A compressibility boundary layer theory similar to the viscous boundary layer theory is presented. The classic hydrodynamics of ideal fluid needs to be modified to account for the compressibility effect in the inner l...A compressibility boundary layer theory similar to the viscous boundary layer theory is presented. The classic hydrodynamics of ideal fluid needs to be modified to account for the compressibility effect in the inner layer when Mach number is small. The compressibility boundary layer exist on the time axis and relates to pressure field. Combined with the viscous boundary layer, it is now clear that the general four dimensional flow of large Re and small M has an inner region where flow is viscous and compressible and an outer region where the now is inviscid and incompressible. The compressible boundary layer theory also facilitate numerical solution of steady and unsteady flows.展开更多
A class of singularly perturbed problem of third order equation with two para-meters is studied. Using singular perturbation method, the structure of solutions to the problem is discussed in three different cases abou...A class of singularly perturbed problem of third order equation with two para-meters is studied. Using singular perturbation method, the structure of solutions to the problem is discussed in three different cases about two small parameters. The asymptotic solutions to the problem are given. The structure of solutions and the different limit behaviors are revealed. And the solutions are compared with the exact solutions to the equation in which the coefficients are constants and a relatively more perfect result is obtained.展开更多
文摘A compressibility boundary layer theory similar to the viscous boundary layer theory is presented. The classic hydrodynamics of ideal fluid needs to be modified to account for the compressibility effect in the inner layer when Mach number is small. The compressibility boundary layer exist on the time axis and relates to pressure field. Combined with the viscous boundary layer, it is now clear that the general four dimensional flow of large Re and small M has an inner region where flow is viscous and compressible and an outer region where the now is inviscid and incompressible. The compressible boundary layer theory also facilitate numerical solution of steady and unsteady flows.
基金Supported by the National Natural Science Foundation of China(No.11071205)the Natural Foundation of Zhejiang Province (No.Y6110502)
文摘A class of singularly perturbed problem of third order equation with two para-meters is studied. Using singular perturbation method, the structure of solutions to the problem is discussed in three different cases about two small parameters. The asymptotic solutions to the problem are given. The structure of solutions and the different limit behaviors are revealed. And the solutions are compared with the exact solutions to the equation in which the coefficients are constants and a relatively more perfect result is obtained.
