Application of hybrid Cartesian grid and gridless approach to moving boundary flow problems

2013 ◽  
Vol 72 (9) ◽  
pp. 994-1013 ◽  
Author(s):  
Xiao Wei Cai ◽  
Jun Jie Tan ◽  
Xin Jian Ma ◽  
Min Zhang ◽  
Hua Sheng Wang
Keyword(s):  
Moving Boundary ◽  
Cartesian Grid ◽  
Boundary Flow ◽  
Flow Problems

Overset Adaptive Cartesian/Prism Grid Method for Stationary and Moving-Boundary Flow Problems

AIAA Journal ◽  
2007 ◽  
Vol 45 (7) ◽  
pp. 1774-1779 ◽  
Author(s):  
Ravishekar Kannan ◽  
Z. J. Wang
Keyword(s):  
Moving Boundary ◽  
Grid Method ◽  
Boundary Flow ◽  
Flow Problems

scholarly journals A Spacetime Meshless Method for Modeling Subsurface Flow with a Transient Moving Boundary

Water ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 2595 ◽  
Author(s):  
Cheng-Yu Ku ◽  
Chih-Yu Liu ◽  
Jing-En Xiao ◽  
Weichung Yeih ◽  
Chia-Ming Fan
Keyword(s):  
Diffusion Equation ◽  
Meshless Method ◽  
Moving Boundary ◽  
Iterative Scheme ◽  
Separation Of Variables ◽  
Subsurface Flow ◽  
Basis Functions ◽  
Method Of Fundamental Solutions ◽  
Trefftz Method ◽  
Flow Problems

In this paper, a spacetime meshless method utilizing Trefftz functions for modeling subsurface flow problems with a transient moving boundary is proposed. The subsurface flow problem with a transient moving boundary is governed by the two-dimensional diffusion equation, where the position of the moving boundary is previously unknown. We solve the subsurface flow problems based on the Trefftz method, in which the Trefftz basis functions are obtained from the general solutions using the separation of variables. The solutions of the governing equation are then approximated numerically by the superposition theorem using the basis functions, which match the data at the spacetime boundary collocation points. Because the proposed basis functions fully satisfy the diffusion equation, arbitrary nodes are collocated only on the spacetime boundaries for the discretization of the domain. The iterative scheme has to be used for solving the moving boundaries because the transient moving boundary problems exhibit nonlinear characteristics. Numerical examples, including harmonic and non-harmonic boundary conditions, are carried out to validate the method. Results illustrate that our method may acquire field solutions with high accuracy. It is also found that the method is advantageous for solving inverse problems as well. Finally, comparing with those obtained from the method of fundamental solutions, we may obtain the accurate location of the nonlinear moving boundary for transient problems using the spacetime meshless method with the iterative scheme.

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