evaluation of roe s method with different limiters in supersonic 2-d and axisymmetric flows

2-d and axisymmetric navier-stokes equations are solved using reiman-roe solver with different limiters for second-order accurate schemes. the results were obtained for supersonic viscous flows over semi-infinite axisymmetric and 2-d bodies. the free stream mach numbers were 7.78 and 16.34. the stability of roe method with different limiters and entropy conditions were considered. the results show that the limiters greatly affect the stability and accuracy of the numerical solution while the entropy conditions do not.