Solving One-Dimensional Moving-Boundary Problems with Meshless Method

2008 ◽  
pp. 672-676 ◽  
Author(s):  
Leopold Vrankar ◽  
Edward J. Kansa ◽  
Goran Turk ◽  
Franc Runovc
Keyword(s):  
Meshless Method ◽  
Moving Boundary ◽  
Moving Boundary Problems ◽  
Boundary Problems ◽  
One Dimensional

A Four-Step Fixed-Grid Method for 1D Stefan Problems

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
M. Tadi
Keyword(s):  
Free Boundary ◽  
Moving Boundary ◽  
Free Boundary Problems ◽  
Grid Method ◽  
Moving Boundary Problems ◽  
Boundary Problems ◽  
One Dimensional ◽  
Nonlinear Part ◽  
Stefan Problems ◽  
Fixed Grid

This note is concerned with a fixed-grid finite difference method for the solution of one-dimensional free boundary problems. The method solves for the field variables and the location of the boundary in separate steps. As a result of this decoupling, the nonlinear part of the algorithm involves only a scalar unknown, which is the location of the moving boundary. A number of examples are used to study the applicability of the method. The method is particularly useful for moving boundary problems with various conditions at the front.

scholarly journals On Solving Nonlinear Moving Boundary Problems with Heterogeneity Using the Collocation Meshless Method

Water ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 835 ◽  
Author(s):  
Cheng-Yu Ku ◽  
Jing-En Xiao ◽  
Chih-Yu Liu
Keyword(s):  
Boundary Conditions ◽  
Laplace Equation ◽  
Meshless Method ◽  
Moving Boundary ◽  
Domain Decomposition Method ◽  
Nonlinear Boundary Conditions ◽  
Surface Flow ◽  
Moving Boundary Problems ◽  
Boundary Problems ◽  
Trefftz Method

In this article, a solution to nonlinear moving boundary problems in heterogeneous geological media using the meshless method is proposed. The free surface flow is a moving boundary problem governed by Laplace equation but has nonlinear boundary conditions. We adopt the collocation Trefftz method (CTM) to approximate the solution using Trefftz base functions, satisfying the Laplace equation. An iterative scheme in conjunction with the CTM for finding the phreatic line with over–specified nonlinear moving boundary conditions is developed. To deal with flow in the layered heterogeneous soil, the domain decomposition method is used so that the hydraulic conductivity in each subdomain can be different. The method proposed in this study is verified by several numerical examples. The results indicate the advantages of the collocation meshless method such as high accuracy and that only the surface of the problem domain needs to be discretized. Moreover, it is advantageous for solving nonlinear moving boundary problems with heterogeneity with extreme contrasts in the permeability coefficient.

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