The modular grad-div stabilized algorithm for a turbulence model

In this paper, we propose a finite element algorithm by use of the modular grad-div stabilization to solve a turbulence model, called the 1/2-equation, which is a simplified version of the standard Kolmogorov–Prandtl 1-equation URANS (unsteady Reynolds-averaged Navier–Stokes equations) model. The modular grad-div stabilized method is proposed to avoid the inefficiency of the solver caused by the selection of large stabilized parameters in the standard grad-div stabilized method. The proposed algorithm can not only reduce velocity error but also enhance mass conservation in finite element calculation. Moreover, we show that the presented algorithm is unconditionally stable. Finally, we conduct a series of numerical experiments to test the stability and effectiveness of the proposed modular grad-div stabilized algorithm for the 1/2-equation.