报告时间：2026年6月25日 上午09:30开始

报 告 人：Jue Yan  Iowa State University

报告地点：9-113

报告题目：Positivity-preserving generalized direct discontinuous Galerkin method with interface correction for a doubly nonlinear diffusion equation arising in shallow water modeling

报告摘要：A generalized direct discontinuous Galerkin method with interface correction is developed for a class of doubly nonlinear diffusion equations arising in shallow water modeling. The diffusion coefficient $A(u,\nabla u)$ depends on both the solution and its gradient. The numerical flux approximation is decomposed into a nonlinear part and a linear part associated with the solution gradient. Two numerical flux formulas are proposed for approximating $\nabla u$ in the diffusion coefficient, using either the direct discontinuous Galerkin approach or gradient averaging. The method is proved stable in the $L^2(L^2)$ norm. Optimal $(k+1)$th order of accuracy is observed for $P^K$ polynomial approximations for both formulations. The solution represents water depth and must remain nonnegative to avoid nonphysical values and anti-diffusive behavior. For the third-order positivity-preserving limiter, a new method is developed that treats the cell average update as a convex combination of local functionals grouped by cells. For the dam-break model with vegetation patches, the positivity-preserving limiter effectively stabilizes the simulation and guarantees nonnegative water-depth approximations. Flow features around vegetation patches are accurately captured and agree well with experimental results and previously reported studies.

报告人简介：闫珏教授，1995年和1998年于吉林大学数学系分别获得学士和硕士学位，2002年于布朗大学应用数学系获得博士学位（导师舒其望教授），2004年-2006年在加利福尼亚大学洛杉矶分校从事博士后研究（导师Stanley Osher），现为美国爱荷华州立大学教授。闫珏教授长期致力于流体力学方程的高阶精度数值方法及其应用研究，在非线性色散波方程、哈密尔顿-雅克比方程、直接间断有限元方法及气体动力学方程组的保正算法等领域取得大量重要成果。近期在气体动力学应用方面的机器学习方法取得了一些创新性成果。闫珏教授主持多项美国NSF项目和Simons基金项目，发表包含SIAM Journal on Numerical Analysis、Journal of Computational Physics、Journal of Scientific Computing在内的高水平论文50余篇。