scholarly journals Weak Formulation for Singular Diffusion Equation with Dynamic Boundary Condition

2017 ◽  
pp. 405-429
Author(s):  
Ryota Nakayashiki ◽  
Ken Shirakawa
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Dynamic Boundary Condition ◽  
Weak Formulation ◽  
Dynamic Boundary ◽  
Singular Diffusion

Re-Entrant Jet Modeling of Partial Cavity Flow on Three-Dimensional Hydrofoils

1999 ◽  
Vol 121 (4) ◽  
pp. 781-787 ◽  
Author(s):  
J. Dang ◽  
G. Kuiper
Keyword(s):  
Boundary Condition ◽  
Three Dimensional ◽  
Leading Edge ◽  
Neumann Boundary ◽  
Cavity Surface ◽  
Dynamic Boundary Condition ◽  
Surface Panel Method ◽  
Kinematic Boundary Condition ◽  
Dynamic Boundary ◽  
Cavity Closure

A potential-based lower-order surface panel method is developed to calculate the flow around a three-dimensional hydrofoil with an attached sheet cavity the leading edge. A Dirichlet type dynamic boundary condition on the cavity surface and a Neumann boundary condition on the wetted surface are enforced. The cavity shape is initially assumed and the kinematic boundary condition on the cavity surface is satisfied by iterating the cavity length and shape. Upon convergence, both the dynamic boundary condition and the kinematic boundary condition on the cavity surface are satisfied, and a re-entrant jet develops at the cavity closure. The flow at the closure of the cavity and the mechanism of the re-entrant jet formation is investigated. Good agreement is found between the calculated results and MIT’s experiments on a 3-D hydrofoil.

scholarly journals Optimal Boundary Control of a Viscous Cahn--Hilliard System with Dynamic Boundary Condition and Double Obstacle Potentials

2015 ◽  
Vol 53 (4) ◽  
pp. 2696-2721 ◽  
Author(s):  
Pierluigi Colli ◽  
M. Hassan Farshbaf-Shaker ◽  
Gianni Gilardi ◽  
Jürgen Sprekels
Keyword(s):  
Boundary Condition ◽  
Boundary Control ◽  
Dynamic Boundary Condition ◽  
Optimal Boundary ◽  
Dynamic Boundary ◽  
Optimal Boundary Control
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