FALCO: Fast Linear Corrector for Modelling DNA-Laden Flows

The paper concerns the development of a numerical algorithm for improving the efficiency of computational fluid dynamics simulations of transport of biomolecules in microchannels at low number densities. For this problem, the continuum approach based on the concentration field model becomes invalid, whereas time scales involved make purely molecular simulations prohibitively computationally expensive. In this context, meta-models based on coupled solution of fluid flow equations and equations of motion for a simplified mechanical model of biomolecules provide a viable alternative. Meta-models often rely on particle-corrector algorithms, which impose length constraints on the mechanical DNA model. Particle-corrector algorithms are not sufficiently robust, thus resulting in slow convergence. A new geometrical particle corrector algorithm — called FALCO — is proposed in this paper, which significantly improves computational efficiency in comparison with the widely used SHAKE algorithm. It is shown that the new corrector can be related to the SHAKE algorithm by an appropriate choice of Lagrangian multipliers. Validation of the new particle corrector against a simple analytic solution is performed and the improved convergence is demonstrated for a macromolecule motion in a micro-cavity. This work has been supported in part by the European Commission under the 6th Framework Program (Project: DINAMICS, NMP4-CT-2007-026804).