A Third-Order Polynomial Expansion Scheme Optimized with Respect to Numerical Stability and Truncation Errors for Advection-Diffusion Equations

摘要：

We investigate the stability of numerical schemes based on a polynomial expansion method. There exist no stable polynomial schemes with higher-order accuracy in case of advection equations according to the Godunov theory. We show that a stable polynomial scheme with third-order accuracy exists in case of advection-diffusion equations. We construct a third-order polynomial scheme with positive coefficients under an allowable condition among the Courant numbers and the diffusion numbers for advection-diffusion equations. We extend the present method into two-dimensional and three-dimensional equations. Numerical experiments of initial shock propagation show good solution with the present scheme. Finally, we apply the present scheme to two-dimensional airfoil analysis.

作者: Katsuhiro Sakai Tomohiro Kanno Hitoshi Arizono Gen.S.Zhang Isao Kimura Hirotoshi Hishida

作者单位: Saitama Institute of Technology, Fukaya, Saitama, 369-0293, Japan Japan Aerospace Exploration Agency, Mitaka, Tokyo, 181-0015, Japan Research Center of Computational Mechanics, Inc., Sinagawaa, Tokyo, 142-0041, Japan Fuchu Giken Inc., Fucyu, Tokyo, 183-0056 Japan Nippon Steel Corporation, Tokai, Aichi, 476-8686, Japan

会议类型: 国际会议

会议名称: 第五届亚洲计算流体力学会议(第五届中日计算流体力学会议)Proceedings of the Fifth Asia Workshop on Computational Fluid Dynamics(Fifth China-Japan Joint Workshop on CFD)

会议地点: 西安

会议语种:英文

页码: 173-188

在线出版日期: 2006-08-19（万方平台首次上网日期，不代表论文的发表时间）