Three point strongly compact weighting high resolution high order scheme and its application

Three-order, four-order and five order accurate numerical flux expressions in grid cell interface which were used in finite volume method with high order and high resolution scheme are present. The expressions of smooth factor which used in confirming the scheme of the weighting function are also be given in the paper. At first, the resolution of the scheme of the model equation is examined, then the scheme is used in calculating the flow field of one turbine stage. The numerical result shows that the high-resolution and high-order scheme presented in the paper has higher resolution on shock-wave problems and higher numerical accuracy. Comparing with common low-order-accurate scheme, fewer grid points are needed in the schemes in computing flow fields.