Integrating adjoint based analysis and advanced interface capturing for accurate hazard prediction in geophysical mass flows
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Multi-scale physics, uncertain parameters, the sparsity of the data, and spurious features in numerical solutions are among the challenges in studying hazardous geophysical mass flows numerically using depth-averaged assumptions. In this dissertation, we discussed and addressed the “thin layer" or wetting/drying problem and the computing and use of discrete adjoints in numerical simulations of this class of flow. Adjoint-based methods allow effective use of the information in simulations for a number of purposes -- notable among them being numerical error estimation in quantities of interest and uncertainty quantification. The thin layer problem or wetting/drying problem is a very important challenge for all of the shallow water type equations. For the first time, here, we used two Eulerian interface capturing techniques to address this problem and compared the obtained results with a heuristic method which is the conventional way to address this problem. By the numerical techniques that we used to decrease the computational cost, we successfully and more accurately captured the interface for flows at Colima volcano with the level set and phase field methods with the same computational cost. On the second part of this dissertation, we introduced a new framework and the data structures for computing discrete adjoints for our finite volume code which has the adaptive mesh refinement and parallel computing features. Moreover, the proper way to compute the discrete Jacobian and also efficient ways to access the data with affordable computational cost were presented. After computing and verifying the computed discrete adjoint its results were used for error estimation and construction of a gradient-enhanced Kriging based surrogate for the different quantity of the interests.