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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