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All Journal MATEMATIKA Jurnal Matematika & Sains
Warsoma Djohan
Department of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung
Mathematics

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Dinamika Gelombang Cnoidal di Atas Dasar Tak Rata Menggunakan Persamaan Gelombang Dua Arah Boussinesq Warsoma Djohan
Jurnal Matematika & Sains Vol 2, No 2 (1997)
Publisher : Institut Teknologi Bandung

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Abstract

Waves over uneven bottom which are running in two directions are governed by Boussinesq equations. When the bottom is flat, the Boussinesq equations have a periodic travelling wave solution, i.e. a solution which is running undisturbed in shape and velocity. This travelling wave is called a cnoidal wave. In this research the distortion of a cnoidal wave due to decreasing depth will be studied numerically. A cnoidal wave is initially running above flat bottom, then the depth decreases and flat again with depth h1 (< h0). First, a cnoidal wave is constructed as solution of the constrained critical point problem, i.e. finding the extremism of energy with constraints momentum and mass. Then the Boussinesq equations are discritized using the direct Fourier truncation method. Numerical simulation shows that the cnoidal wave constructed above is indeed a travelling wave solution. By choosing h1 to be the eigendepth of the two-soliton solution of KdV according to the inverse scattering theory, numerical simulations show the splitting process of an initial cnoidal wave into two waves.
METODA BEDA HINGGA PADA PERSAMAAN KDV GELOMBANG INTERFACE Wiryanto, L.H; Djohan, Warsoma
MATEMATIKA Vol 9, No 1 (2006): JURNAL MATEMATIKA
Publisher : MATEMATIKA

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Abstract

Propagation of interfacial wave, modeled in an equation of KdV type, is solved numerically. A finite different method is used to construct a system of linear equations from the model, and the system is solved by Gauss-Seidel method. This numerical procedure is firstly tested for solitary wave, which gives agreement to the analytical solution, and is then used to observe a simulation of wave propagation generated on the left by a generator, for some various values of parameters, depth and fluid density
Co-Authors L.H Wiryanto