A new finite volume solver for all Mach number flows suitable for the solution on unstructured meshes with the collocated arrangement of variables is presented. The solver is based on the primitive variable equations. The newly proposed method utilizes the fractional step method that resembles the projection methods used in incompressible flow simulations. The proposed solver is suitable for the computations ranging from incompressible to supersonic flows. A notable characteristic of the newly proposed method is that the new formulation of the compressible pressure equation contains the pressure Laplacian term pre-multiplied by the time step size. Unlike the incompressible projection methods, the new pressure equation is derived from the discrete form of the continuity equation, resulting in the equation that has the potential (elliptic) and the hyperbolic (convective) parts of the pressure field separated. Central flux formulation is used for the approximation of numeric fluxes, resulting in small numerical dissipation thus making it suitable for the high fidelity computations including direct and large eddy simulations. A set of validation problems is presented in this work demonstrating the main characteristics of the newly proposed solver.
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