A continuously differentiable upwinding scheme for the simulation of fluid flow problems

This paper deals with the numerical solution of complex fluid dynamics problems using a new bounded high resolution upwind scheme (called SDPUS‐C1 henceforth), for convection term discretization. The scheme is based on TVD and CBC stability criteria and is implemented in the context of the finite volume/difference methodologies, either into the CLAWPACK software package for compressible flows or in the Freeflow simulation system for incompressible viscous flows. The performance of the proposed upwind non‐oscillatory scheme is demonstrated by solving two‐dimensional compressible flow problems, such as shock wave propagation and two‐dimensional/axisymmetric incompressible moving free surface flows. The numerical results demonstrate that this new cell‐interface reconstruction technique works very well in several practical applications.