Three-dimensional and two-dimensional wavelet sigularity analysis was introduced in complicated flow and a high-order

high-resolution numerical method was developed.The core of this new method is the analysis of Hlder exponent α of complicated flow.The Hlder exponent α depends on wavelet transform and multi-dimensional wavelet analysis.In order to complete the multi-resolution analysis in two-dimensional and three-dimensional Euclidean space

scale basis and wavelet basis have been introduced in scale space and wavelet space.For two-dimensional and three-dimensional cases

scale basis and wavelet basis were constructed by one scale function and by three wavelet functions and seven wavelet functions respectively.High-resolution

high-order WENO (weighted essential non-oscillatory) scheme and high-order central difference scheme can be chosen adaptively according to the results of wavelet sigularity analysis.A series of examples in two-dimensional ( (1) forward facing step problem

(2) double Mach reflection of a strong shock problem

(3) two-dimensional Riemann problem

(4) two-dimensional transonic flow past RAE2822 airfoil problem

(5) two-dimensional transonic VKI-LS 59 turbine cascade flow problem) and three-dimensional ( (6) transonic axial compressor

NASA (National Aeronautics and Space Administration) Rotor 37 three-dimensional viscous flow and (7) NASA Rotor 67 three-dimensional viscous flow) were computed.The computation results have been compared with the experiment results in related references and showed that this new numerical method can not only improve the computation efficiency significantly(the efficiency can be increased by 3~5 times for most examples)

but also capture the shock with high-resolution and vortices with an acceptable order.