A unsplitting finite volume method for models with stiff relaxation source terms

Author(s)

Abreu, Eduardo ^[1] ; Bustos, Abel ^[2] ; Lambert, Wanderson ^[3]

Affiliation

^[1] Univ Estadual Campinas, Dept Appl Math, IMECC, BR-13083859 Campinas, SP - Brazil

^[2] Natl Lab Sci Comp, LNCC, BR-25651075 Petrpolis, RJ - Brazil

^[3] Fed Univ Rural Rio de Janeiro, Rod BR 465, Km 7, BR-23890000 Seropedica, RJ - Brazil

• Document type: Journal article
• Source: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY; v. 47, n. 1, p. 5-20, MAR 2016.
• Web of Science Citations: 1

Abstract

We developed an unsplitting finite volume scheme to account the delicate nonlinear balance between numerical approximations of the hyperbolic flux function and the source linked to balance laws. The method is Riemann-solver-free and no upwinding technique is used. By means of this new approach, we conducted an analysis for two new models of balance laws linked to compositional and thermal flow in porous media problems, under and without a thermodynamic equilibrium hypothesis. For concreteness, we adopt the nitrogen and steam injection models in a porous media. To this model we found an interesting behavior linked to the relaxation term, which is the existence of a non-monotonic traveling wave. We applied this numerical technique to others well-known differential models with relaxation terms available in the literature. Qualitatively we were able to reproduce the expected results. (AU)

• FAPESP's process: 14/03204-9 - Computing qualitatively correct approximations of partial differential equations in porous media transport phenomena
• Grantee: Eduardo Cardoso de Abreu
• Support Opportunities: Regular Research Grants
• FAPESP's process: 11/23628-0 - Systems of Balance Laws Problems in Fluid Dynamics in Porous Media: Mathematical Modeling and Numerical Approximation
• Grantee: Abel Alvarez Bustos
• Support Opportunities: Scholarships in Brazil - Doctorate
• FAPESP's process: 11/11897-6 - Numerical analysis and mathematical modeling of non-linear PDEs applied to fluid dynamics in porous media
• Grantee: Eduardo Cardoso de Abreu
• Support Opportunities: Regular Research Grants