Open AccessImprovement of a nonnegative preserved efficient solver for atmospheric chemical kinetic equations
Author(s) -
Atika Radid,
Karim Rhofir
Publication year - 2018
Publication title -
international journal of engineering and technology
Language(s) - English
Resource type - Journals
ISSN - 2227-524X
DOI - 10.14419/ijet.v7i4.24694
Subject(s) - solver , ordinary differential equation , backward euler method , nonlinear system , euler equations , mathematics , relaxation (psychology) , numerical analysis , differential equation , euler method , explicit and implicit methods , iterative method , stiff equation , mathematical analysis , physics , mathematical optimization , differential algebraic equation , quantum mechanics , psychology , social psychology
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.