A new numerical method-basic function method is proposed.This method can directly discrete differential operators on unstructured grids.By using the expansion of basic function to approach the exact function,the centr...A new numerical method-basic function method is proposed.This method can directly discrete differential operators on unstructured grids.By using the expansion of basic function to approach the exact function,the central and upwind schemes of derivative are constructed.By using the polynomial as basic function,applying the technique of flux splitting method and the combination of central and upwind schemes,the non-physical fluctuation near the shock wave is suppressed.The first-order basic function scheme of polynomial type for solving inviscid compressible flow numerically is constructed in this paper.Several numerical results of many typical examples for one-,two-and three-dimensional inviscid compressible steady flow illustrate that it is a new scheme with high accuracy and high resolution for shock wave.Especially,combining with the adaptive remeshing technique,the satisfactory results can be obtained by these schemes.展开更多
A new numerical method named as basic function method is proposed. It can directly discretize differential operators on unstructured grids. By expanding the basic function to approach the exact function, the central a...A new numerical method named as basic function method is proposed. It can directly discretize differential operators on unstructured grids. By expanding the basic function to approach the exact function, the central and upwind schemes of derivative are constructed. By using the second-order polynomial as a basic function and applying the flux splitting method and the combination of central and upwind schemes to suppress non-physical fluctuation near shock waves, a second-order basic function scheme of polynomial type is proposed to solve inviscid compressible flows numerically. Numerical results of typical examples for two-dimensional inviscid compressible transonic and supersonic steady flows indicate that the new scheme has high accuracy and high resolution for shock waves. Combined with the adaptive remeshing technique, satisfactory results can be obtained.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.19889210)
文摘A new numerical method-basic function method is proposed.This method can directly discrete differential operators on unstructured grids.By using the expansion of basic function to approach the exact function,the central and upwind schemes of derivative are constructed.By using the polynomial as basic function,applying the technique of flux splitting method and the combination of central and upwind schemes,the non-physical fluctuation near the shock wave is suppressed.The first-order basic function scheme of polynomial type for solving inviscid compressible flow numerically is constructed in this paper.Several numerical results of many typical examples for one-,two-and three-dimensional inviscid compressible steady flow illustrate that it is a new scheme with high accuracy and high resolution for shock wave.Especially,combining with the adaptive remeshing technique,the satisfactory results can be obtained by these schemes.
基金supported by the National Natural Science Foundation of China (No. 19889210)
文摘A new numerical method named as basic function method is proposed. It can directly discretize differential operators on unstructured grids. By expanding the basic function to approach the exact function, the central and upwind schemes of derivative are constructed. By using the second-order polynomial as a basic function and applying the flux splitting method and the combination of central and upwind schemes to suppress non-physical fluctuation near shock waves, a second-order basic function scheme of polynomial type is proposed to solve inviscid compressible flows numerically. Numerical results of typical examples for two-dimensional inviscid compressible transonic and supersonic steady flows indicate that the new scheme has high accuracy and high resolution for shock waves. Combined with the adaptive remeshing technique, satisfactory results can be obtained.
