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Enforcing realizability in explicit multi-component species transport



Randall J. McDermott, Kevin B. McGrattan, Jason Floyd


A strategy is proposed to guarantee realizability of species mass fractions in explicit time integration of the partial differential equations governing fire dynamics, which is multi-component transport problem. For a mixture of $n$ species, the conventional strategy is to solve for $n-1$ species mass fractions and to obtain the $n$th (or ``background'') species mass fraction from one minus the sum of the others. The numerical difficulties inherent in the background species approach are discussed and the potential for realizability violations is illustrated. To guarantee realizability the mass density must remain positive (semidefinite). A scalar boundedness correction is proposed that is based on a minimal diffusion operator. The overall scheme is implemented in a publicly available large-eddy simulation code called the Fire Dynamics Simulator. A set of test cases is presented to verify that the new strategy (1) maintains realizability, (2) does not generate spurious mass, and (3) maintains second-order accuracy for transport.
Journal of Fluids Engineering-Transactions of the ASME


Realizability, Boundedness, Multi-component flow


McDermott, R. , McGrattan, K. and Floyd, J. (2015), Enforcing realizability in explicit multi-component species transport, Journal of Fluids Engineering-Transactions of the ASME, [online], (Accessed May 18, 2024)


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Created October 5, 2015, Updated June 2, 2021