Pressure velocity decoupling in low mach compressible flow
 

Hi,
I'm working on low speed compressible navier stokes equation to simulate heat transfer in differentially heated cavity (Say left wall heated and right wall cold). Will there be pressure velocity decoupling eventhough I use equation of state to compute pressure? Is it better to solve the equations by pressure based method or density based method? I dont want to use Boussinesq approximation.

with regards,
Meera