Species Concentration Gradient Method for Solution of Reacting Flow
Abstract
In this article, a new error balance approach utilizing local error per unit step (LEPUS) control strategy has been developed. The error control strategy has been upgraded to incorporate the temporal and spatial discretization error by an adjusting parameter, which has been linked with species gradient present in the chemical mechanism. The accuracy and efficiency of the proposed improved LEPUS (ILEPUS) have been checked by solving the one-dimensional compressible gaseous flow in the absence of a reaction mechanism and compared with the old local error per step (LEPS) and traditional LEPUS strategies. With respect to the concentrations of nitrogen oxide and nitrogen dioxide for the winter season, the simulation predictions have been found to have a positive correlation with the recent experimental data collected in Changchun city, China. For further insights into the scheme, both one- and two-dimensional reacting flows with complex chemical reactions have also been solved using ILEPUS and LEPS, where the ILEPUS scheme has proven better performance as compared with LEPS and LEPUS.
References
I. Ahmad and M. Berzins, “An algorithm for ODEs from atmospheric dispersion problems”, Appl. Numer. Math., vol. 25, no. 2–3, pp. 137–149, 1997.
L.K. Peters et al., “The current state and future direction of Eulerian models in simulating the tropospheric chemistry and transport of trace species: a review”, Atmos. Environ., vol. 29, no. 2, pp. 189–222, 1995.
M. Berzins, A.S. Tomlin, S. Ghorai, I. Ahmad, and J. Ware, “Unstructured Adaptive Mesh MOL Solvers for Atmospheric Reacting-Flow Problems”, in Adaptive Method of Lines, Chapman and Hall/CRC, pp. 337–372, 2001.
R.P. Fedkiw, “A survey of chemicallyreacting, compressible flows”, University of California, Los Angeles, 1996.
J. Lawson, M. Berzins and P.M. Dew, “Balancing space and time errors in the method of lines for parabolic equations”, SIAM J. Sci. Stat. Comput., vol. 12, no. 3, pp. 573–594, 1991.
M. Berzins and J.M. Ware, “Positive cell-centered finite volume discretization methods for hyperbolic equations on irregular meshes,” Appl. Numer. Math., vol. 16, no. 4, pp. 417–438, 1995.
I. Ahmad and M. Berzins, “MOL solvers for hyperbolic PDEs with source terms,” Math. Comput. Simul., vol. 56, no. 2, pp. 115–125, 2001.
M. Berzins, “Temporal error control for convection-dominated equations in two space dimensions,” SIAM J. Sci. Comput., vol. 16, no. 3, pp. 558–580, 1995.
Q. Sheng and A.Q. M. Khaliq, “Linearly implicit adaptive schemes for singular reaction-diffusion equations,” in Adaptive Method of Lines, Chapman and Hall/CRC, 2001, pp. 283–314.
L. Wang, J. Wang, X. Tan, and C. Fang, “Analysis of NOx pollution characteristics in the atmospheric environment in Changchun City,” Atmosphere (Basel)., vol. 11, no. 1, p. 30, 2020.
K. Gasmi, A. Aljalal, W. Al-Basheer, and M. Abdulahi, “Analysis of NOx, NO and NO2 ambient levels in Dhahran, Saudi Arabia,” Urban Clim., vol. 21, pp. 232–242, 2017.
A. Neupane, N. Raj, R. Deo, and M. Ali, “Development of data-driven models for wind speed forecasting in Australia,” in Predictive Modelling for Energy Management and Power Systems Engineering, Elsevier, pp. 143–190, 2021.
M. Azzi, G.M. Johnson, and M.E. Cope, “An introduction to the generic reaction set photochemical smog mechanism”, 1992.
J. Zhong, “Modelling air pollution within a street canyon”, University of Birmingham, 2016.
L.J. Carpenter, K.C. Clemitshaw, R.A. Burgess, S.A. Penkett, J.N. Cape, and G.G. McFadyen, “Investigation and evaluation of the NOx/O3 photochemical steady state”, Atmos. Environ., vol. 32, no. 19, pp. 3353–3365, 1998.
J.M. Haussaire and M. Bocquet, “A low-order coupled chemistry meteorology model for testing online and offline data assimilation schemes: L95-GRS (v1. 0)”, Geosci. Model Dev., vol. 9, no. 1, pp. 393–412, 2016.
T.J. Wallington, E.W. Kaiser, and J.T. Farrell, “Automotive fuels and internal combustion engines: a chemical perspective”, Chem. Soc. Rev., vol. 35, no. 4, pp. 335–347, 2006.
Y. Wu, F. Ma, and V. Yang, “Space--Time Method for Detonation Problems with Finite-rate Chemical Kinetics”, Int. J. Comut. Fluid Dyn., vol. 18, no. 3, pp. 277–287, 2004.
