References
- C. J. Roy and W. L. Oberkampf, “A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing,” Comput. Methods Appl. Mech. Eng., vol. 200, pp. 2131–2144, 2011. DOI: 10.1016/j.cma.2011.03.016.
- Z. Y. Li and W. Q. Tao, “A new stability-guaranteed second-order difference scheme,” Numer. Heat Transfer Part B, vol. 42, pp. 349–365, 2002. DOI: 10.1080/10407790190053987.
- R. Abedian, H. Adibi, and M. Dehghan, “A high-order symmetrical weighted hybrid ENO-flux limiter scheme for hyperbolic conservation laws,” Comput. Phys. Commun., vol. 185, pp. 106–127, 2014. DOI: 10.1016/j.cpc.2013.08.020.
- D. L. Sun, Z. G. Qu, Y. L. He, and W. Q. Tao, “An efficient segregated algorithm for incompressible fluid flow and heat transfer problems-IDEAL (inner doubly iterative efficient algorithm for linked equations), part I: Mathematical formulation and solution procedure,” Numer. Heat Transfer Part B, vol. 53, pp. 1–17, 2008. DOI: 10.1080/10407790701632543.
- D. L. Sun, Z. G. Qu, Y. L. He, and W. Q. Tao, “An efficient segregated algorithm for incompressible fluid flow and heat transfer problems-IDEAL (inner doubly iterative efficient algorithm for linked equations), part II: Application examples,” Numer. Heat Transfer, Part B, vol. 53, pp. 18–38, 2008. DOI: 10.1080/10407790701632527.
- L. Duchemin and J. Eggers, “The explicit-implicit-null method: Removing the numerical instability of PDEs,” J. Comput. Phys., vol. 263, no. 15, pp. 37–52, 2014. DOI: 10.1016/j.jcp.2014.01.013.
- L. Eça and M. Hoekstra, “A procedure for the estimation of the numerical uncertainty of CFD calculations based on grid refinement studies,” J. Comput. Phys., vol. 262, no. 1, pp. 104–130, 2014. DOI: 10.1016/j.jcp.2014.01.006.
- J. Teixeira, C. A. Reynolds, and K. Judd, “Time step sensitivity of nonlinear atmospheric models: Numerical convergence, truncation error growth, and ensemble design,” J. Atmos. Sci., vol. 64, pp. 175–189, 2007. DOI: 10.1175/jas3824.1.
- J. Li, “Computational uncertainty principle: Meaning and implication,” Bull. Chin. Acad. Sci., vol. 15, pp. 428–430, 2000.
- J. Li and S. Wang, “Some mathematical and numerical issues in geophysical fluid dynamics and climate dynamics,” Commun. Comput. Phys. vol. 3, pp. 759–793, 2008. DOI: 10.1007/978-1-4614-8963-4_5.
- P. Wang, J. Li, and Q. Li, “Computational uncertainty and the application of a high-performance multiple precision scheme to obtaining the correct reference solution of Lorenz equations,” Numer. Algorithms, vol. 59, pp. 147–159, 2012. DOI: 10.1007/s11075-011-9481-6.
- X. H. Zhang and D. Angeli, “Flow transitions in a Joule-heated cavity of a low-Prandtl number fluid,” Int. J. Therm. Sci., vol. 50, pp. 2063–2077, 2011. DOI: 10.1016/j.ijthermalsci.2011.06.008.
- G. Sugilal, P. K. Wattal, and K. Iyer, “Convective behaviour of a uniformly Joule-heated liquid pool in a rectangular cavity,” Int. J. Therm. Sci., vol. 44, pp. 915–925, 2005. DOI: 10.1016/j.ijthermalsci.2005.03.012.