High Order Semi-discrete Multidimensional Central-Upwind Scheme with Applications
Cai Li(1),Feng Jianhu(2),Xie Wenxian(1),Zhou Jun(1)
(1 Northwestern Polytechnical University, Xi’an 710072, China) (2 Chang’an University, Xi’an 710064, China)

Abstract: A fourth-order, semi-discrete central-upwind scheme for multidimens ional convection-diffusion equation is presented, where the local speed of wave propagation in the Riemann fans is considered based on a central weighted essen tially nonoscillatory (CWENO) reconstruction, and much lower numerical viscosity is encountered and the staggering between two grids is avoided, which is regarded as a semi-discrete central-upwind schem situated between upwind scheme and central scheme. Combining the semi-discrete central-upwind scheme with the Vorticity-Stream method, 2D incompressible Euler and Navier-Stokes equations are solved effectively.
Keywords: central weighted essentially nonoscillatory scheme, semi-discrete cen tral-upwind scheme, convection-diffusion equation, incompressible euler equati ons, incompressible navier-stokes equations.