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Using accurate multi-component diffusion treatment in numerical combustionstudies remains formidable due to the computational cost associated withsolving for diffusion velocities. To obtain the diffusion velocities, for lowdensity gases, one needs to solve the Stefan-Maxwell equations along with thezero diffusion flux criteria, which scales as $\mathcal{O}(N^3)$, when solvedexactly. In this article, we propose an accurate, fast, direct and robustalgorithm to compute multi-component diffusion velocities. To our knowledge,this is the first provably accurate algorithm (the solution can be obtained upto an arbitrary degree of precision) scaling at a computational complexity of$\mathcal{O}(N)$ in finite precision. The key idea involves leveraging the factthat the matrix of the reciprocal of the binary diffusivities, $V$, is lowrank, with its rank being independent of the number of species involved. Thelow rank representation of matrix $V$ is computed in a fast manner at acomputational complexity of $\mathcal{O}(N)$ and the Sherman-Morrison-Woodburyformula is used to solve for the diffusion velocities at a computationalcomplexity of $\mathcal{O}(N)$. Rigorous proofs and numerical benchmarksillustrate the low rank property of the matrix $V$ and scaling of thealgorithm.

An accurate, fast, mathematically robust, universal, non-iterative algorithm for computing multi-component diffusion velocities