An upwind finite volume method on non-orthogonal quadrilateral meshes for the convection diffusion equation in porous media

References

• Hyman JM, Li S, Knuppy P, Shashkov M. An algorithm for aligning a quadrilateral grid with internal boundaries. J. Comput. Phys. 2002;631:133–149.
   Google Scholar
• Alvarez A, Jiménez O, Buitrago S. Generación de mallas 2D conformes no estructuradas de cuadriláteros, para dominios con fronteras internas [Generation of 2D conform non-structured quadrilateral meshes for domains with internal boundaries]. Proceedings of the VII Jornadas de Aplicaciones Matemáticas, Valencia, Venezuela; 2008.
   Google Scholar
• Borregales M, Jiménez O, Buitrago S. Generación de mallas de cuadriláteros para yacimientos bidimensionales con fronteras internas complejas [Quadrilateral mesh generation for bidimensional reservoirs with complex internal boundaries]. In: García T, Martínez C, editors. Proceedings of the VI Encuentro Colombia-Venezuela de Estadística, VIII Jornadas de Aplicaciones Matemáticas. ISBN: 978-980-12-4063-1, Valencia, Venezuela; 2009.
   Google Scholar
• Valido J, Jiménez O, Buitrago S. Gradient spectral methods for 2D quadrilateral mesh generation aligned to complex internal boundaries in oil reservoirs. In: Dávila E, Uzcátegui G, Cerrolaza M, editors. Proceeding of the XI international congress of numerical methods in engineering and applied sciences, CIMENICS 2012. ISBN:978-980-7161-03-9, Margarita Island, Venezuela, p. MM55–MM60; 2012.
   Google Scholar
• Buitrago S, Jiménez O. Quadrilateral grid generation for 2D oil reservoir with complex internal boundaries using gradient techniques. Proceedings of the 6th international conference on approximation methods and numerical modelling in environment and natural resources (MAMERN’15). Pau, France, ISBN: 978-84-338-5783-5, p. 245–264, June 1--5, 2015.
   Google Scholar
• La Cruz W, Raydan MM. Nonmonotone spectral methods for large-scale nonlinear systems. Optim. Methods Softw. 2003;18:583–599.
   Web of Science ®Google Scholar
• Chen Z, Li B, Huan G, Espin D, Klie H, Buitrago S. Control volume function approximation method for the black oil model. Proceeding of the 2nd Meeting on Reservoir Simulation 2002 Nov 5--6; Buenos Aires, Argentina; 2002.
   Google Scholar
• Gao F-Z, Yuan Y-R. An upwind finite volume element method based on quadrilateral meshes for nonlinear convection-diffusion problems. Numer. Methods Partial Differ. Equ. 2009;25:1067–1085. doi:10.1002/num.20387.
   Web of Science ®Google Scholar
• Buitrago S, Jiménez O, Borregales M. Resolution of the Dirichlet problem using finite difference methods on non-orthogonal meshes. In: Chacón R, León F, Duarte V, Verastegui O, editors. Proceeding of the X international congress of numerical methods in engineering and applied sciences, CIMENICS 2010. Mérida, Venezuela. ISBN: 978-980-7161-02-2, p. MF1-MF6; 2010.
   Google Scholar
• Gao F, Yuan Y, Du N. An upwind finite volume element method for nonlinear convection diffusion problem. Am. J. Comput. Math. 2011;1:264–270. doi:10.4236/ajcm.2011.14032.
   Google Scholar
• Sosa G, Jiménez O, Buitrago S. Numerical resolution of the diffusion equation using finite volumes and quadrilateral non-orthogonal meshes in complex structural reservoirs. In: Davila E, Del Rio J, Cerrolaza M, Chacon R, editors. Proceeding of the XII international congress of numerical methods in engineering and applied sciences, CIMENICS 2014. Margarita Island, Venezuela, ISBN: 978-980-7161-04-6, p. TCA43-TCA48; 2014.
   Google Scholar
• Leveque R. Finite volume methods for hyperbolic problems. New York (NY): Cambridge University Press; 2002.
   Google Scholar
• Eymard R, Gallouet T, Herbin R. Finite volume methods. In: Ciarlet PG, Lions JL, editors. Handbook of numerical analysis, volume 7. Amsterdam: North-Holland; 2000. p. 713–1020.2006.
   Google Scholar