流体力学问题的三次样条配置法

本文给出了三次样条配置法在流体力学问题数值解中的应用以及在这一领域的新进展。给出了流体力学方程中主要的样条函数关系和解算步骤。所有情形都是便于反演的三对角形矩阵。简要评述了SADI方法和样条方法在每一坐标方向的分步计算方法、截断误差和稳定性。给出了处理混合边界条件的一般公式。最后简要讨论了样条近似引起的数值弥散和耗散。 

CUBIC SPLINE COLLOCATION TECHNIQUE FOR PROBLEMS OF FLUID MECHANICS

This paper presents techniques for the numerical solution of problems in fluid mechanics using cubic spline collocation and some of their recent developments in this field.The main spline relations are presented and incorporated into solution procedures for fluid mechanics equations. The computational algorithm in every case is a tridiagonal matrix system amenable to efficient inversion methods. SADI method and a spline method of fractional steps in each coordinate direction as well as truncation errors and its stability are briefly reviewed. General formulations for treating mixed boundary condition are presented. Finally, numerical dispertive and dissipative effects for spline approximation are briefly discussed.