Oisin Tong

Strand Grid Solution Procedures for Sharp Corners

The strand/Cartesian-grid approach provides many advantages for complex moving-body-flow simulations, including fully automatic volume grid generation, highly scalable domain connectivity, and high-order accuracy. In this work, the authors evaluate methods of handling sharp corners with strand grids through combinations of strand vector smoothing, multiple strands emanating from a single surface node, and telescoping Cartesian refinement into corner regions of the near-body grid. A new discretization strategy is introduced to better tolerate mesh skewness induced by strand smoothing. These approaches are tested for unsteady, laminar, and high-Reynolds-number turbulent flows. For standard viscous high-aspect-ratio grids, smoothed strands with telescoping Cartesian refinement provide the most accurate results with the least complexity. Mesh discontinuities associated with the use of multiple strands at sharp corners produce more error than with smoothed strands. With both strand approaches—vector smoothing ...

High-order strand grid methods for shock turbulence interaction

ABSTRACT In this work, we examine the flux correction method for three-dimensional transonic turbulent flows on strand grids. Building upon previous work, we treat flux derivatives along strands with high-order summation-by-parts operators and penalty-based boundary conditions. A finite-volume like limiting strategy is implemented in the flux correction algorithm in order to sharply capture shocks. To achieve turbulence closure in the Reynolds-Averaged Navier–Stokes equations, a robust version of the Spalart–Allmaras turbulence model is employed that accommodates negative values of the turbulence working variable. Validation studies are considered which demonstrate the flux correction method achieves a high degree of accuracy for turbulent shock interaction flows.

High-Order Methods for Three-Dimensional Strand-Cartesian Grids

The flux correction method combines unstructured flux correction along body surfaces and high-order finite differences normal to surfaces. This paper builds on previous twodimensional developments of the flux correction method and extends it to three-dimensional laminar and turbulent flow on strand grids. The development of flux correction scheme applied to three-dimensions is presented. Where turbulence modeling is required, a robust version of the Spalart-Allmaras turbulence model is employed that accommodates negative values of the turbulence working variable. A unique parallel communication strategy for high-order strand grid topologies is presented which eliminates the need for “fringe” nodes or cells in each partitioned block. A semi-implicit multigrid solution algorithm is described that allows for several advantageous solution techniques to be combined for optimal efficiency in terms of memory and computation time. Fundamental verification studies are conducted, which show the flux correction method achieves high-order accuracy for both laminar and turbulent flows. A three-dimensional steady-state study of a sphere is conducted over a range of laminar Reynolds numbers. The flux correction method accurately predicts the centers and length of recirculation vortices for each Reynolds number examined, and shows excellent comparison to experimental data. The three-dimensional unsteady capabilities of flux correction are displayed through a qualitative study of vortex shedding from a sphere.

Asymptotic Geometry Representation for Complex Configurations

The strand-Cartesian approach provides many advantages for complex moving-body flow simulations, including fully-automatic volume grid generation, highly scalable domain connectivity, and high-order accuracy. The purpose of this work is to evaluate methods of handling small-scale features, such as sharp corners and ridges, with strand grids by smoothing the geometry, thus allowing strands to preserve orthogonality regardless of the corner or edge concavity and acuteness. Specifically, we investigate surface smoothing as a function of mesh refinement, creating an “asymptotic geometry”. Results provided qualitatively demonstrate superior strand grid meshing compared to previous methods.

Assessment of a Two-Equation Turbulence Model in the High-Order Flux Correction Scheme

In this work, we examine a two-equation turbulence model in the flux correction method for three-dimensional turbulent flows on strand grids. Building upon previous work, flux derivatives along strands are treated with high-order summation-by-parts operators and penalty-based boundary conditions. To achieve turbulence closure in the ReynoldsAveraged Navier-Stokes equations, the two-equation Menter SST k-ω turbulence model is employed. Oscillations caused by the large specific dissipation rate viscous wall boundary condition are damped with selected techniques and the symmetric limited positive scheme of Jameson. Verification and validation studies are considered and demonstrate the flux correction method achieves a high degree of accuracy for the Menter SST turbulence model without any oscillations in the solution. High-order turbulent flux correction results demonstrate improvements in accuracy with minimal computational and algorithmic overhead over traditional second-order algorithms.

Critical Evaluation of Turbulence Modeling with the Flux Correction Method on Strand Grids

In this work, we examine the accuracy of the flux correction method for resolving turbulent flows on a strand based volume-mesh. The method uses a robust “negative” Spalart-Allmaras model to achieve turbulence closure of the Reynolds-Averaged NavierStokes equations. Flux correction is employed along body surfaces coupled with source terms containing derivatives in the strand direction to achieve high-order of accuracy. To demonstrate the method’s capabilities, we assess flow over three geometries, including a three-dimensional bump, an infinite wing, and a hemisphere-cylinder configuration. Comparison to results obtained from established codes show that the turbulent flux correction scheme accurately predicts both subsonic and transonic turbulent flows and accurately captures flow properties such as pressure, velocity profiles, shock location, and strength.