A positivity-preserving finite volume scheme for convection–diffusion equation on general meshes

References

• E. Bertolazzi and G Manzini, A cell-centered second-order accurate finite volume method for convection–diffusion problems on unstructured meshes, Math Models Methods Appl Sci. 14 (2004), pp. 1235–1260.
   Web of Science ®Google Scholar
• E. Bertolazzi and G. Manzini, A second-order maximum principle preserving finite volume method for steady convection–diffusion problems, SIAM J. Numer. Anal. 43 (2005), pp. 2172–2199.
   Web of Science ®Google Scholar
• J. Bey and G. Wittum, Downwind numbering: robust multigrid for convection–diffusion problems, Appl. Numer. Math. 23 (1997), pp. 177–192.
   Web of Science ®Google Scholar
• Y. Coudiere and G. Manzini, The discrete duality finite volume method for convection–diffusion problems, SIAM J. Numer. Anal. 47 (2010), pp. 4163–4192.
   Web of Science ®Google Scholar
• Y. Coudiere, J. Vila, and P. Villedieu, Convergence rate of a finite volume scheme for a two-dimensional diffusion convection problem, ESAIM: Math. Model. Numer. Anal. 33 (1999), pp. 493–516.
   Web of Science ®Google Scholar
• Z. Gao and J. Wu, A linearity-preserving cell-centered scheme for the heterogeneous and anisotropic diffusion equations on general meshes, Int. J. Numer. Methods Fluids 67 (2011), pp. 2157–2183.
   Web of Science ®Google Scholar
• Z. Gao and J. Wu, A second-order positivity-preserving finite volume scheme for diffusion equations on general meshes, SIAM J. Sci. Comput. 37 (2015), pp. 420–438.
   Web of Science ®Google Scholar
• F. Gao, Y. Yuan, and D. Yang, An upwind finite-volume element scheme and its maximum-principle-preserving property for nonlinear convection–diffusion problem, Int. J. Numer. Meth. Fluids 56 (2008), pp. 2301–2320.
   Web of Science ®Google Scholar
• F. Hermeline, A finite volume method for the approximation of convection–diffusion equations on general meshes, Int. J. Numer. Methods Engng. 91 (2012), pp. 1331–1357.
   Web of Science ®Google Scholar
• B. Lan, Z. Sheng, and G. Yuan, A new positive finite volume scheme for two-dimensional convection–diffusion equation, Z Angew. Math. Mech. 99 (2018), pp. 1–13.
   Web of Science ®Google Scholar
• K. Lipnikov, D. Svyatskiy, and Y. Vassilevski, Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes, J. Comput. Phys. 228 (2009), pp. 703–716.
   Web of Science ®Google Scholar
• K. Lipnikov, D. Svyatskiy, and Y. Vassilevski, A monotone finite volume method for advection–diffusion equations on unstructured polygonal meshes, J. Comput. Phys. 229 (2010), pp. 4017–4032.
   Web of Science ®Google Scholar
• Le. Potier, Finite volume monotone scheme for highly anisotropic diffusion operators on unstructured triangular meshes, C. R. Acad. Bulg. Sci. 341 (2005), pp. 787–792.
   Google Scholar
• P. Sharma and G. Hammett, Preserving monotonicity in anisotropic diffusion, J. Comput. Phys. 227 (2007), pp. 123–142.
   Web of Science ®Google Scholar
• Z. Sheng and G. Yuan, An improved monotone finite volume scheme for diffusion equation on polygonal meshes, J. Comput. Phys. 231 (2012), pp. 3739–3754.
   Web of Science ®Google Scholar
• S. Wang, G. Yuan, Y. Li, and Z. Sheng, A monotone finite volume scheme for advection-diffusion equations on distorted meshes, Int. J. Numer. Methods Fluids 69 (2012), pp. 1283–1298.
   Web of Science ®Google Scholar
• J. Wu and Z. Gao, Interpolation-based second-order monotone finite volume schemes for anisotropic diffusion equations on general grids, J. Comput. Phys. 275 (2014), pp. 569–588.
   Web of Science ®Google Scholar
• G. Yuan and Z. Sheng, Monotone finite volume schemes for diffusion equations on polygonal meshes, J. Comput. Phys. 227 (2008), pp. 6288–6312.
   Web of Science ®Google Scholar
• Q. Zhang, Z. Sheng, and G. Yuan, A finite volume scheme preserving extremum principle for convection–diffusion equations on polygonal meshes, Int. J. Numer. Methods Fluids 84 (2017), pp. 616–632.
   Web of Science ®Google Scholar
• X. Zhang, S. Su, and J. Wu, A vertex-centered and positivity-preserving scheme for anisotropic diffusion problems on arbitrary polygonal grids, J. Comput. Phys. 344 (2017), pp. 419–436.
   Web of Science ®Google Scholar