A pressure-based semi-implicit procedure has been developed for computation of compressible flows on a system with collocated finite volume formulations. The method includes the implementation of a high order accurate weighted essentially non-oscillatory (WENO) scheme within the pressure-based algorithm which employs an approximate Riemann solver for the computation of the cell face inviscid fluxes. The developed scheme is applied to the computation of unsteady compressible flow through a shock tube which experiences various Mach numbers, andthe computations are compared with analytical solution. The computations indicate that the developed procedure leads to crisp discontinuity representation without creation of fake oscillations. Then, the developed numerical method is utilized to investigate unsteady two-dimensional flow for lax configuration andthe results are compared with the results of similar the scheme in the density-based algorithm. At the end, the investigation of steady compressible flows in bump and wedge channel is considered. The simulations show a considerable improvement over the existing pressure-based method. The investigations show that the developed method is suitable for studying compressible steady and unsteady flows.

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