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 (mat+i) 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 us to develop a theory for numerical treatment of 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 (the so-called magnetic particle inspection, MPI): 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 when using transient numerical simulation.