Development and applications of hydrodynamic model SPheRIO

Author(s)

Weixian Chen

• Document type: Master's Dissertation
• Institution: Universidade Estadual Paulista (Unesp)
• Defense date: 2017-08-30
• Advisor: Weiliang Qian; Kai Lin

Abstract

In this dissertation, we investigate the numerical algorithm known as the Smoothed Particle Hydrodynamics (SPH). The SPH interpolation algorithm are widely used for partial differential equations and for applications such as problems in heavy ion collisions for instance one dimensional Landau model and transverse expansion under a longitudinal scaling expansion. Important properties accuracy, efficiency, stability are discussed. As SPH IS a mesh free method, the merits and drawbacks comparing with previous grid based methods are summarized. For high energy collision, the compound system can be modeled by hydrodynamics. In particular, the Euler equation and its relativistic version are addressed. Besides the conventional SPH method, the finite particle method (FPM) which makes use of the Taylor series expansion of unknown smooth functions is also investigated. For the one dimensional Landu model, both algorithms are applied and results are compared. Owing to the better accuracy of the FPM, the corresponding hydrodynamic equation of motion is derived. We show that the derived equation of motion guarantees better particle consistency. Efforts have also been made in developing programs to study the numerical solution of Landau’s hydrodynamical model. We write some short programs in c++ to numerically calculate the temporal evolution of Landau’s model. The results are then compared to those of the analytic approach. Moreover the code based on the standard SPH algorithm is modified to investigate FPM scheme. (AU)

• FAPESP's process: 15/06212-5 - Development and applications of hydrodynamic model SPheRIO
• Grantee: Weixian Chen
• Support Opportunities: Scholarships in Brazil - Master