Application of High-resolution scheme based on WENO Scheme in Pressure-Based Algorithm for capturing discontinuities

In this study, a high-resolution scheme based on the WENO family has been developed in a pressure-based algorithm to prevent non-physical fluctuations based on Riemannian solver for steady and unsteady one dimensional and two dimensional compressible flows. The solution method is based on finite volume which uses an implicit solver with a structured collocated grid. Boundedness is applied by a high resolution essentially non-oscillatory scheme. To evaluate the numerical method, a shock tube containing shock wave, contact discontinuity and expansion waves has been considered, and the results obtained have been compared with the analytical results and the results based on the density based algorithm. The developed method is evaluated for lax configuration in two-dimensional inviscid flow. In addition, this method has been used to simulate two dimensional steady flow in a channel containing bump. The results show that the developed method is able to capture the physical and numerical discontinuities well.