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Talk Abstract
Preserving Natural Invariants in Numerical Chemical Kinetics

Adrian Sandu
Department of Computer Science
Michigan Technological University

Mass action chemical kinetics conserves mass and renders non-negative solutions; a good numerical simulation would ideally produce a mass balanced, positive numerical concentration vector. Many time stepping methods are mass conservative; however, unconditional positivity restricts the order of a traditional method to one.

The positive projection method presented in the 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 using a primal-dual optimization routine; this vector is shown to better approximate the true solution. A simpler version involves just one projection step and stabilizes the reaction simplex.

The techniques works best when the underlying time-stepping scheme favors positivity. Projected methods are able to use larger integration time steps, being more efficient then traditional methods for systems which are unstable outside the positive quadrant.

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