Systems of Balance Laws Problems in Fluid Dynamics in Porous Media: Mathematical Modeling and Numerical Approximation

• Grant number: 11/23628-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Effective date (Start): March 01, 2012
• Effective date (End): July 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Eduardo Cardoso de Abreu
• Grantee: Abel Alvarez Bustos
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

Multiphase fluid flows with mass transfer between different phases are governed by compositional models, in the context of petroleum engineering. These are evolution equations that represent the conservation of mass of each chemical component, supplemented by equations of state and thermodynamic relationships. Analytical solutions for this type of problems are very poor, then accurate numerical methods to simulate these class of systems are a very important and powerfull tool to get insight about the qualitative behavior of the structure of the solution. In this paper we concerned of a class of 2 by 2 system of balance laws with phase change. Here we introduce new mathematical theory for such systems and a fractional time-step method is presented and used to address the problem at hand.Key words: Balance Laws, Operator Splitting, Central Differencing Scheme, Thermal Porous Media Flow.

Scientific publications

(6)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

ABREU, E.; LAMBERT, W.; PEREZ, J.; SANTO, A.. A new finite volume approach for transport models and related applications with balancing source terms. MATHEMATICS AND COMPUTERS IN SIMULATION, v. 137, n. SI, p. 2-28, JUL 2017. (11/23628-0, 14/03204-9)

ABREU, EDUARDO; BUSTOS, ABEL; LAMBERT, WANDERSON. Non-monotonic traveling wave and computational solutions for gas dynamics Euler equations with stiff relaxation source terms. COMPUTERS & MATHEMATICS WITH APPLICATIONS, v. 70, n. 9, p. 2155-2176, NOV 2015. (14/03204-9, 11/23628-0)

ABREU, E.; LAMBERT, W.; PEREZ, J.; SANTO, A.. A new finite volume approach for transport models and related applications with balancing source terms. MATHEMATICS AND COMPUTERS IN SIMULATION, v. 137, p. 27-pg., 2017-07-01. (11/23628-0, 14/03204-9)

ABREU, EDUARDO; BUSTOS, ABEL; LAMBERT, WANDERSON. A unsplitting finite volume method for models with stiff relaxation source terms. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 47, n. 1, p. 5-20, MAR 2016. (14/03204-9, 11/23628-0, 11/11897-6)

ABREU, EDUARDO; VIEIRA, JARDEL. Computing numerical solutions of the pseudo-parabolic Buckley Leverett equation with dynamic capillary pressure. MATHEMATICS AND COMPUTERS IN SIMULATION, v. 137, p. 20-pg., 2017-07-01. (11/23628-0, 14/03204-9)

ABREU, EDUARDO; VIEIRA, JARDEL. Computing numerical solutions of the pseudo-parabolic Buckley Leverett equation with dynamic capillary pressure. MATHEMATICS AND COMPUTERS IN SIMULATION, v. 137, n. SI, p. 29-48, JUL 2017. (11/23628-0, 14/03204-9)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

BUSTOS, Abel Alvarez. Sistema de leis de balanço em problemas de dinâmicas de fluidos: modelagem matemática e aproximação numérica. 2015. Doctoral Thesis - Universidade Estadual de Campinas (UNICAMP). Instituto de Matemática, Estatística e Computação Científica Campinas, SP.