CMI is interested in projects where the physics being modeled is as important an unknown as the numerical methods required to approximate it. We leverage open source tools like FEniCS to automate code generation and accelerate the time to solution, allowing multiple models and numerical methods to be tested rapidly. Some examples follow.
NonNewtonian Fluids

CMI is actively pursuing simulation software for a broad range of models for rheological flow, including the grade two model and several Oldroyd models. This work is based on recent theoretical advances regarding mathematical properties of these equations. It can be expected to revolutionize many areas, including medical treatments, food processing, and industrial manufacturing.

Conservation Laws

It has been recently discovered that systems of conservation laws in more than one dimension have uniunique solutions satisfying physical entropy conditions. CMI is acvtively investigating the role of physical dissipation on the selection process for physically meaningful solutions of conservation laws.