Prandtl-Meyer Expansion Waves to study the effect of Sub Grid Scaling Parameter on capture of expansion waves

1) Shock flow problems can be formulated as free boundary problems involving nonlinear partial differential equations (PDEs) of mixed elliptic–hyperbolic type. Understanding these shock flow phenomena requires a complete mathematical solution of the corresponding free boundary problems for nonlinear mixed PDEs.

In particular, these shock problems include von Neumann\'s problem for shock reflection–diffraction by two-dimensional wedges with concave corner, Lighthill\'s problem for shock diffraction by two-dimensional wedges with convex corner, and Prandtl-Meyer\'s problem for supersonic flow impinging onto solid wedges.

Thus, the fundamental scientific issues include the following:

• (i) structure of the shock reflection–diffraction configurations;
• (ii) transition criteria between the different patterns of shock reflection–diffraction configurations; and
• (iii) dependence of the patterns upon physical parameters such as the wedge angle, the incident-shock-wave Mach number.

2) Shock waves are steep wavefronts that propagate in compressible fluids in which convection dominates diffusion. They are fundamental in nature, especially in high-speed fluid flows. Basically, it is a type of propagating disturbance that is generated when a wave moves faster than the local speed of sound in a fluid.

A shock wave carries energy and can propagate through a medium; however, it is characterized by an abrupt, nearly discontinuous change in pressure, temperature, velocity and density of the medium but the mass, momentum and energy is conserved.

3) The effect of SGS temperature value on cell count and the shock location:

Temperature with the standard SGS setup of 0.05 K for both subsonic and supersonic flow.

AMR is switched on with SGS temperature as the criteria for refinement. Three SGS temperature parameters were selected namely 0.01, 0.05, 0.1.

For Subsonic flow;

Fig (a) AMR at 0.05

Fig (b) Temperature at 0.05K

Fig (c) Velocity for subsonic flow

For Supersonic flow;

Fig (d) AMR at 0.05

Fig (e) Temperature at 0.05K

Fig (f) Velocity for supersonic flow