The SUPER Numerical Scheme for the Discretization of the Convection Terms in Computational Fluid Dynamics Computations
- 127 Downloads
The numerical simulation of fluid flow and heat/mass transfer phenomena requires the numerical solution of the Navier–Stokes and energy conservation equations coupled with the continuity equation. Numerical or false diffusion is the phenomenon of producing errors in the calculations that compromise the accuracy of the computational solution. According to Spalding, the Taylor series analysis that reveals the truncation/discretization errors of the differential equations terms should not be classified as false diffusion. Numerical diffusion, in the strict sense of definition, appears in multidimensional flows when the differencing scheme fails to account for the true direction of the flow. Numerical errors associated with false diffusion are investigated via two- and three-dimensional problems. A numerical scheme must satisfy some necessary criteria for the successful solution of the convection–diffusion formulations. The common practice of approximating the diffusion terms via the central-difference approximation is satisfactory. Attention is directed to the convection terms since their approximations induce false diffusion. The conservation equations of all the dependent variables in this study are discretized by the finite volume method. The performance of different numerical schemes (e.g. hybrid, van Leer, SUCCA and the novel SUPER version) is studied in this chapter by the numerical simulation of the transport of a scalar quantity in an inclined and tubular airflow, heat conduction in a cylindrical heat exchanger, and the water vapour condensation in an enclosed space. The numerical accuracy of the predictions obtained when using the various schemes was also studied in the classical cases of the backward-facing step and of an inclined inflow. The study focused on the transport of a contaminant concentration by means of an airflow, the diffusion of temperature in an water flow and at the solid surface of a triple tube, the mass transfer interaction between liquid droplets and humid air and on circular airflow predictions. An Eulerian one- and two-phase flow model is developed within the CFD general-purpose computer program PHOENICS, which considers the phases as interpenetrating continua. The phases may move at different velocities (slip velocity) in a manner that is dictated by the interphase friction. According to the numerical results obtained, it is concluded that the predictions improve when using SUPER in all cases of inclined flow and of humid air precipitation while they are similar to the predictions of the other schemes in the case of heat conduction in the tubular flow.
KeywordsFalse diffusion Numerical dispersion Computational errors Finite volume method Discretization schemes The SUPER scheme
The second author (D. P. Karadimou) gratefully acknowledges the financial support from the State Scholarships Foundation of Greece through the ‘‘IKY Fellowships of Excellence for Postgraduate studies in Greece-SIEMENS’’ Program.
- 7.Leonard, B. P. (1979). A stable and accurate convective modelling procedure based on quadratic upstream interpolating. Computational Mechanics and Applied Mechanical Engineering, 4, 557–559.Google Scholar
- 13.Versteeg, H. K., & Malalasekera, W. (1995). An introduction to computational fluid dynamics—The finite volume method. Essex, England: Longman Group Ltd.Google Scholar
- 14.Spalding, D. B. (1978). Numerical computation of multiphase flow and heat-transfer. In C. Taylor, & K. Morgan (Eds.), Contribution to recent advances in numerical methods in fluids (pp. 139–167). Pineridge Press.Google Scholar
- 19.Karadimou, D. P., & Markatos, N. C. (2018). Study of the numerical diffusion in computational calculations (pp. 65–78). London, UK: Intechopen Publisher.Google Scholar
- 26.Padfield, T. Conservation physics. An online textbook in serial form. http://www.conservationphysics.org/atmcalc/atmoclc2.pdf.
- 27.Wexler, A. (1983). ASHRAE Handbook: Thermodynamic properties of dry air, moist air and water and SI psychrometric charts (p. 360). New York.Google Scholar
- 29.Karadimou, D. P., & Markatos, N. C. (2013). Two-phase transient mathematical modelling of indoor aerosol by means of a flow-oriented discretization scheme. In CD Proceedings of 10th HSTAM International Congress on Mechanics, Chania, Crete, May 2013.Google Scholar
- 42.Ishii, M., & Mishima, K. (1984). Two-fluid model and hydrodynamic constitutive relations. Nuclear Engineering and Design, (82), 107–126.Google Scholar
- 45.ASHRAE handbook-Fundamentals, 2013.Google Scholar