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. We will discuss a new stable and convergent method for flow of an Oldroyd-B fluid which captures the full range of elastic flows including the benchmark high Weissenberg number problem. We have also fully coupled the Newtonian continuum method to a discrete polymer representation with constrained and unconstrained particle dynamics in order to predict the fate of individual DNA molecules in post microarrays. Our methods are based on higher-order finite difference methods in complex geometry with adaptivity. Our Cartesian grid embedded boundary approach to treating 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.