Time-accurate flow simulations using an efficient Newton-Krylov-Schur approach with high-order temporal and spatial discretization

In order to demonstrate the potential advantages of high-order spatial and temporal discretizations, implicit large-eddy simulations of the Taylor-Green vortex flow and transitional flow over an SD7003 wing are computed using a variable-order finite-difference code on multi-block structured meshes. The spatial operators satisfy the summation-by-parts property, with block interface coupling and boundary conditions enforced through simultaneous approximation terms. The solution is integrated in time with explicit-first-stage, singly-diagonally-implicit Runge-Kutta methods. Simulations of the Taylor-Green vortex show the clear advantage of high-order spatial discretizations in terms of accuracy and efficiency. The higher-order methods are better able to delay excessive dissipation on coarser grids and are better able to capture the details of the flow on finer grids. Similar dissipation and enstrophy profiles are obtained with a second-order spatial discretization, and a fourth-order spatial discretization with half the number of grid points in each direction, half the number of time steps, and approximately 85% less CPU time. Temporal convergence studies demonstrate the relatively high efficiency of the fourth-order explicit-first-stage, singly-diagonally-implicit Runge-Kutta method, except for simulations requiring only a minimum level of accuracy. Results of the simulation of transitional flow over the SD7003 wing show good agreement with experiment and other computations, despite a relatively coarse grid. The use of high-order discretizations is shown to be essential in obtaining this accuracy efficiently. These results give a clear picture of the bene fits of high-order discretizations, along with the advantages of the novel parallel Newton-Krylov-Schur algorithm presented, for high-accuracy unsteady flow simulation.