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We present our recent work on discontinuous Galerkin scheme for incompressible flow problems, including global divergence-free DG schemes for incompressible Naver-Stokes equations and incompressible MHD, ALE-HDG scheme for free surface flows, div-free HDG for the phase-field model of incompressible two phase flow, and an entropy-stable DG scheme for the shallow water equations.
These schemes are designed to preserve certain secondary structures of the underlying PDEs (e.g., energy/entropy stability, pressure-robustness, well-balanced property), besides their usual conservation properties. Moreover, upwinding DG treatments of the convection terms make them robust in the convection-dominated regimes. We also discuss the hybridization technique to further reduce the computational cost associated with the linear system solvers.
Dr. Fu has been a Robert and Sara Lumpkins Assistant Professor with the university of the University of Notre Dame since 2019. Before that, he was a Prager Assistant Professor of Applied Mathematics at Brown University. In 2016, he received his Ph.D. in Mathematics from the University of Minnesota, Twin Cities. His research interest include Numerical analysis and scientific computing, Discontinuous Galerkin methods, and Computational fluid dynamics and computational mechanics