In this paper, we perform comparative studies of compressible Kolmogorov flow in the two-dimensional strongly coupled dusty plasma by means of atomistic or molecular dynamics (MD) and continuum or computational fluid dynamics (CFD) methods. Recently, using MD simulation, generation of molecular shear heat at the atomistic level is shown to reduce the average coupling strength of the system and destruct the vortical structures. To suppress the molecular heat, a novel method of a thermostat, namely, the configurational thermostat is introduced by which the microscale heat generated by the shear flow has shown to be thermostatted out efficiently without compromising the large scale vortex dynamics. While using a configurational thermostat, it has been found that the growth rate obtained from both the studies is the same with the marginal difference. To make the comparison with the continuum fluid model, we perform the same study using the generalised hydrodynamic model, wherein molecular shear heating phenomena is completely absent, however, viscous dissipation is there at the macroscale level. For this purpose, an Advanced Generalised SPECTral Code has been developed to study the linear and nonlinear aspects of the Kolmogorov flow in the incompressible and compressible limit for viscoelastic fluids. All the phenomenological parameters used in CFD simulations have been calculated from MD simulations. Code is benchmarked against the eigen value solver in the linear regime. Linear growth-rates calculated from the phenomenological fluid model is found to be close to that obtained from MD simulation for the same set of input parameters. The transition from laminar to turbulent flow has been found at a critical value of Reynolds number Rc in both the macroscopic (CFD) and microscopic (MD) simulation. Rc in MD is smaller than the one obtained by CFD simulation. In the nonlinear regime of CFD, the mode becomes unstable and vortex formation happens earlier than in MD. The peak vorticity value is better preserved in MD whereas in the CFD model, we find that the peak vorticity is dissipated relatively earlier.