Transport Processes in Inland and Coastal Waters

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In an era of climate change and urban sprawl where flood damage to human life and property are occurring with increasing frequency, the renditions of catastrophic events by severe storms are still very much reliant on models, and these in turn depend on the expert deployment of computational resources. Our research has been focusing on the fronts between water/air masses of different density (Chu 2014; Karimpour Chu Wang PhD thesis 2016; Xie, Karimpour & Chu 2017) and the impact forces of tsunami waves on coastal structures (Xie & Chu 2018a,b). These processes are dependent on waves and turbulence over a wide range of lengths and depths, and in inland and coastal waters the horizontal length of these processes are one or more orders of magnitude greater than the depths of the currents. Our unique numerical method addresses the steep gradient of the shock waves that feed energy toward the fronts of waves. We have successfully implemented our shock-capturing method within the framework of the classical method (Ghanadi & Chu 2015; Karimpour & Chu 2014, 2016, 2018). More importantly, we have invented a novel Lagrangian block simulation method where the computations are conducted by advection of blocks in a Lagrangian reference frame (Tan & Chu 2009; Chu & Altai 2012). The way in which our Lagrangian block simulation eliminates the spurious oscillations and false numerical damping that are inherent in the classical method has allowed us to address many previously unsolvable problems (Tan & Chu 2010a,b,c, 2012 & 2014; Chu and Altai 2018). Our research in the next five years will continue to focus on the modelling of turbulence and waves by simulation. Although a host of rapid advances in computational infrastructure currently have the potential to revolutionize engineering design and research, spurious oscillations and false diffusion have remained insurmountable obstacles. Our research plan will further develop our novel Lagrangian simulation codes for three-dimensional models that overcome these obstacles. We will also further develop our models of ocean currents and atmospheric wind, focusing on the brief and intense exchange at the "window of instability" that is believed to be associated with severe storms using the Lagrangian block simulation method. Our recent simulations of the wave force on a vertical seawall (Xie & Chu 2018a) and the force on coastal structures of finite width (Xie & Chu 2018b) were obtained using open-source codes. The considerable expertise that we acquired with the open-source-code repository tools will support our further studies of the classical method and the novel Lagrangian block simulation method.