Bergen Open Research Archive

Boundary-value problems and shoaling analysis for the BBM equation

Bergen Open Research Archive

Show simple item record Senthilkumar, Amutha 2012-04-24T07:57:19Z 2012-04-24T07:57:19Z 2012-02-20 2012-02-20 en
dc.description.abstract In this thesis we study the BBM equation u_t+u_x+ \frac{3}{2}uu_x - \frac{1}{6} u_{xxt}= 0 which describes approximately the two-dimensional propagation of surface waves in a uniform horizontal channel containing an incompressible and inviscid fluid which in its undisturbed state has depth $h$. Here $u(x,t)$ represents the deviation of the water surface from its undisturbed position, and the flow is assumed to be irrotational. The BBM equation features a bounded dispersion relation (Benjamin, Bona and Mahony ). We utilize this boundedness to prove existence, uniqueness and regularity results for solutions of the BBM equation supplemented with an initial condition and various types of boundary conditions. We also treat the water-wave problem over an uneven bottom. In particular, we consider two different models for the propagation of long waves in channels of decreasing depth and we provide both analytical and numerical results for these models. For the numerical simulation we use a spectral discretization coupled with a four-stage Runge-Kutta time integration scheme. After verifying numerically that the algorithm is fourth-order accurate in time, we run the solitary wave with uneven bottom and examine how solitary waves respond to this non-uniform depth. Our numerical simulations are compared with previous numerical and experimental results of Madsen and Mei and Peregrine. en
dc.format.extent 747345 bytes en
dc.format.mimetype application/pdf en
dc.language.iso eng en
dc.publisher The University of Bergen en
dc.subject BBM equation en
dc.title Boundary-value problems and shoaling analysis for the BBM equation en
dc.type Master thesis eng Master i Anvendt og beregningsorientert matematikk en
dc.type.course MAB399 en
dc.subject.nsi VDP::Mathematics and natural science: 400::Mathematics: 410::Analysis: 411 en
dc.subject.archivecode Mastergrad en
dc.subject.nus 753109 en
dc.type.program MAMN-MAB en

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