Simulation of Water Wave Transformation Using Higher Order Mild-Slope Equation

2009 ◽  
Author(s):  
Tai-Wen Hsu ◽  
Ta-Yuan Lin ◽  
Kuan-Yu Hsiao ◽  
Shiao-Yin Chen
Keyword(s):  
Multiple Scale ◽  
Higher Order ◽  
Wave Transformation ◽  
Radiation Boundary Conditions ◽  
Depth Function ◽  
Mild Slope Equation ◽  
Scale Perturbation ◽  
Radiation Boundary ◽  
Wave Nonlinearity ◽  
Sloping Beach

A higher-order mild-slope equation (HOMSE) was developed using classical Galerkin method in which the depth function is expanded to the third-order. Wave nonlinearity and bottom slope parameters are involved in the depth function solved on the bases of the multiple-scale perturbation method. The equation is solved subject to the radiation boundary conditions by means of the procedure of parabolic formulation. Good agreement between numerical results and experimental data has been observed for wave propagation over a submerged obstacle and a sloping beach.

Numerical Simulation of Wave Transformation Across the Surf Zone Over a Steep Bottom

2010 ◽  
Author(s):  
Tai-Wen Hsu ◽  
Ta-Yuan Lin ◽  
Hwung-Hweng Hwung ◽  
Yaron Toledo ◽  
Aron Roland
Keyword(s):  
Energy Dissipation ◽  
Wave Breaking ◽  
Surf Zone ◽  
Numerical Models ◽  
Dissipation Factor ◽  
Wave Transformation ◽  
Bottom Slope ◽  
Mild Slope Equation ◽  
Efficient Scheme ◽  
Sloping Beach

The combined effect of shoaling, breaking and energy dissipation on a sloping bottom was investigated. Based on the conservation principle of wave motion, a combined shoaling and bottom slope coefficient is included in the mild-slope equation (MSE) which is derived as a function of the bottom slope perturbed to the third-order. The model incorporates the nonlinear shoaling coefficient and energy dissipation factor due to wave breaking to improve the accuracy of the simulation prior to wave breaking and in the surf zone over a steep bottom. The evolution equation of the MSE is implemented in the numerical solution which provides an efficient scheme for describing wave transformation in a large coastal area. The model validity is verified by comparison to accurate numerical models, laboratory experiments and analytical solutions of waves travelling over a steep sloping beach.

A complementary mild-slope equation derived using higher-order depth function for waves obliquely propagating on sloping bottom

2006 ◽  
Vol 18 (8) ◽  
pp. 087106 ◽  
Author(s):  
Tai-Wen Hsu ◽  
Ta-Yuan Lin ◽  
Chih-Chung Wen ◽  
Shan-Hwei Ou
Keyword(s):  
Higher Order ◽  
Depth Function ◽  
Mild Slope Equation ◽  
Sloping Bottom

scholarly journals Atmospheric radiation boundary conditions for the Helmholtz equation

2018 ◽  
Vol 52 (3) ◽  
pp. 945-964 ◽  
Author(s):  
Hélène Barucq ◽  
Juliette Chabassier ◽  
Marc Duruflé ◽  
Laurent Gizon ◽  
Michael Leguèbe
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Acoustic Waves ◽  
Numerical Study ◽  
Outgoing Wave ◽  
Atmospheric Radiation ◽  
Angle Of Incidence ◽  
Radiation Boundary Conditions ◽  
Radiation Boundary ◽  
Dirichlet To Neumann Map

This work offers some contributions to the numerical study of acoustic waves propagating in the Sun and its atmosphere. The main goal is to provide boundary conditions for outgoing waves in the solar atmosphere where it is assumed that the sound speed is constant and the density decays exponentially with radius. Outgoing waves are governed by a Dirichlet-to-Neumann map which is obtained from the factorization of the Helmholtz equation expressed in spherical coordinates. For the purpose of extending the outgoing wave equation to axisymmetric or 3D cases, different approximations are implemented by using the frequency and/or the angle of incidence as parameters of interest. This results in boundary conditions called atmospheric radiation boundary conditions (ARBC) which are tested in ideal and realistic configurations. These ARBCs deliver accurate results and reduce the computational burden by a factor of two in helioseismology applications.

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