1,720,997 research outputs found
A coupling concept for Stokes-Darcy systems: The ICDD method
Full text linkWe present a coupling framework for Stokes-Darcy systems valid for arbitrary flow direction at low Reynolds numbers and for isotropic porous media. The proposed method is based on an overlapping domain decomposition concept to represent the transition region between the free-fluid and the porous-medium regimes. Matching conditions at the interfaces of the decomposition impose the continuity of velocity (on one interface) and pressure (on the other one) and the resulting algorithm can be easily implemented in a non-intrusive way. The numerical approximations of the fluid velocity and pressure obtained by the studied method converge to the corresponding counterparts computed by direct numerical simulation at the microscale, with convergence rates equal to suitable powers of the scale separation parameter ε in agreement with classical results in homogenization
A Primer on Mathematical Modelling
No full textIn this book we describe the magic world of mathematical models: starting from real-life problems, we formulate them in terms of equations, transform equations into algorithms and algorithms into programs to be executed on computers.
A broad variety of examples and exercises illustrate that properly designed models can, e.g.: predict the way the number of dolphins in the Aeolian Sea will change as food availability and fishing activity vary; describe the blood flow in a capillary network; calculate the PageRank of websites.
This book also includes a chapter with an elementary introduction to Octave, an open-source programming language widely used in the scientific community. Octave functions and scripts for dealing with the problems presented in the text can be downloaded from https://paola-gervasio.unibs.it/quarteroni-gervasio
This book is addressed to any student interested in learning how to construct and apply mathematical models
I delfini delle Eolie, i battiti del cuore, i motori di ricerca
No full textChe cos'hanno in comune la dinamica tra prede e predatori, la circolazione del sangue e l'ordinamento delle pagine web svolto da un motore di ricerca? La risposta è la matematica, o meglio, i modelli matematici, che consentono di descrivere i fenomeni della realtà.
Con questo volume per le scuole superiori (corredato da una piattaforma online) viene presentata la matematica che sta sotto la realtà. I modelli matematici sono infatti come scatole magiche: partendo dal mondo reale si formulano equazioni e si calcolano soluzioni al computer.
Se i congegni dentro la scatola sono ben costruiti, si può prevedere come cambia il numero dei delfini delle Eolie al variare della disponibilità di cibo e dell'attività umana, si può descrivere il flusso del sangue in una rete di capillari o calcolare il PageRank delle pagine del web
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