报告人：邱竞梅副教授

              美国特拉华大学

报告题目：Semi-Lagrangian Discontinuous Galerkin Methods for Fluid and Kinetic Applications

报告时间：2018年12月14日下午15:00

报告地点：实验楼108

报告摘要：We propose Semi-Lagrangian discontinuous Galerkin (SLDG) schemes for convection-diffusion and convection-relaxation problems with fluid and kinetic applications.  The classical grid-based Eulerian methods, e.g. finite difference (FD) methods, finite volume (FV) methods and DG methods, can achieve arbitrary spatial and temporal order of accuracy, yet they suffer quite stringent time stepping size restriction with explicit time-stepping methods.  In order to be free of the time step constraint, we propose to use the grid-based SL approach, which propagates information along characteristics, allowing very large CFL numbers and leading to computational efficiency. Due to it’s efficiency property, SL schemes are widely used in incompressible flows, plasma physics, and global multi-tracer transport in atmospheric modeling. 

For fluid problems, such as linear convection-diffusion, we propose to apply the SLDG [Guo, Nair and Qiu, MWR, 2014] method to the convection term, together with the LDG discretization of the diffusion term coupled with diagonally implicit RK (DIRK) time discretization along characteristics.  For the nonlinear incompressible Navier-Stokes equation, backward characteristics tracing with high order accuracy could be challenging. We propose to apply the RK exponential integrator [Celledoni and Comet, JSC, 2009], to frozen the nonlinear advection coefficients and to couple with implicit treatment of linear diffusion terms. Our proposed schemes are mass conservative, truly multi-dimensional without dimensional splitting errors, genuinely high order accurate in both space and time, and highly efficient by allowing extra large time stepping size.

For kinetic problems, such as the BGK equation, we propose to treat the convection term by the SLDG method, while the relaxation term is evolved with DIRK methods along characteristics. Our schemes enjoy mass conservation, high order space-time accuracy and are free of the CFL constraint.  Moreover, our proposed schemes possess asymptotic-preserving property which preserves the asymptotic Euler limit as the Knudsen’s number going to zero. The performance is showcased by several benchmark problems.

报告人简介：特拉华大学副教授。2003年于中国科技大学获得理学学士学位，2007年博士毕业于布朗大学，随后在美国密歇根大学做博士后研究。2008年在科罗拉多矿业大学做助理教授；2011年开始在休斯敦大学做助理教授，2014年提升为副教授；2017年在特拉华大学任副教授。研究领域为多尺度流体力学问题的高精度数值方法。

联系人：熊涛教授

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