A new modified skew upwind differencing scheme for convective flows

References

• D. Zhang, C. Jiang, C. Yang and Y. Yang, “Assessment of different reconstruction techniques for implementing the NVSF schemes on unstructured meshes,” Int. J. Numer. Methods Fluids, vol. 74, no. 3, pp. 189–221, 2014. DOI: 10.1002/fld.3846.
   Web of Science ®Google Scholar
• G. D. Raithby and K. E. Torrance, “Upstream weighted differencing schemes and their application to elliptic problems involving fluid flow,” Comput. Fluids, vol. 2, no. 2, pp. 191–206, 1974. DOI: 10.1016/0045-7930(74)90013-9.
   Google Scholar
• W. Barga, “On the use of some weighted upwind schemes for strongly convective flows,” Numer. Heat Transfer B, vol. 18, pp. 43–60, 1990.
   Web of Science ®Google Scholar
• M. Kobayashi, J. M. C. Pereira and J. C. F. Pereira, “A second-order upwind least-squares scheme for incompressible flows on unstructured hybrid grids,” Numer. Heat Transfer B, vol. 34, no. 1, pp. 39–60, 1998. DOI: 10.1080/10407799808915047.
   Web of Science ®Google Scholar
• Y. H. Zurigat and A. J. Ghajar, “Comparative study of weighted upwind and second order upwind difference schemes,” Numer. Heat Transfer B, vol. 18, no. 1, pp. 61–80, 1990. DOI: 10.1080/10407799008944942.
   Web of Science ®Google Scholar
• T. Chourishi, “Proposition of modified convection boundedness criterion and its evaluation for the development of bounded schemes,” Appl. Math. Comput., vol. 346, pp. 710–739, 2019.
   Web of Science ®Google Scholar
• B. P. Leonard, “Simple high accuracy resolution program for convective modelling of discontinuities,” Int. J. Numer. Methods Fluids, vol. 8, no. 10, pp. 1291–1318, 1988. DOI: 10.1002/fld.1650081013.
   Web of Science ®Google Scholar
• S. B. Paramane and A. Sharma, “Consistent implementation and comparison of FOU, CD, SOU, and QUICK convection schemes on square, skew, trapezoidal, and triangular lid-driven cavity flow,” Numer. Heat Transfer B, vol. 54, no. 1, pp. 84–102, 2008. DOI: 10.1080/10407790802122519.
   Web of Science ®Google Scholar
• C. Shu, “TVB uniformly high-order schemes for conservation law,” Math. Comput, vol. 49, no. 179, pp. 105–121, 1987. DOI: 10.1090/S0025-5718-1987-0890256-5.
   Web of Science ®Google Scholar
• G. D. Raithby, “Skew upstream differencing schemes for problem involving fluid flow,” Comput. Methods Appl. Mech. Eng., vol. 9, no. 2, pp. 153–164, 1976. DOI: 10.1016/0045-7825(76)90058-X.
   Google Scholar
• M. Darwish and F. Moukalled, “A new approach for building bounded skew upwind schemes,” Comput. Methods Appl. Mech. Eng., vol. 129, no. 3, pp. 221–233, 1996. DOI: 10.1016/0045-7825(95)00881-0.
   Web of Science ®Google Scholar
• P. H. Gaskell and A. K. C. Lau, “Curvature compensated convective transport: SMART, a new boundedness-preserving transport algorithm,” Int. J. Numer. Methods Fluids, vol. 8, no. 6, pp. 617–641, 1988. DOI: 10.1002/fld.1650080602.
   Web of Science ®Google Scholar
• Y. A. Hassan, J. G. Rice and J. H. Kim, “A stable mass-flow-weighted two-dimensional skew upwind scheme,” Numer. Heat Transfer, vol. 6, no. 4, pp. 395–408, 1983. DOI: 10.1080/01495728308963096.
   Google Scholar
• F. Moukalled and M. Darwish, “A new family of streamline-based very-high resolution Schemes,” Numer. Heat Transfer B, vol. 32, no. 3, pp. 299–320, 1997. DOI: 10.1080/10407799708915011.
   Web of Science ®Google Scholar
• F. Moukalled and M. Darwish, “New bounded skew central difference scheme, part I: formulation and testing,” Numer. Heat Transfer B, vol. 31, no. 1, pp. 91–110, 1997. DOI: 10.1080/10407799708915101.
   Web of Science ®Google Scholar
• M. A. R. Sharif, “An evaluation of the bounded directional transportive upwind differencing scheme for convection-diffusion problems,” Numer. Heat Transfer B, vol. 23, no. 2, pp. 201–219, 1993. DOI: 10.1080/10407799308914897.
   Web of Science ®Google Scholar
• C. R. Swaminathan, V. R. Voller and S. V. Patankar, “A streamline upwind control volume finite element method for modeling fluid flow and heat transfer problems,” Finite Elements Anal. Design, vol. 13, no. 2-3, pp. 169–184, 1993. DOI: 10.1016/0168-874X(93)90055-U.
   Google Scholar
• M. A. R. Sharif and A. A. Busnaina, “Evaluation and comparison of bounding techniques for convection-diffusion problems,” J. Fluids Eng. ASME, vol. 115, no. 1, pp. 33–40, 1993. DOI: 10.1115/1.2910109.
   Web of Science ®Google Scholar
• S. Zhou, J. A. Mccorquodale and Z. Ji, “Semi-implicit skew upwind method for problems in environmental hydraulics,” Int. J. Numer. Methods Fluids, vol. 17, no. 9, pp. 803–823, 1993. DOI: 10.1002/fld.1650170905.
   Web of Science ®Google Scholar
• S. V. Patankar, Numerical Heat Transfer and Fluid Flow. New York: Hemisphere Publishing Corporation, 1980.
   Google Scholar
• H. K. Versteeg and W. Malalasekera, An Introduction to Computational Fluid Dyanmics the Finite Volume Method. Harlow: Longman Scientific & Technical, 1995.
   Google Scholar
• T. Chourishi, “A high resolution equi-gradient scheme for convective flows,” Appl. Math. Comput., vol. 338, pp. 123–140, 2018.
   Web of Science ®Google Scholar
• D. L. Sun, Z. G. Qu, Y. L. He and W. Q. Tao, “A novel segregated algorithm for incompressible fluid flow and heat transfer problems- CLEAR (Coupled and Linked Equations Algorithm Revised) Part I: Mathematical formulation and solution procedure,” Numer. Heat Transfer B, vol. 45, no. 1, pp. 1–17, 2004. DOI: 10.1080/1040779049025485.
   Web of Science ®Google Scholar
• U. Ghia, K. N. Ghia and C. T. Shin, “High-resolutions for incompressible flow using the Navier-Stokes equations and a multigrid method,” J. Comput. Phys., vol. 48, no. 3, pp. 387–411, 1982. DOI: 10.1016/0021-9991(82)90058-4.
   Web of Science ®Google Scholar