Advanced stable algorithm for an explicit solution of steady incompressible flow

An explicit algorithm was introduced to obtain an accurate solution of pseudo-compressible time dependent flow equations (i.e., in which a virtual time-dependent pressure term is added to the continuity equation). The finite volume method for unstructured meshes was adopted to obtain numerical solutions of mass and momentum conservation equations in an uncoupled fashion. The sequential convergences of the velocity and pressure fields were enhanced by iterative solutions of incompressible momentum and pseudo-compressible continuity equations. At each computational step, some iteration were made to computed velocity field with solving incompressible momentum equations followed by computing the pressure field with solution of the pseudo-compressible continuity equation in a sequential manner and thus velocity and pressure fields (in each virtual time step) was improved. The developed solution algorithm relaxes the need for adding extra terms (i.e., artificial dissipation operators) to stabilize the solution procedure with averaging of the computed variables in each iteration with those calculated at every previous virtual-time step. This innovative technique caused oscillations of explicit solution are controlled and also there is no need to utilize control approaches such as TVD scheme and artificial dissipation method. The introduced method was used to solve inviscid and viscous incompressible flow problems. To verify th