Efficient Software for Computing Correlated K-Ss Tomographs Dr. Chin Man ‘ Bill ’ Mok, Institute of Advanced Studies Dr. Iason Papaioannou, Engineering Risk Analysis
Computational Modeling of Saturated Flow Governing differential equation: Finite element solution: ( ) + S Ñ× K Ñ h s h = q { } = q [ ] h [ ] h { } + S { } K s ( ) K = K x , y , z = hydraulic conductivity ( ) s = S S s x , y , z = specific storage ( ) h = h x , y , z , t = potentiometric head ( ) Hydraulic Tomography – q = q x , y , z , t = source/sink rate ‘CAT scan’ of the subsurface (e ) T ru e K fie ld K (m /d ) Yeh and Liu (2000) to estimate 2 .8 0 2 .2 0 the spatial distributions of K 1 5 1 .7 3 and Ss (tomographs/images) 1 .3 6 1 0 1 .0 7 by applying hydraulic stresses 0 .8 4 z (m ) at various locations 0 .6 6 5 0 .5 2 sequentially and observing the 0 .4 1 0 0 hydraulic responses at other 0 .3 2 0 5 5 0 .2 5 y (m ) x (m ) 1 0 1 0 measurement locations 0 .2 0 1 5 1 5 (From Professor Jim Yeh at University of Arizona) 2
Software Lab Project Tasks In this software lab project, the students will: (1) develop a program to compute the hydraulic responses (h) to hydraulic stresses (q) by using linear 3D finite elements to solve the governing differential equation; (2) implement the adjoint sensitivity method to efficiently compute the first-derivatives of h with respect to K and Ss at each pixel; (3) test the significance of incorporating K-Ss correlation on the tomographs using data at University of Waterloo experimental site. (Optional) – If time allows, implement efficient representations of correlated K-Ss fields to obtain compressed high-resolution tomographs for large scale problems.
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