Title
Positive Numerical Integration Methods for Chemical Kinetic Systems
Document Type
Article
Publication Date
7-1-2001
Abstract
Chemical kinetics conserves mass and renders nonnegative solutions; a good numerical simulation would ideally produce mass-balanced, positive concentration vectors. Many time-stepping methods are mass conservative; however, unconditional positivity restricts the order of a traditional method to one. The projection method presented in this paper ensures mass conservation and positivity. First, a numerical approximation is computed with one step of a mass-preserving traditional scheme. If there are negative components, the nearest vector in the reaction simplex is found by solving a quadratic optimization problem; this vector is shown to better approximate the true solution. A simpler version involves just one projection step and stabilizes the reaction simplex. This technique works best when the underlying time-stepping scheme favors positivity. Projected methods are more accurate than clipping and allow larger time steps for kinetic systems which are unstable outside the positive quadrant. © 2001 Academic Press.
Publication Title
Journal of Computational Physics
Recommended Citation
Sandu, A.
(2001).
Positive Numerical Integration Methods for Chemical Kinetic Systems.
Journal of Computational Physics,
170(2), 589-602.
http://doi.org/10.1006/jcph.2001.6750
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/3963