Could 1 explain us why MUSCL is aimed at external, and not internal flow ? (expecting 2 beeing told: "yep, can be applied to internals for sure)

MUSCL is a variation of Godunov method, which is orginally developed for conservation laws. MUSCL reconstructs piecewise (or cellwise) constant conserved variables to improve spatial accuracy. After reconstruction, the spatial gradients are limited to prevent wiggles. Anyway .. goverining eqs of external flows are compressible NS eqs and continuity eq. Both are strictly hyperbolic, therefore godunov classes are applied. Since "shock" is an important problem in external flows MUSCL-like schemes are generally preferred.

On the other hand, governing eqs of internal flows are incompressible NS eqs and continuity eq. Both are not strictly hyperbolic, because time derivative term of continuity eq vanishes. Traditionally, SIMPLE is preferred. "Shock" is not a problem in internal flows.

There exist, however, SIMPLE method which adopts spatial reconstruction. See J of Comp. Phys. 150, 40-75 (1999)

The governing equations are the same for both internal and external flows. The form (incompressible or compressible) merely depends on your choice of equation of state and has nothing to do with the geometry.

Depending on the physical problem, you can get shocks in internal flows just as easily as you can get them on external flows. There is no good reason that MUSCL couldn't be appiled in either case.

The bigger challenge for external flows is implementing a decent non-reflecting boundary condition in the farfield which does not produce non-physical behaviour when a shock runs into it. The difficulty of doing this may influnce your choice of advection scheme.

Dan.

P.S. MUSCL assumes a piecewise linear variation of the primitive variables within a grid cell, not constant (as the last post mentions). The average (constant) cell values are reconstructed assuming that variation which is how MUSCL gets second order accuracy.

I did not write MUSCL is based on piecewise constant procedure. What I meant is MUSCL reconstructs piecewise constant variables to piecewise linear one and therefore obtains second order accuracy. It is because of my poor English.

As you stated, fundamentally, the governing equation of internal and external flows are the same. I agree. We know all flows can be described by the full Navier-Stokes equations. But, sometimes, solving full N-S eqs is not necessary or impossible. For example, for ocean circulation modelling, shallow water equation or Boussinessq equation is enough and more appropriate. We hardly solve compressible flow eqs to simulate water flow in pipes or channels. And incompressible flow eqs are not frequently used in aerodynamics.

I did not say MUSCL cannot applied to incompressible flows; I also know sometimes shock is seriously considered in incompressible flows. It is reasonable to use MUSCL-like techniques for incompressible/compressible advection dominated flows.

Just to say that flows around car can be considered as incompressible (Ma ~< 0.1) even if they are external flows. And flows in ICE are both compressed and locally compressible (Ma ~ 0.5) and they are internal.