Verification and validation of a high-order strand grid method for two-dimensional turbulent flows

In this paper, we construct a novel hybrid of two one-dimensional schemes in order to leverage several advantages for solving two-dimensional turbulent flows. Building upon previous work by the authors and others, we combine one-dimensional flux correction along body surfaces along with high-order summation-by-parts finite differences normal to surfaces. A new semi-implicit multigrid solution method is presented that capitalizes on the unique directional properties of each scheme, utilizing an explicit multigrid scheme along the surface direction, and an implicit Gauss-Seidel scheme along the strand direction. Turbulence closure is achieved with a robust version of the Spalart-Allmaras turbulence model that accommodates negative values of the turbulence working variable. The hybrid scheme exhibits fourth-order convergence using the method of manufactured solutions. Fundamental validation studies of the turbulent flux correction method are conducted in two dimensions, using the NASA-Langley turbulence resource as a means for comparison. Results are presented that demonstrate improvements in accuracy with minimal computational and algorithmic overhead over traditional second-order algorithms.