Numerical realization of the generalized Carrier-Greenspan Transform for the shallow water wave equations

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Show simple item record Harris, Matthew W. 2015-10-28T01:03:37Z 2015-10-28T01:03:37Z 2015-08
dc.description Thesis (M.S.) University of Alaska Fairbanks, 2015 en_US
dc.description.abstract We study the development of two numerical algorithms for long nonlinear wave runup that utilize the generalized Carrier-Greenspan transform. The Carrier-Greenspan transform is a hodograph transform that allows the Shallow Water Wave equations to be transformed into a linear second order wave equation with nonconstant coefficients. In both numerical algorithms the transform is numerically implemented, the resulting linear system is numerically solved and then the inverse transformation is implemented. The first method we develop is based on an implicit finite difference method and is applicable to constantly sloping bays of arbitrary cross-section. The resulting scheme is extremely fast and shows promise as a fast tsunami runup solver for wave runup in coastal fjords and narrow inlets. For the second scheme, we develop an initial value boundary problem corresponding to an Inclined bay with U or V shaped cross-sections that has a wall some distance from the shore. A spectral method is applied to the resulting linear equation in order to and a series solution. Both methods are verified against an analytical solution in an inclined parabolic bay with positive results and the first scheme is compared to the 3D numerical solver FUNWAVE with positive results. en_US
dc.language.iso en_US en_US
dc.title Numerical realization of the generalized Carrier-Greenspan Transform for the shallow water wave equations en_US
dc.type Thesis en_US ms en_US
dc.identifier.department Department of Mathematics and Statistics en_US
dc.contributor.chair Rybkin, Alexei
dc.contributor.committee Williams, Gordon
dc.contributor.committee Nikolsky, Dmitry

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