I am a postdoctoral scholar in the Center for Computational Sciences and Engineering (CCSE) in the Computing Sciences Directorate at the Lawrence Berkeley National Laboratory.
My research focuses on efficient algorithms for complex unsteady hydrodynamics and compressible fluid flows.
My doctoral research at the University of Michigan involved development of a new class of high-order CFD schemes called the Active Flux (AF) method. The AF method can be best described as a finite-volume method with additional degrees of freedom (DOF) at interfaces so that the interface fluxes evolve independently from the cell-averages. It is a fully discrete, maximally stable method that uses continuous data representation and truly multidimensional solvers (no Riemann solvers necessary!). With a focus on solving conservation laws that describe acoustic processes, we confirmed that the AF method is able to achieve third-order accuracy using the same number of DOFs as the second-order discontinuous Galerkin method using linear reconstruction (DG1). In a direct comparison between the two methods for acoustics problems, we found that the AF method displays superior circular symmetry with significantly less scatter, and takes one magnitude less in computation time to achieve the same level of error than DG1.
My masters' research at the University of Toronto Institute for Aerospace Studies (UTIAS) explored the numerical evaluation of radiative heat transfer equation using the M1 model, which uses the maximum entropy moment closure for the two-moment approximation of the governing equation. We found that while this model cannot accurately resolve multi-directional radiation transport occurring in low-absorption media, it does provide reasonably accurate solutions in more realistic radiation transport problems involving absorbing-emitting or scattering media. The M1 model is also much less computationally expensive than other radiative heat transfer solvers such as the discrete ordinates method (DOM) on complex geometries.
- Fan, D. and Roe, P.L.. Investigations of a New Scheme for Wave Propagation. AIAA Aviation, Dallas, TX, 2015.
- Fan, D., Charest, M.R.J., and Liu, F.. Evaluation of Maximum Entropy Moment Closure for Solutions of Radiative Heat Transfer. CICS Spring Technical Meeting, Toronto, ON, 2012.