This thesis investigates the smoothed particle hydrodynamics (SPH) method, which is a numerical mesh-less method particularly suited for the simulation of free surface flows. The formulation is based on a total Lagrangian description of a system of first-order conservation laws, expressed in terms of the linear momentum and the Jacobian of the deformation. In this framework, the evaluation of spatial integrals is performed with respect to the initial undeformed configuration, resulting in an efficient approach that completely circumvents the need for continuous particle neighbor searching. To ensure stability and consistency at the SPH discretisation level, a characteristic-based Riemann solver is employed, designed to preserve both the accuracy and conservation properties of the overall algorithm. This work develops a new time integration scheme based on an implicit strategy, specifically a Crank-Nicolson integrator combined with with a Newton-Raphson iterative procedure to efficiently address the nonlinearities. Unlike traditional explicit schemes, the proposed method removes the restrictions in the time steps imposed by the Courant-Friedrichs-Lewy (CFL) condition, enabling simulations over longer time scales, expanding the range of applications.

Objectius de Desenvolupament Sostenible::9 - Indústria, Innovació i Infraestructura

Objectius de Desenvolupament Sostenible::6 - Aigua Neta i Sanejament

Objectius de Desenvolupament Sostenible::13 - Acció per al Clima