Numerical implementation of efficient grid-free integral wall models in unstructured-grid LES solvers

Two zonal wall-models based on integral form of the boundary layer differential equations, albeit with algebraic complexity, have been implemented in an unstructured-grid cell-centered finite-volume LES solver. The first model is a novel implementation of the ODE equilibrium wall model where the velocity profile is expressed in the integral form using the constant shear-stress layer assumption and the integral is evaluated using a spectral quadrature method, resulting in a local and algebraic (grid-free) formulation. The second model, which closely follows the integral wall model of Yang et al. (Phys. Fluids 27, 025112 (2015)), is based on the vertically-integrated thin-boundary-layer PDE along with a prescribed composite velocity profile in the wall-modeled region. The prescribed profile allows for a grid-free analytical integration of the PDE in the wall-normal direction, rendering this model algebraic in space. Several numerical challenges unique to the implementation of these integral models in unstructured mesh environments are identified and possible remedies are proposed. The performance of the wall models is also assessed against the traditional finite-volume-based ODE Equilibrium wall model.