For high Re number flows,a new computational fluid dynamics （CFD） validation method,namely,wall-surface compatibility criteria method and also called Gao＇s criteria,is proposed to verify near wall flows.As examples,Gao＇s criteria method and other two CFD verification methods （analytic solutions method and grid convergence analysis） are used to verify FLUENT＇s near wall flows solutions for two-dimensional incompressible laminar stagnation-point flows.The exact solution of the Navier-Stokes equations for laminar stagnation-point flows satisfy accurately all Gao＇s criteria,numerical simulations of laminar stagnation-point flows show that when physical parameters （the pressure coefficient and the Stanton number at wall surface） achieve convergence with more and more fine-screen grid,a part of Gao＇s criteria are not satisfied.
When the pressure ratio increases from the perfectly expanded condition to the third limited condition in which a normal shock is located on the exit plane, shock wave configurations outside the nozzle can be further assorted as no shock wave on the perfectly expanded condition, weak oblique shock reflection in the regular reflection （RR） pressure ratio condition, shock reflection hysteresis in the dual-solution domain of pressure ratio condition, Mach disk configurations in the Mach reflection （MR） pressure ratio condition, the strong oblique shock wave configurations in the corresponding condition, and a normal shock forms on the exit plane in the third limited con- dition. Every critical pressure ratio, especially under regular reflection and Mach reflection pressure ratio conditions, is deduced in the paper according to shock wave reflection theory. A hysteresis phenomenon is also theoretically possible in the dual-solution domain. For a planar Laval nozzle with the cross-section area ratio being 5, different critical pressure ratios are counted in these con- ditions, and numerical simulations are made to demonstrate these various shock wave configurations outside the nozzle. Theoretical analysis and numerical simulations are made to get a more detailed understanding about the shock wave structures outside a Laval nozzle and the RR←→MR transition in the dual-solution domain.
Gao＇s viscous/in-viscid interacting shear flows （ISF） theory, proposed by professor Gao Zhi in Institute of Mechanics, China Academy of Science, and its inferences and their applications in computational fluid dynamics （CFD） are reviewed and some subjects worthy to be studied are pro- posed in this paper. The flow-field and motion law of ISF, mathematics definition of strong viscous shear layer flow in ISF, ISF equations, wall-surface compatibility criteria （Gao＇s criteria ）, space scale variety law of strong viscous shear layer reveals flow mechanism and local space small scale triggered by strong interaction that cause some abnormal severe local pneumatic heating phenomenon in hypersonic flow. Gao＇s ISF theory was used in near wall flow, free ISF flow simulation and design of computing grids, Gao＇s wall-surface criteria were used to verify calculation reliability and accuracy of near wall flows, ISF theory approximate analytical result of shock waves-boundary layer interac- tion and ISF equations were used to obtain the numerical exact solution of local area flow （ such as stationary point flow）. Some new subjects, such as, improving near-wall turbulent models according to the turbulent flow simulation satisfying the wall-criteria and illustrating relation between grid-con- vergence based on the wall criteria and other convergence tactics, are suggested. The necessity of applying Gao＇s ISF theory and wall criteria is revealed. Difficulties and importance of hypersonic vis- cous/in-viscid interaction phenomenon were also emphasized.
