Positive Numerical Integration Methods for Chemical Kinetic Systems

Document Type

Article

Publication Date

7-1-2001

Department

Department of Computer Science

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.

Publication Title

Journal of Computational Physics

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