Abstract
A new pressure-based finite volume algorithm is developed for simulating all-speed viscous flows. In this algorithm, the semidiscretized transport equations are integrated in the framework of stiffly accurate diagonally implicit Runge–Kutta methods. At each stage of time integration, the density–pressure–velocity coupling is fully solved, and mass conservation is ensured. The algorithm is verified and validated for several canonical cases over a wide range of freestream Mach number, from incompressible to supersonic flow. The performance and accuracy of the proposed algorithm are benchmarked against established methods for simulating unsteady flow, namely, SIMPLE and SIMPLER.
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