Enforcing realizability in explicit multi-component species transport

Abstract

We propose a strategy to guarantee realizability of species mass fractions in explicit time integration of the partial differential equations governing fire dynamics, which is a multi-component transport problem (realizability requires all mass fractions that are greater than or equal to zero and that the sum equals unity). For a mixture of n species, the conventional strategy is to solve for n−1 species mass fractions and to obtain the nth (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. The new strategy solves all n species transport equations and obtains density from the sum of the species mass densities. To guarantee realizability the species mass densities 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 enforces realizability, does not generate spurious mass, and maintains second-order accuracy for transport.