Shallow water equations

ce od f th to i mpo result in undesirable errors, a general benchmark test has been undertaken to provide a parameter range for expected accuracy and stability. Long wave propagation onto a shallow shelf is simulated to validate over a a tran nges re itting w 100 km in the deep ocean, is considerably larger than water depth. Therefore, the usual approach to describe tsunami evolution is to take either the linear or nonlinear shallow-water models as the governing equations. A number of computational models based on this approximation exist, and some are introduced here. Meth-od of splitting tsunami (MOST) developed by Titov and Synolakis (1998) is capable of predicting wave height or inundation using a tions. Depending on the wavelength of the tsunami, however, frequency dispersion effects can be significant. Specifically, neither hydro-static pressure nor depth-constant horizontal velocity can be presumed. For transoceanic propagation of a tsunami as well as landslide-generated tsunami, the dispersive effects, estimated through the ratio of water depth to wavelength, should be included to yield more accurate results (e.g., Yoon, 2002; Lynett et al., 2003; Grilli et al., 2007). For this reason, some efforts to add the frequency dispersion effect into non-dispersive models through numerical truncation error have been made (e.g., Yoon, 2002