The Spectral Method Is Applied Research In Computational Fluid Dynamics

Spectral method is perhaps the most esthetically pleasing of the method of weighted residuals, it has high-order accuracy and exponential convergence in theory. Along the development of computer and numerical simulation technology, spectral method becomes one of three important numerical methods in computational fluid dynamics and gains significant attention.Spectral method has already got too much successful application in many fields, especially in computational fluid dynamics. As the incessant improvement of both numerical approximation technology and industry technology, high-order accuracy simulation of complex fluid becomes one of the most active topics in fluid mechanics. In this paper, the application of spectral method in computational fluid dynamic is mostly studied because of the accuracy of spectral method, the main contents of this paper are summarized as follows:a) The paper first presentes an overview of spectral method in computational fluid dynamics and points out the most common problems of spectral method in practical applications, then introduceds the main idea and basic knowledge about spectral method. All these work are finished above the study of abundant interrelated literatures.b) Two-dimensional Poisson equation is solved by both Chebyshev Tau method and Chebyshev Galerkin method, the numerical uncoils are compared with the exact one. At last, we analyzed the error of these methods. The results show spectral accuracy of spectral method.c) In order to simulate the rheological behaviors of upper-convected Maxwell fluid in a horizontal circular pipe accurately, the curves of the velocity at the axes parallel with the centre axis of the cube as well as the cutaway view of it on the whole pipe are obtained using Chebyshev Tau method. They can easilly show the behavior of the flow in the cube, reveal the phenomenon of velocity overshooting and damping oscillation of the flow. At the same time, the results display the effects of the elasticity and the viscosity of the fluid on the flow.d) It is well know that spectral method can not handle the problems with irregularly shaped domains directly. In the end of this paper we propose the idea of the spectral smoothed boundary (SSB) method, which makes the solution of partial...