High-Order and High Accurate CFD Methods and Their Applications for Complex Grid Problems

The purpose of this article is to summarize our recent progress in high-order and high accurate CFD methods for flow problems with complex grids as well as to discuss the engineering prospects in using these methods. Despite the rapid de- velopment of high-order algorithms in CFD, the applications of high-order and high accurate methods on complex configurations are still limited. One of the main rea- sons which hinder the widely applications of these methods is the complexity of grids. Many aspects which can be neglected for low-order schemes must be treated carefully for high-order ones when the configurations are complex. In order to implement high- order finite difference schemes on complex multi-block grids, the geometric conserva- tion law and block-interface conditions are discussed. A conservative metric method is applied to calculate the grid derivatives, and a characteristic-based interface condition is employed to fulfil high-order multi-block computing. The fifth-order WCNS-E-5 proposed by Deng (9,10) is applied to simulate flows with complex grids, including a double-delta wing, a transonic airplane configuration, and a hypersonic X-38 con- figuration. The results in this paper and the references show pleasant prospects in engineering-oriented applications of high-order schemes.

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