An unstructured finite volume method based on the projection method combined momentum interpolation with a central scheme for three-dimensional nonhydrostatic turbulent flows

This paper presents a three-dimensional nonhydrostatic model to solve the Navier–Stokes equations using an unstructured finite volume method. The physical domain could be geometrically arbitrary. To avoid the checkerboard problem caused by non-staggered grids, a momentum interpolation method is used by introducing face-normal velocities at the mid-points of the cell faces. As the Large Eddy Simulation (LES) requires at least second-order accuracy in time and in space for all the terms, a central scheme combined with an explicit Adams–Bashforth scheme is proposed in this model. The projection method is applied to decouple the velocity field and pressure. Several benchmark test cases are used to validate the second-order accuracy, the numerical stability and the performance of the model. Analysis on divergence noise using an unstructured collocated triangular grid, as well as on the ratio between vertical and horizontal spacing steps have been done to show the reliability of the model. The proposed model has been used to simulate backward-facing step flows, lid-cavity flows, turbulent open channel flows and the turbulent flows around a vertical cylinder. The convergence of the linear solver is analyzed in terms of the iterations and CPU time. The results are fairly in agreement with the references in the literature. The proposed model is able to correctly reproduce the characteristic flow features in all the test cases.