SUMMARYIn this paper, we report our development of an implicit hybrid flow solver for the incompressible NavierStokes equations. The methodology is based on the pressure correction or projection method. A fractional step approach is used to obtain an intermediate velocity field by solving the original momentum equations with the matrix-free implicit cell-centred finite volume method. The Poisson equation derived from the fractional step approach is solved by the node-based Galerkin finite element method for an auxiliary variable. The auxiliary variable is closely related to the real pressure and is used to update the velocity field and the pressure field. We store the velocity components at cell centres and the auxiliary variable at cell vertices, making the current solver a staggered-mesh scheme. Numerical examples demonstrate the performance of the resulting hybrid scheme, such as the correct temporal convergence rates for both velocity and pressure, absence of unphysical pressure boundary layer, good convergence in steady-state simulations and capability in predicting accurate drag, lift and Strouhal number in the flow around a circular cylinder.

SUMMARYIn this paper, we describe an implicit hybrid finite volume (FV)/element (FE) incompressible NavierStokes solver for turbulent flows based on the Spalart-Allmaras detached eddy simulation (SA-DES). The hybrid FV/FE solver is based on the segregated pressure correction or projection method. The intermediate velocity field is first obtained by solving the original momentum equations with the matrix-free implicit cell-centered FV method. The pressure Poisson equation is solved by the node-based Galerkin FE method for an auxiliary variable. The auxiliary variable is closely related to the real pressure and is used to update the velocity field and the pressure field. We store the velocity components at cell centers and the auxiliary variable at vertices, making the current solver a staggered-mesh scheme. The SA-DES turbulence equation is solved after the velocity and the pressure fields have been updated at the end of each time step. The same matrix-free FV method as the one used for momentum equations is used to solve the turbulence equation. The turbulence equation provides the eddy viscosity, which is added to the molecular viscosity when solving the momentum equation. In our implementation, we focus on the accuracy, efficiency and robustness of the SA-DES model in a hybrid flow solver. This paper will address important implementation issues for high-Reynolds number flows where highly stretched elements are typically used. In addition, some aspects of implementing the SA-DES model will be described to ensure the robustness of the turbulence model. Several numerical examples including a turbulent flow past a flat plate and a high-Reynolds number flow around a high angle-of-attack NACA0015 airfoil will be presented to demonstrate the accuracy and efficiency of our current implementation.