Biological flow is complex, not well-understood and inherently multiscale due to the presence of macromolecules whose molecular weights are comparable to length scales in the typical flow geometries of microfluidic devices or critical anatomies. Modeling these types of flows such as DNA in solution or blood is a challenge because their constitutive behavior is not easily represented. For example, a highly concentrated solution of suspended polymer molecules may be represented at the system level with a continuum viscoelastic constitutive model. However, when geometry length scales are comparable to the inter-polymer spacing, a continuum approximation is no longer appropriate, but, rather, a discrete particle representation coupled to the continuum fluid is needed. Furthermore, fluid-particle methods are not without their issues as stochastic, diffusive and advective processes can result in disparate time scales which make stability difficult to determine while capturing all the relevant physics.
At Lawrence Livermore National Laboratory we have developed advanced numerical algorithms to model particle-laden fluids at the microscale using the software framework developed under the APDEC ISIC. The first is a fundamentally new approach to the numerical modeling of viscoelastic continuum flow in an effort to model semi-dilute and concentrated solutions of DNA in microchannels. The algorithm is convergent and stable for a single CFL condition for the full range of elastic flows, including the benchmark ``high Weissenberg number'' problem. The second foundation of our computational effort is an approach for modeling individual molecules of DNA as ``bead-rod'' polymers whose dynamics are fully coupled to an incompressible viscous solvent. The method is capable of modeling short range forces and interactions between particles using soft potentials and rigid constraints.
Our methods are based on higher-order finite difference methods in complex geometry with adaptivity in the APDEC Framework. The Cartesian grid embedded boundary approach to irregular geometries has also been interfaced to a fast and accurate level-set method for extracting surfaces from volume renderings of medical image data and used to simulate cardio-vascular and pulmonary flows in critical anatomies.