Speaker: Dr. Chen Liu, Assistant Professor, Department of Mathematics, University of Arkansas
Date: Friday, September 6, 2024, 4:15 – 5:15 PM
Location: Science Engineering Hall (SCEN 404) in-person.
If you wish to receive the Zoom link, please contact Dr. Jiahiu Chen
Title: Discontinuous Galerkin Methods for Fluid Dynamics Simulations: Incompressible, Multi- phase, and Compressible Flows
Abstract: The Navier–Stokes (NS) equations are a widely used and important mathematical model with applications in computational mathematics and various interdisciplinary fields. These equations can be categorized into incompressible and compressible models based on compressibility. They are fundamental in hydrodynamics and gas dynamics, as well as in complex coupling systems like phase-field models. Research on solving the NS equations has been very active and of interest to both mathematicians and engineering researchers in recent years.
In this talk, we will discuss discontinuous Galerkin methods combine with splitting schemes for solving incompressible single and multi-phase systems, as well as compressible systems. Our numerical algorithms are efficient, high order accurate, and preserve important physical properties such as the conservation and energy dissipation for incompressible flow simulations; and conservation and positivity for compressible flow simulations. Numerical experiments suggest that our schemes produces satisfactory solutions, which is highly preferred and well-suited for simulating realistic physical and engineering problems. If time allows, advanced numerical techniques for constructing limiters will also be covered.
Short Bio: Dr. Chen Liu is an Assistant Professor of Mathematics in the Department of Math- ematical Sciences at the University of Arkansas. His research focuses on high-order numerical methods to solve partial differential equations in fluid dynamics. Specifically, he is focusing on dis- continuous Galerkin methods, incompressible single-phase and multi-phase flows, hyperbolic con- servation laws, and compressible flow. Additionally, he is also conducting research on non-smooth convex optimization. Prior to joining the University of Arkansas, Dr. Liu was a Golomb Visiting Assistant Professor in the Department of Mathematics at Purdue University under the supervision of Prof. Xiangxiong Zhang. He earned his Ph.D. degree from the Department of Computational and Applied Mathematics at Rice University, where his advisor was Prof. Beatrice Riviere.
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