Development of strategies to capture discontinuities for conservation laws and related problems in fluid dynamics

Author(s)

Giseli Aparecida Braz de Lima

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2010-03-23

Examining board members

Valdemir Garcia Ferreira; Jesús Salvador Pérez Guerrero; Marcello Augusto Faraco de Medeiros

• Advisor: Valdemir Garcia Ferreira

Abstract

This dissertation deals with the numerical solution of fluid dynamics problems using two new high resolution upwind schemes,. namely FDPUS-C1 and SDPUS-C1, for the discretization of the linear and non-linear convection terms. The Schemes are based on TVD and DBC stability criteria and are implemented in the context of the finite difference and finite volume methodologies, either into the Freeflow code for 2D, 2D-1/2 and 3D incompressible flows or in the well-known CLAWPACK code for 1D and 2D compressible flows. Several computational tests are performed to verify and validate the numerical methods against other popularly used upwind schemes. The new schemes are then applied to solve a wide range of problems in CFD, such as shock wave propagation and incompressible fluid flows involving moving free msurfaces. In particular, the numerical results for 2D hyperbolic conservation laws and 2D, 2D-1/2 and 3D incompressible Navier-Stokes eqautions show that new polynomial upwind convection schemes perform very well (AU)

• FAPESP's process: 08/01258-3 - Development, analysis and implementation of polynomials upwind schemes of high resolution with Aplication in unsteady incompressíble flow with free surface
• Grantee: Giseli Aparecida Braz de Lima
• Support Opportunities: Scholarships in Brazil - Master