Hi, I want to know about shock ways why its generates and why its generates only in supersonic flows. bye

Solution of flow problems based on invicid theory breakdown at certain level. The discontinuties called Shock waves are accepted as jump discontinuties to save the solution. This happens when the true physics i.e., viscosity & thermal conductivity are ignored in modeling the fluid.

My question is that why this discontineuties generate

The reason shock waves are generated is simply that in a hyperbolic system information is propagated along the so-called characteristic directions and when two members of the same characteristic family intersect the solution becomes multivalued; i.e. for the same instant in time and position in space there are two different values for the density,velocity, etc. In physical space the multivaluedness is removed by replacing it with a surface of discontinuity - the shock wave.

See the books

Linear and nonlinear waves by G.B. Whitham

High speed flow by C. J. Chapman

Supersonic flow and shock waves by Courant and Friedrichs

Tom.

Thanks, I need this one