系列学术讲座
题 目：Jump discontinuities and piecewise regularity of compressible Navier-Stokes flows: Numerical simulations （I，II，III）
报告人：Prof. Jae Ryong Kweon （韩国浦项工科大学 Postech）
时 间：2018年10月10日周三下午2点到4点，
11日周四上午9点到11点，
12日周五上午9点到11点
地 点：闵行校区办公楼12楼 偏微分方程中心1202教室
报告内容简介：I will survey recent results regarding corner singularities, jump discontinuities, and piecewise regularity for compressible Navier-Stokes equations on bounded polygonal domains. In particular the jump discontinuities come from difference of pressure values on inflow boundary, disconnected inflow boundaries or differences of pressure values along streamlines emanating from corner, etc. Consequently the pressure gradient in the momentum equation is not well-defined. A main issue is how to handle this difficulty. Eventually piecewise regularity of solutions is shown by subtracting singular parts. We will demonstrate such singular behaviors by numerical simulations.
References
[1] J. R. Kweon, R. B. Kellogg, Regularity of Solutions to the Navier-Stokes Equations for Compressible Flows on a Polygon. SIAM J. Math. Anal. 35 (2004) 1451-1485.
[2] J. R. Kweon. Corner singularity dynamics and regularity of compressible viscous Navier-Stokes flows. SIAM J. Math. Anal. 44 (2012) 3127-3161.
[3] J. R. Kweon. A jump discontinuity of compressible viscous flows grazing a non-convex corner. J. Math. Pures Appl. 100 (2013) 410-432.
[4] O-Sung Kwon and J. R. Kweon. Interior jump and regularity of compressible viscous Navier-Stokes flows through a cut. SIAM J. Math. 49 (2017) 1982 - 2008.
[5] J. H. Han and J. R. Kweon. A numerical scheme for approximating interior jump discontinuity solution of a compressible Stokes system. J. Computational App. Math. 345 (2019) 320-337
[6] J. R. Kweon and Minje Park. Vertex circulation and regularity of compressible Stokes flows: Numerical simulations. Commun Nonlinear Sci. Numer. Simulat. 68 (2019) 106-124.
