Positive Numerical Integration Methods for Chemical Kinetic Systems |
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Authors: | Adrian Sandu |
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Affiliation: | Department of Computer Science, 205 Fisher Hall, Michigan Technological University, 1400 Townsend Drive, Houghton, Michigan, 49931, f1 |
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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. |
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Keywords: | Abbreviations: chemical kineticsAbbreviations: linear invariantsAbbreviations: positivityAbbreviations: numerical time integrationAbbreviations: quadratic optimization |
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