At Berkeley Lab, we are developing advanced mathematical frameworks and numerical algorithms for computing interface dynamics across a variety of applications, including industrial spray painting, semiconductor manufacturing, inkjet printing, wind turbines, shock tracking, combustion, and foamy materials in manufacturing.

We develop methods that are both mathematically and physically consistent; tackling these problems with enough accuracy to be useful requires some of the most advanced computational resources. To that end, part of our work is aimed at developing the mathematics behind higher-order accurate algorithms that naturally lend themselves to modern architectures, where attention to communication, data exchange, and computation throughput offer the opportunity for tremendous speedup.

Our methods in interface dynamics include level set methods, Voronoi implicit interface methods, interfacial gauge methods, implicit-mesh discontinuous Galerkin methods, and high-order quadrature schemes. We are also developing fundamental new advances in areas such as complex non-Newtonian multiphase fluid flow, high-order curvilinear meshing, and adaptive mesh refinement methods, as well as new algorithms for implementing these methods on systems at the Department of Energy’s scientific supercomputing facilities.