Mathematical analysis for simulation of incompressible fluid flow

Abstract

The omnipresence and complexity of physical phenomena drive the strong search for tools capable of simulating them, since many applications require computationally viable, reliable and, preferably, low-cost simulations. Thus, a priori, this work has two objectives: i) understand the theoretical foundations of fluid dynamics with an important computational method aimed at simulating incompressible flows, called SPH (Smoothed Particle Hydrodynamic), which will subsequently be implemented; and ii) assist in the consolidation and application of key concepts in mathematical analysis for computer simulation. Our efforts in this work provide mathematical foundations, which in turn, describe the dynamics of fluid dynamic motion.