Higher order implicit time integration schemes to solve incompressible Navier-Stokes on co-located grids using consistent unsteady Rhie-Chow

Noting that time-accurate computations of the unsteady incompressible Navier-Stokes (INS) equations can be computationally expensive, a family of higher order implicit multi-stage time integration schemes (namely ESDIRK) is used for advancing the solution to the unsteady INS in time. The higher order time integration schemes have the potential to decrease the computational cost of obtaining engineering levels of accuracy relative to the traditionally used 2nd order implicit schemes. The finite volume method is used for spatial discretization, and co-located arrangement of the primitive variables is considered. Furthermore, an iterated PISO algorithm is used to solve the incompressible Navier-Stokes equations. By using a temporally consistent Rhie-Chow interpolation, higher order temporal accuracy in solving the INS equations on co-located grids is achieved. For a two-dimensional lid driven cavity test case, the temporal convergence of the solution is investigated, with the third and fourth order ESDIRK schemes for time integration. The results demonstrate the temporal consistency and temporal order preservation of the algorithm.
Aerodynamics, Wind Energy and Propulsion
Aerospace Engineering