical solution of partial differential equations (PDEs). One of the common characteristics of all mesh-free methods is their ability to construct functional approximation or interpolation entirely from the information at a set of scattered nodes, among which there is no relationship. During the past decade, increasing attention has been given to the development of meshless methods using radial basis functions (e.g. multiquadric -MQ) for the numerical solution of PDEs. The usual method of solving PDEs with RBFs is similar to standard mesh based methods by constructing a uniform grid that is consecutively refined, yielding progressively to more ill-conditioned systems of equations. To overcome the problems of ill-conditioned matrices many efforts have been made to find a new computational method that is capable of circumventing the ill-conditioning problems using linear solvers. In the literature the following methods are reported: pre-conditioning the coefficient matrix, the greedy algorithm, etc. Level set methods have become an attractive design tool for tracking, modelling and simulating the motion of free boundaries in fluid mechanics, combustion, computer animation and image processing. The goal is to include MQ RBFs into level set methods to construct a more efficient approach and stabilize the solution process with the adaptive greedy algorithm.