Some case studies in environmental and industrial mathematics
This presentation deals with four case studies in environmental and industrial mathematics developed by the Mathematical Engineering research group from the University of Santiago de Compostela and the Technological Institute for Industrial Mathematics (ITMATI). The ﬁrst case involves environmental ﬂuid mechanics: optimizing the location of submarine outfalls on the coast. This work, related to shallow water equations with variable depth led to develop a theory for dealing with source terms in nonlinear ﬁrst order hyperbolic balance laws. More recently, these techniques have been applied to solve Euler equations with source terms arising from numerical simulation of gas transportation networks when topography via gravity force is considered in the model. The last two problems concerns electromagnetism. One of them is related to nondestructive testing of car parts by using magnetic nanoparticles: mathematical modelling of magnetic hysteresis to simulate demagnetization. Finally, we present a mathematical procedure to reduce the computing time needed to achieve the stationary state of an induction electric machine by numerical simulation.
Keywords: Numerical simulation. Environmental hydraulics. Gas networks. Nondestructive testing. Electric machines.