Calculation Accuracy Study Of High-order Spectral Volume Method

Computational Fluid Dynamics has been developing very fast in recent years. For solving the actual project problem, many methods have been deeply researched and then are applied to practical engineering. Importance has been attached on the Spectral Volume method for it can save computation resources and time and get high precision, and it is quite necessary to research the high-order Spectral Volume method.The paper begins with the developing of CFD in earlier years, and summarizes some information on the recent research about CFD in both here and aboard. It also introduces some numerical implementations like finite volume method, finite difference method, finite element method, boundary element method, and so on. Focuses on the basic principle of SV, the author derives the second-order and high-order schemes to solve linear wave equation and Euler system in one dimension.With the compare between SV method and others, the results show that SV method can get higher accuracy than FV method and FE method with the same computational resources. The comparison between different order schemes of SV method shows that: though high-order SV method can get high accuracy theoretically, the errors can be also accumulated by iterative calculations. With less number of iterations, the second or third-order schemes can get better results than the high-order one. From the view of optimization design, the third-order scheme of SV method is optimal.Through this paper, we can know that it is more optimal to use SV method solving the one dimensional problems than FV or FE method, and the best scheme to solve linear wave equation and Euler equations is the third-order SV method.