Improvement of a nonnegative preserved efficient solver for atmospheric chemical kinetic equations

  • Authors

    • Atika RADID University Hassan II Casablanca FSAC-MACS
    • Karim RHOFIR University Sultan Moulay Slimane ENSA-LISERT
    2018-07-06
    https://doi.org/10.14419/ijet.v7i4.24694
  • Atmospheric Chemical kinetic, Stiff ODE’s, Positivity preservation, Iterative-Modified-Backward-Euler, Iterated QSSA.

  • Generally, chemical reactions from atmospheric chemistry models are described by a strongly coupled, stiff and nonlinear system of ordinary differential equations, which requires a good numerical solver. Several articles published about the solvers of chemical equations, during the numerical simulation, indicate that one renders the concentration null when it becomes negative. In order to preserve the positivity of the exact solutions, recent works have proposed a new solver called Modified-Backward-Euler (MBE). To improve this solver, we propose in this paper an iterative numerical scheme witch is better fitted to stiff problems. This new approach, called Iterative-Modified-Backward-Euler (IMBE), is based on iterative solution of the P-L structure of the implicit nonlinear ordinary differential equations on each time step. The efficiency of the iteration process is increased by using the Gauss and Successive-Over-Relaxation (SOR). In the case of fast/slow chemical kinetic reactions, we proposed an other variant called Iterative-Quasi-Steady-State-Approximation (IQSSA). The numerical exploration of stiff test problem shows clearly that this formalism is applicable to a wide range of chemical kinetics problems and give a good approximation compared to the recent solver. The numerical procedures give reasonable accurate solutions when compared to exact solution.

    Generally, chemical reactions from atmospheric chemistry models are described by a strongly coupled, stiff and nonlinear system of ordinary differential equations, which requires a good numerical solver. Several articles published about the solvers of chemical equations, during the numerical simulation, indicate that one renders the concentration null when it becomes negative. In order to preserve the positivity of the exact solutions, recent works have proposed a new solver called Modified-Backward-Euler (MBE). To improve this solver, we propose in this paper an iterative numerical scheme witch is better fitted to stiff problems. This new approach, called Iterative-Modified-Backward-Euler (IMBE), is based on iterative solution of the P-L structure of the implicit nonlinear ordinary differential equations on each time step. The efficiency of the iteration process is increased by using the Gauss and Successive-Over-Relaxation (SOR). In the case of fast/slow chemical kinetic reactions, we proposed an other variant called Iterative-Quasi-Steady-State-Approximation (IQSSA). The numerical exploration of stiff test problem shows clearly that this formalism is applicable to a wide range of chemical kinetics problems and give a good approximation compared to the recent solver. The numerical procedures give reasonable accurate solutions when compared to exact solution.

  • References

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    RADID, A., & RHOFIR, K. (2018). Improvement of a nonnegative preserved efficient solver for atmospheric chemical kinetic equations. International Journal of Engineering & Technology, 7(4), 6657-6664. https://doi.org/10.14419/ijet.v7i4.24694