Before revision:  Our schemes follow the finite volume methodology and preserve the stationary solutions and allow us to investigate the global asymptotic behavior of such flows and reach definite conclusions about the behavior of the mass density and velocity field  .
After revision:  Our schemes follow the finite volume methodology and preserve the stationary solutions . Importantly, they allow us to investigate the global asymptotic behavior of such flows and reach definite conclusions about the behavior of the mass density and velocity field .