Application of High-Order Summation-by-Parts Operators to the Steady Reynolds-Averaged Navier-Stokes Equation

Third- and fourth-order methods have been implemented to solve the steady Reynolds-averaged Navier-Stokes equations with the Spalart-Allmaras turbulence model. Summation-by-parts operators are used for spatial discretization along with simultaneous approximation terms to enforce boundary and interface conditions in a weak sense. Two validation cases are tested to verify the high-order implementation of the turbulence model and to examine the efficiency and robustness of the high-order methods. It is shown that the third-order method generally produces the most accurate results on a given mesh. The use of the fourth-order method also shows the potential of increasing numerical accuracy over the second-order method on coarse meshes. In terms of computational cost, the results demonstrate that the high-order methods are more efficient as the same level of accuracy can be achieved within less computational time on a coarser mesh.