Staggered Semi-Implicit Hybrid Finite Volume/Finite Element Schemes for Turbulent and Non-Newtonian Flows

This paper presents a new family of semi-implicit hybrid finite volume/finite element schemes on edge-based staggered meshes for the numerical solution incompressible Reynolds-Averaged Navier–Stokes (RANS) equations in combination with k?? turbulence model. The rheology calculating laminar viscosity coefficient under consideration this work is one non-Newtonian Herschel–Bulkley (power-law) fluid yield stress, which includes Bingham and classical Newtonian fluids as special cases. For spatial discretization, we use unstructured simplex meshes, well non-uniform Cartesian grids. In order to get simple computationally efficient algorithm, apply an operator splitting technique, where hyperbolic convective terms RANS are discretized explicitly at aid Godunov-type volume scheme, while viscous parabolic terms, elliptic pressure stiff algebraic source model implicitly. discretization Poisson equation, conforming P1 Q1 elements triangles rectangles, respectively. implicit mandatory fluids, since apparent can tend infinity stress certain power-law fluids. It carried out triangular volumes rectangles. grids more general orthogonal prove that our scheme preserve positivity k ?. achieved via relaxation using suitable discrete evolution logarithms method applied some academic benchmark problems turbulent flows two space dimensions, comparing obtained results available exact or reference solutions. all cases, excellent agreement observed.