Subgrid-scale modeling of tsunami inundation in coastal urban areas

Numerical tsunami inundation simulations using high-resolution (HR) topographical data are important to predict tsunami damage in urban areas at individual building levels accurately but are challenging due to the high computational cost. To address this issue, a subgrid-scale (SGS) model of tsunami inundation, called the individual drag force model (iDFM), is developed. In this model, the sum of the building drag forces in a computational mesh is fed back to the flow field by taking into account spatial information about multiple structures in the mesh. To evaluate the model performance, idealized numerical experiments using simple urban topography with several types of spatial layout patterns and hindcast physical experiments focusing upon Onagawa Town affected by the 2011 Tohoku, Japan tsunami as a historical event are conducted. Results are compared with HR tsunami simulations using building-resolved topographical data, called the structure resolving model (SRM). In general, the iDFM (and other SGS models) characterizes the effects of structures as resistance elements that reduce the fluid velocity in momentum conservation. On the other hand, the SRM evaluates these effects as topography and feeds them back into not only momentum conservation but also mass conservation and wet/dry boundary conditions. Therefore, the iDFM can model the overall inundation characteristics, such as the limits of inundation, more than 102 times efficiently compared with the SRM, although it cannot capture local phenomena driven by structures, such as surface rising due to blocking and contracting current between structures. In both numerical and historical tsunami (Onagawa) cases, there were small differences between the modeled inundation characteristics, such as the maximum surface elevation and fluid velocity, and the time series of inundation leading edges determined by the iDFM due to the computational grid cell sizes. The observed differences between the idealized numerical experiment and the historical tsunami case can be affected by the drag coefficient and the Froude number during the tsunami run-up.