Tsunami Modelinghttp://hdl.handle.net/1773/466772021-05-15T06:34:30Z2021-05-15T06:34:30ZSpectral Methods for Partial Differential Equations that Model Shallow Water Wave PhenomenaFabien, Maurice S.http://hdl.handle.net/1773/265352021-02-11T20:23:16ZSpectral Methods for Partial Differential Equations that Model Shallow Water Wave Phenomena
Fabien, Maurice S.
Mathematical models for waves on shallow water surfaces has been of interest to researchers dating back to the 1800's. These models are governed by partial differential equations, and many of them have rich mathematical structure as well as real world applications. This thesis explores a class of numerical techniques for partial differential equations called spectral methods. One can use these spectral methods to approximate solutions to many partial differential equations that model wave type phenomena. Of particular interest are the KdV, BBM, Camassa-Holm, Boussinesq systems, Shallow Water, and Serre Green- Naghdi equations. For all examples presented Matlab code is provided. These files will be uploaded to the GitHub page https://github.com/msfabien/.
Thesis (Master's)--University of Washington, 2014
Finite volume methods for Tsunamis generated by submarine landslidesKim, Jihwanhttp://hdl.handle.net/1773/253742021-02-11T20:32:58Z2014-04-30T00:00:00ZFinite volume methods for Tsunamis generated by submarine landslides
Kim, Jihwan
Submarine landslides can generate tsunamis, and the generated waves can be catastrophic when a large volume of landslide material is involved. Moreover, large earthquakes are often accompanied by submarine landslides that can enhance the magnitude of the resulting tsunamis. In this thesis, numerical schemes are developed to solve the wave propagation problems generated by submarine landslides. Assuming the landslides in a flow regime, depth-averaged models are studied, and finite volume methods are extended to the fully coupled multi-layer shallow water equations. From the fully coupled model, an efficient simplified approach is derived that is often appropriate for tsunamis generated by submarine landslides. These waves can have relatively short wavelength, and another class of equations may be necessary that can handle the dispersion of waves. Several types of the Boussinesq equations have been reviewed and implemented with a hybrid of high-resolution finite volume and finite difference methods. Stability analysis and convergence tests have been performed for the hybrid scheme. The develpoment has been done in the context of the textsc{Geoclaw} framework, a code designed to handle the single-layer shallow water equations, that uses adaptive mesh refinement to model tsunami propagation on a global scale with inundation of specific regions on a fine grid. The newly developed methods, tested on the exact solutions, are validated by comparing to laboratory experiments and by applying to historic events such as the Papua New Guinea 1998 and Storegga slides. Possible scenarios of submarine landslides and resulting tsunamis on the Washington coast were investigated.
Thesis (Ph.D.)--University of Washington, 2014
2014-04-30T00:00:00Z