Computational Fluid Dynamics
The goal behind computational fluid dynamics (CFD) is to generate a numerical model for fluid motion. In this field of fluid mechanics, there exist many techniques to form a model, each with their own strengths and weaknesses. Most computational techniques for solving fluid flow can be described by the following processes. You first define the geometry of the flow you are trying to model. This domain is then discretized using many small elements. Boundary conditions (typically a velocity or stress) are then specified at the edges of the domain. The governing equations (Stokes equations in our case) are then expressed at each element utilizing many unknowns. This generates a massive number of equations, each representing an element within the domain. If the problem is well formulated, the number of equations is equal to the number of unknowns and a linear algebraic system is created. From here, well-established numerical techniques are applied to efficiently solve for the unknown values at each element.
Stokes Flow
A common factor used to determine which technique is most appropriate is the type of fluid flow under investigation. When studying microfluidics, one is typically working within a realm of fluid flow in which inertial effects are negligible and viscous effects dominate. This fluid motion, referred to as Stokes flow can be well represented by the motion of syrup or honey (fluids with high viscosity). It is because of the length scale defining microfluidics (down to 10-6 meters - thinner than human hair) that it moves in a manner that is well described by the Stokes equations. The technique I use to model this type of flow is the Boundary Element Method (BEM).
Advantages of the BEM
The BEM uses a novel technique in which the solution to the model is found at the boundary of the domain using Green's functions. If needed, interior fields can then be calculated explicitly using the boundary solution. This provides an ideal technique when studying domains with strongly varying length scales due to ease of discretization. Although it is considered a mathematically-intense method to apply, it can serve to either reduce simulation time or improve accuracy when compared to other techniques. My current research utilizes this approach to model various phenomena within microfluidics where commercial software and other more common CFD techniques leave unanswered questions.
