1.报告时间：2023年03月18日08: 15-12: 00

 2.报告地点：腾讯会议（ID: 903 586 093）

 3.报告日程：

 4.报告摘要和报告人简介：

 An Essential Seventh-Order Weighted Compact Adaptive Scheme for Hyperbolic Conservation Laws

  郭彦（中国矿业大学）

 摘要: A new seventh-order weighted compact adaptive scheme is proposed in this paper. The proposed reconstruction is inspired by the upwind compact scheme and the adaptive order weighted essentially non-oscillatory (WENO) scheme. The proposed seventh-order scheme is a convex combination of a linear seventh-order compact scheme and three linear third order compact schemes. The reconstruction of the proposed scheme is based on the same stencil as the reconstruction of the original fifth-order weighted compact scheme. Various classical tests are presented to show the performance of the proposed numerical scheme.  

 个人简介：郭彦，中国矿业大学，副教授，硕士生导师。

 多尺度动理学方程的高阶渐近保持间断Galerkin有限元方法

 熊涛（厦门大学）

 摘要: 本报告中，我们将介绍多尺度动理学方程的一类高阶渐近保持间断Galerkin有限元方法。我们从简化的BGK方程出发，基于宏观-微观分解框架，空间采用间断Galerkin有限元离散，时间采用刚性稳定的显隐结合Runge-Kutta格式，构造了多尺度动理学方程的高阶格式，对多尺度参数Knudsen数能一致稳定。进一步，为克服动理学方程的高维问题，我们基于动态区域分解，采用分层和杂交两种方式，发展了多尺度动理学方程的两类高效格式。我们在大部分接近热平衡的区域仅求解低维宏观流体动力学方程，仅在必要的地方求解高维动理学方程，能大大提升计算效率。数值算例验证了我们方法的可行性和高效性，以及在不同问题中的良好表现。

 个人简介：熊涛，厦门大学数学科学学院教授。

 High order inverse Lax-Wendroff boundary treatment on moving boundary

 蒋琰（中国科学技术大学）

 摘要: In this talk, we will introduce a boundary treatment for solving general convection-diffusion equations on time-varying domain on a fixed Cartesian mesh. This method can achieve high order accuracy, and has a unified form for pure convection, convection-dominated, convection-diffusion, diffusion-dominated and pure diffusion cases. We also extend the boundary treatment to the compressible Navier-Stokes equations. Numerical tests demonstrate that our boundary treatment is high order accurate for problems with smooth solutions and also performs well for problems involving interactions between viscous shocks and moving rigid bodies.

 个人简介：蒋琰，中国科学技术大学特任研究员、博士生导师。

 SCQ formulas for fractional calculus

 刘洋（内蒙古大学）

 摘要：In this talk, we introduce the shifted convolution quadrature (SCQ) formulas that approximate fractional derivatives at a shifted node xn-θ where θ may not necessarily be an integer. First, we develop a Crank-Nicolson difference scheme with an SCQ formula for solving a space-fractional advection-diffusion equation. We explore the impact of different θ on the robustness of our scheme for weak regular solutions and compare that with the shifted Grünwald-Letnikov formula. The results confirm the necessity of introducing non-integer shifted parameters θ. Further, we will discuss finite element method, LDG method with SCQ formulas to solve numerically other fractional DEs.  

 个人简介：刘洋，内蒙古大学数学科学学院教授、博导。

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