scholarly journals Generalized solvability of a problem with a dynamic boundary condition for the hyperbolic equation

2021 ◽  
Vol 1902 (1) ◽  
pp. 012031
Author(s):  
A Bogatov
Keyword(s):  
Boundary Condition ◽  
Hyperbolic Equation ◽  
Dynamic Boundary Condition ◽  
Dynamic Boundary

scholarly journals PROBLEM WITH DYNAMIC BOUNDARY CONDITIONS FOR A HYPERBOLIC EQUATION

2017 ◽  
Vol 23 (1) ◽  
pp. 21-27
Author(s):  
V. A. Kirichek ◽  
L. S. Pulkina
Keyword(s):  
Boundary Condition ◽  
Hyperbolic Equation ◽  
A Priori Estimates ◽  
A Priori ◽  
Initial Boundary ◽  
Generalized Solution ◽  
Dynamic Boundary Condition ◽  
Initial Boundary Problem ◽  
Dynamic Boundary ◽  
Priori Estimates

We consider an initial-boundary problem with dynamic boundary condition for a hyperbolic equation in a rectangle. Dynamic boundary condition represents a relation between values of derivatives with respect of spacial variables of a required solution and first-order derivatives with respect to time variable. The main result lies in substantiation of solvability of this problem. We prove the existence and uniqueness of a generalized solution. The proof is based on the a priori estimates obtained in this paper, Galyorkin’s procedure and the properties of Sobolev spaces.

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.

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