Variational boundary integral approach for asymmetric impinging jets of arbitrary two-dimensional nozzle

2018 ◽  
Vol 88 (4) ◽  
pp. 193-216
Author(s):  
Sung Sic Yoo ◽  
Wing Kam Liu ◽  
Do Wan Kim
Keyword(s):  
Impinging Jets ◽  
Boundary Integral ◽  
Integral Approach ◽  
Two Dimensional

The Diffraction of Multidirectional Random Waves by Rectangular Submarine Pits

2004 ◽  
Vol 126 (1) ◽  
pp. 9-15 ◽  
Author(s):  
Hong Sik Lee ◽  
A. Neil Williams
Keyword(s):  
Water Wave ◽  
Wave Theory ◽  
Boundary Integral ◽  
Integral Approach ◽  
Two Dimensional ◽  
Random Waves ◽  
Discrete Form ◽  
Random Surface ◽  
Directional Spectrum ◽  
Dimensional Boundary

The diffraction of multidirectional random surface waves with one or more rectangular submarine pits is investigated theoretically. The incident wave conditions are specified using a discrete form of the Mitsuyasu directional spectrum. The numerical model involves the superposition of regular-wave diffraction solutions based on linearized shallow water wave theory obtained by a two-dimensional boundary integral approach for water of uniform depth. Numerical results are presented for multi-directional random waves that illustrate the effect of the various wave and pit parameters on the diffraction characteristics of typical single and multiple pit systems.

The Diffraction of Multidirectional Random Waves by Rectangular Submarine Pits

2002 ◽  
Author(s):  
Hong Sik Lee ◽  
A. Neil Williams
Keyword(s):  
Boundary Integral ◽  
Integral Approach ◽  
Two Dimensional ◽  
Regular Wave ◽  
Random Waves ◽  
Shallow Water Theory ◽  
Discrete Form ◽  
Random Surface ◽  
Directional Spectrum ◽  
Dimensional Boundary

The diffraction of multidirectional random surface waves with one or more rectangular submarine pits is investigated theoretically. The incident wave conditions are specified using a discrete form of the Mitsuyasu directional spectrum. The numerical model involves the superposition of regular-wave diffraction solutions based on linearized shallow water theory obtained by a two-dimensional boundary integral approach for water of uniform depth. Numerical results are presented for multi-directional random waves that illustrate the effect of the various wave and pit parameters on the diffraction characteristics of typical single and multiple pit systems.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

scholarly journals Fractional order elliptic problems with inhomogeneous Dirichlet boundary conditions

2020 ◽  
Vol 23 (2) ◽  
pp. 378-389
Author(s):  
Ferenc Izsák ◽  
Gábor Maros
Keyword(s):  
Fractional Order ◽  
Boundary Data ◽  
Dirichlet Boundary ◽  
Elliptic Problems ◽  
Integral Form ◽  
Uniqueness Result ◽  
Boundary Integral ◽  
Dirichlet Boundary Conditions ◽  
Two Dimensional ◽  
Potential Operators

AbstractFractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping properties of the corresponding potential operators. The existence-uniqueness result is stated also for two-dimensional domains. Finally, a mild condition is provided to ensure the existence of the classical solution of the boundary integral equation.

scholarly journals Existence and uniqueness in the theory of bending of elastic plates

1986 ◽  
Vol 29 (1) ◽  
pp. 47-56 ◽  
Author(s):  
Christian Constanda
Keyword(s):  
Existence And Uniqueness ◽  
Integral Equation Method ◽  
Fundamental Solutions ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Elastic Plates ◽  
Equilibrium Equations ◽  
Dimensional Theory ◽  
Neumann Problems ◽  
Image Position

Kirchhoff's kinematic hypothesis that leads to an approximate two-dimensional theory of bending of elastic plates consists in assuming that the displacements have the form [1]In general, the Dirichlet and Neumann problems for the equilibrium equations obtained on the basis of (1.1) cannot be solved by the boundary integral equation method both inside and outside a bounded domain because the corresponding matrix of fundamental solutions does not vanish at infinity [2]. However, as we show in this paper, the method is still applicable if the asymptotic behaviour of the solution is suitably restricted.

Closed-form solutions of an elliptical crack subjected to coupled phonon–phason loadings in two-dimensional hexagonal quasicrystal media

2018 ◽  
Vol 24 (6) ◽  
pp. 1821-1848 ◽  
Author(s):  
Yuan Li ◽  
CuiYing Fan ◽  
Qing-Hua Qin ◽  
MingHao Zhao
Keyword(s):  
Closed Form ◽  
Integral Equations ◽  
Analytical Solutions ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Elliptical Crack ◽  
Two Dimensional ◽  
Crack Face ◽  
Penny Shaped Crack ◽  
Crack Problems

An elliptical crack subjected to coupled phonon–phason loadings in a three-dimensional body of two-dimensional hexagonal quasicrystals is analytically investigated. Owing to the existence of the crack, the phonon and phason displacements are discontinuous along the crack face. The phonon and phason displacement discontinuities serve as the unknown variables in the generalized potential function method which are used to derive the boundary integral equations. These boundary integral equations governing Mode I, II, and III crack problems in two-dimensional hexagonal quasicrystals are expressed in integral differential form and hypersingular integral form, respectively. Closed-form exact solutions to the elliptical crack problems are first derived for two-dimensional hexagonal quasicrystals. The corresponding fracture parameters, including displacement discontinuities along the crack face and stress intensity factors, are presented considering all three crack cases of Modes I, II, and III. Analytical solutions for a penny-shaped crack, as a special case of the elliptical problem, are given. The obtained analytical solutions are graphically presented and numerically verified by the extended displacement discontinuities boundary element method.

Sign in / Sign up

Export Citation Format

Share Document