报告人： 程自强 副教授

报告题目： Dispersion Analysis and Flux Optimization of Discontinuous Galerkin Methods for Computational Aeroacoustics

时间： 2026年10月31日（周六）10:00—12:00

地点： 西安交通大学数学与统计学院423会议室

邀请人： 束俊 教授

报告摘要：

The dispersion and dissipation properties of a numerical scheme dictate the accuracy of long-distance acoustic wave propagation in computational aeroacoustics (CAA). Grounded in dispersion-relation-preserving (DRP) framework and its integral error measure, this study investigates the aeroacoustic resolution characteristics of discontinuous Galerkin (DG) schemes through a rigorous dispersion and dissipation analysis.

The initial wave in a DG-(P^q) scheme decomposes into (q+1) eigenmodes. In the long-wave limit, only the physical mode faithfully tracks the exact solution, whereas the spurious modes exhibit strong dissipation. Overall, DG schemes maintain favorable dispersion and dissipation properties that systematically improve with increasing polynomial degree (q) and depend crucially on the choice of numerical flux.

For canonical benchmark problems, including nozzle flows, DG achieves a resolution comparable to that of same-stencil DRP schemes, while offering distinct geometric flexibility on non-uniform and unstructured meshes. Based on this dispersion analysis, we optimize the upwind-biased flux parameter for DG-(P^q) to enhance phase accuracy while preserving numerical stability.

Finally, by employing characteristic decomposition to decouple 1D linear hyperbolic systems into independent scalar fields, we extend this scalar optimization framework to systems, resulting in the formulation of an upwind-biased system (UBS) flux.

报告人简介：

程自强，博士，合肥工业大学数学学院副教授。主要从事偏微分方程数值方法和生物模型的研究工作。

主持或参与国家级科研项目，在 Journal of Computational Physics（J. Comput. Phys.）、Journal of Computational and Applied Mathematics（J. Comput. Appl. Math.）、Communications in Nonlinear Science and Numerical Simulation（Commun. Nonlinear Sci. Numer. Simul.）、Journal of Theoretical Biology（J. Theor. Biol.）、Journal of Scientific Computing（J. Sci. Comput.） 等国际学术期刊发表论文10余篇。