This paper outlines the implementation and verification of the negative Spalart-Allmaras turbulence model into the SENSEI CFD code. The SA-neg turbulence model is implemented in a flexible, object-oriented framework where additional turbulence models can be easily added. In addition to outlining the new turbulence modeling framework in SENSEI, an overview of the other general improvements to SENSEI is provided. The results for four 2D test cases are compared to results from CFL3D and FUN3D to verify that the turbulence models are implemented properly. Several differences in the results from SENSEI, CFL3D, and FUN3D are identified and are attributed to differences in the implementation and discretization order of the boundary conditions as well as the order of discretization of the turbulence model. When a solid surface is located near or intersects an inflow or outflow boundary, higher order boundary conditions should be used to limit their effect on the forces on the surface. When the turbulence equations are discretized using second order spatial accuracy, the edge of the eddy viscosity profile seems to be sharper than when a first order discretization is used. However, the discretization order of the turbulence equation does not have a significant impact on output quantities of interest, such as pressure and viscous drag, for the cases studied.
This paper examines the effectiveness of several 2-D r-adaptation schemes in reducing discretization error in numerical solutions. The adaptation schemes used include an adaptive Poisson grid generator, a variational grid generator, a center of mass based scheme, and a scheme based on deforming maps. These schemes are applied to Mach 1.2 flow around a 12 • downward turn and Mach 0.2 flow over a Karman-Trefftz airfoil. Discretization error is computed using known exact solutions for each case. Discretization error reductions of up to six times are achieved on adapted grids relative to the discretization error present on a uniform grid of the same size.
In this study, an r-adaptation technique for mesh adaptation is employed for reducing the solution discretization error, which is the error introduced due to spatial and temporal discretization of the continuous governing equations in numerical simulations. In r-adaptation, mesh modification is achieved by relocating the mesh nodes from one region to another without introducing additional nodes. Truncation error (TE) or the discrete residual is the difference between the continuous and discrete form of the governing equations. Based upon the knowledge that the discrete residual acts as the source of the discretization error in the domain, this study uses discrete residual as the adaptation driver. The r-adaptation technique employed here uses structured meshes and is verified using a series of one-dimensional (1D) and two-dimensional (2D) benchmark problems for which exact solutions are readily available. These benchmark problems include 1D Burgers equation, quasi-1D nozzle flow, 2D compression/expansion turns, and 2D incompressible flow past a Karman–Trefftz airfoil. The effectiveness of the proposed technique is evident for these problems where approximately an order of magnitude reduction in discretization error (when compared with uniform mesh results) is achieved. For all problems, mesh modification is compared using different schemes from literature including an adaptive Poisson grid generator (APGG), a variational grid generator (VGG), a scheme based on a center of mass (COM) analogy, and a scheme based on deforming maps. In addition, several challenges in applying the proposed technique to real-world problems are outlined.
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