References

Spalding DB (1972) A novel finite difference formulation for differential expressions involving both first and second derivatives. Int J Numer Meth Eng 4:551–559
Leonard BP (1979) A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput Methods Appl Mech Eng 19:59–98
Raithby GD (1976) A critical evaluation of upstream differencing applied to problems involving fluid flow. Comput Methods Appl Mech Eng 9:75–103
Patankar SV (1980) Numerical heat transfer and fluid flow. Hemisphere Publishing Corporation, McGraw-Hill
Patankar SV, Baliga BR (1978) A new finite-difference scheme for parabolic differential equations. Numer Heat Transf 1:27–37
Courant R, Isaacson E, Rees M (1952) On the solution of nonlinear hyperbolic differential equations by finite differences. Commun Pure Appl Math 5:243–255
Moukalled F, Darwish M (2012) Transient schemes for capturing interfaces of free-surface flows. Numer Heat Transf Part B Fundam 61(3):171–203
Darwish M, Moukalled F (2006) Convective schemes for capturing interfaces of free-surface flows on unstructured grids. Numer Heat Transf Part B Fundam 49(1):19–42
Leonard BP (1979) A survey of finite difference of opinion on numerical muddling of the incomprehensible defective confusion equation. In: Hughes TJR (ed) Finite element methods for convection dominated flows, AMD-34, ASME
Shyy W (1985) A study of finite difference approximations to steady state convection dominate flow problems. J Comput Phys 57:415–438
Leonard BP, Leschziner MA, McGuirk J (1978) Third order finite-difference method for steady two-dimensional convection. In: Taylor C, Morgan K, Brebbia CA (eds) Numerical methods in laminar and turbulent flows. Pentech Press, London, pp 807–819
Fromm JE (1968) A method for reducing dispersion in convective difference schemes. J Comput Phys 3:176–189
Stubley GD, Raithby GD, Strong AB (1980) Proposal for a new discrete method based on an assessment of discretization errors. Numerical Heat Transfer 3:411–428
de Vahl Davis G, Mallinson GD (1972) False diffusion in numerical fluid mechanics. University of New South Wales, School of Mechanical and Industrial Engineering (Report 1972/FMT/1)
Raithby GD (1976) Skew upstream differencing schemes for problems involving fluid flow. Comput Methods Appl Mech Eng 9:153–164
Darwish M, Moukalled F (1996) A new route for building bounded skew-upwind schemes. Comput Methods Appl Mech Eng 129:221–233
Khosla PK, Rubin SG (1974) A diagonally dominant second-order accurate implicit scheme. Comput Fluids 2:207–209
OpenFOAM (2015) Version 2.3.x. http://www.openfoam.org
OpenFOAM Doxygen (2015) Version 2.3.x. http://www.openfoam.org/docs/cpp/