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dc.contributor.authorSenthilkumar, Amuthaeng
dc.date.accessioned2012-04-24T07:57:19Z
dc.date.available2012-04-24T07:57:19Z
dc.date.issued2012-02-20eng
dc.date.submitted2012-02-20eng
dc.identifier.urihttp://hdl.handle.net/1956/5772
dc.description.abstractIn 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.extent747345 byteseng
dc.format.mimetypeapplication/pdfeng
dc.language.isoengeng
dc.publisherThe University of Bergeneng
dc.subjectBBM equationeng
dc.titleBoundary-value problems and shoaling analysis for the BBM equationeng
dc.typeMaster thesiseng
dc.type.degreeMaster i Anvendt og beregningsorientert matematikknob
dc.type.courseMAB399eng
dc.subject.nsiVDP::Mathematics and natural science: 400::Mathematics: 410::Analysis: 411eng
dc.subject.archivecodeMastergradeng
dc.subject.nus753109eng
dc.type.programMAMN-MABeng


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