[pcg]

Hi, right, in the context of an academic code, like SU2, these concepts require a lot of experimenting to gain a feel for how to setup the solver, more time than a master thesis allows I would say. But let me try to give you an answer.

Your first mission is getting the solver to converge, i.e. for the residuals to drop 5-6 orders of magnitude (for external aero starting from free-stream), and for relevant coefficients (lift, drag, etc.) to not be fluctuating or still changing significantly.
The common parameters (CFL, etc.) and linear solver settings help you achieve this for a given choice of numerical methods (you can find some advice here: https://su2code.github.io/docs_v7/Li...econditioners/)

The second objective is to get accurate results, and this is where numerical methods are important.
In general, you want a choice of methods (gradient methods, convective schemes, etc.) that has the lowest amount of numerical dissipation while still giving you a physical solution (i.e. without wiggles, spurious oscillations, carbuncle, etc.).

Needless to say, it is easier to get convergence with more numerical dissipation.

So, if you are approaching this without any experience you'd start with something very dissipative like ROE with MUSCL_FLOW= NO (i.e. 1st order convection) and GREEN_GAUSS gradients, and then try to improve upon it in the direction of MUSCL_FLOW= YES with WEIGHTED_LEAST_SQUARES gradients (2nd order convection with the most accurate gradients).

Then there are tuning parameters for the methods (like Roe's entropy fix) and auxiliary methods (in particular limiters) that help you operate close to the potentially more accurate end of the spectrum without instabilities...
A good compromise (in my experience with compressible subsonic cases) is to use the Venkatakrishnan-Wang limiter with a 0.05-0.15 constant, and Roe entropy correction of 1e-3.

This is all application-dependent as you can imagine, if you are interested in low-Mach, or supersonic, etc. you may need other schemes that try to cope with the particular challenges of those regimes.

P.S. This all assumes you have a good mesh for what you are doing