scholarly journals Consistent Dirichlet boundary conditions for numerical solution of moving boundary problems

2009 ◽  
Vol 59 (6) ◽  
pp. 1337-1353 ◽  
Author(s):  
M.E. Hubbard ◽  
M.J. Baines ◽  
P.K. Jimack
Keyword(s):  
Boundary Conditions ◽  
Numerical Solution ◽  
Dirichlet Boundary ◽  
Moving Boundary ◽  
Dirichlet Boundary Conditions ◽  
Moving Boundary Problems ◽  
Boundary Problems

scholarly journals On the existence of non-flat profiles for a Bernoulli free boundary problem

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Giovanni Gravina ◽  
Giovanni Leoni
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Boundary Problem ◽  
Dirichlet Boundary ◽  
Free Boundary Problems ◽  
Energy Functional ◽  
Dirichlet Boundary Conditions ◽  
Boundary Problems ◽  
Global Minimizers ◽  
Flat Profile

AbstractIn this paper, we consider a large class of Bernoulli-type free boundary problems with mixed periodic-Dirichlet boundary conditions. We show that solutions with non-flat profile can be found variationally as global minimizers of the classical Alt–Caffarelli energy functional.

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.

Numerical Solution of a Class of Moving Boundary Problems with a Nonlinear Complementarity Approach

2015 ◽  
Vol 168 (2) ◽  
pp. 534-550 ◽  
Author(s):  
Grigori Chapiro ◽  
Angel E. R. Gutierrez ◽  
José Herskovits ◽  
Sandro R. Mazorche ◽  
Weslley S. Pereira
Keyword(s):  
Numerical Solution ◽  
Moving Boundary ◽  
Moving Boundary Problems ◽  
Boundary Problems ◽  
Nonlinear Complementarity ◽  
Complementarity Approach
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