I am trying to use a combination of JST and ROE scheme for the RANS solution of an aerodynamic problem. I notice that the ROE scheme performs poorly in terms of the convergence in the drag counts for higher angle of attacks compared to the JST scheme. I am now wondering if to run the ROE scheme to a certain degree of convergence and then start the JST scheme for final convergence. Will the spatial order of accuracy of the ROE scheme be preserved? Do i get a more accurate solution than just running the JST scheme from the beginning?
Order of accuracy in a combined scheme
fluid dynamics
The Jameson-Schmidt-Turkel (JST) is an impressive high-resolution scheme for steady state simulations involving shock waves. It tries to retain a second-order spatial accuracy in the smooth flow regions and employs some kind of limiter in the shock region. There are various versions of this scheme, some of which can be reformulated as the TVD scheme [1]. Roe scheme on the other hand is a very popular scheme based on local linearization of fluxes. However, the spatial order of accuracy of the original Roe scheme is $O(1)$. If you are using a higher-order reconstruction method along with the Roe fluxes, then the solution will be higher-order accurate in space. Otherwise, Roe scheme is just an upwind scheme. The numerical dissipation can vanish at sonic as well as stagnation points for the Roe scheme [2].Thus, coming to the questions:1. Will the spatial order of accuracy of the ROE scheme be preserved?Yes. Since JST scheme is a TVD-like scheme, it will preserve atleast first-order accuracy on the domain, unless you are using a higher-order reconstruction for the Roe simulation.2.  Do i get a more accurate solution than just running the JST scheme from the beginning?No. You will get a more accurate solution if you are using JST from the beginning. In your strategy, you are using a lower-order method followed by a high-resolution method. So a lot of diffusion is already being added. References (you may have to search online if links are broken):A. Jameson, The origins and Further Development of the Jameson-Schmidt-Turkel (JST) Scheme (link).C. Praveen, JST, SLIP and CUSP schemes, notes on Computational Fluid Dynamics (link).  