University of Georgia

Mathematics Department Colloquium

Jian-Guo Liu

Institute for Physical Science and Technology and Mathematics Department

University of Maryland

March 25, 1999

High Order Simulation of Viscous Incompressible Flows at Large Reynolds Numbers

Abstract: We will survey a class of efficient high order finite difference schemes and finite element methods for viscous incompressible flows suitable for the computation of flows at very high Reynolds numbers and complicated geometry. The viscous term is treated explicitly and a high order local vorticity boundary formula is used. The main computation is reduced to solving a standard Poisson equation at each time step. We will present computations using the above methods for such problems as the > backward-facing step flow with 500 \leq Re \leq 2500; 3D lid-driven cavity flow at Reynolds number 3200, revealing the detailed structure of the Taylor-Gortler-like vortices; Impulsively started flow past a cylinder at Reynolds numbers as high as 100,000, revealing highly resolved vortical structures in boundary layer speartion; Zero mach combustion at high Reynolds, etc.