Application of Strand-Cartesian Interfaced Solver on Flows Around Various Geometries

This work examines the application of a high-order numerical method to strand-based grids to solve the Navier-Stokes equations. Coined Flux Correction , this method eliminates error terms in the fluxes of traditional second-order finite volume Galerkin methods. Flux Correction is first examined for applications to the Reynolds-Averaged Navier-Stokes equations to compute turbulent flows on a strictly strand-based domain. Flow over three geometries are examined to demonstrate the method’s capabilities: 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 flow properties such as pressure, velocity profiles, shock location and strength. However, it can be seen that an overset Cartesian solver is necessary to more accurately capture certain flow properties in the wake region. The Strand-Cartesian Interface Manager(SCIM) uses a combination of second-order trilinear interpolation and mixed-order Lagrange interpolation to establish domain connectivity between the overset grids. Verification of the high-order SCIM code are conducted through the method of manufactured solutions. Steady and unsteady flow around a sphere are used to validate the SCIM library. The method is found to be have a combined order of accuracy of approximately 2.5, and has improved accuracy for steady cases. However, for unsteady cases the method fails to accurately predict the time-dependent flow field

Extensions of High-order Flux Correction Methods to Flows With Source Terms at Low Speeds

A novel high-order finite volume scheme using flux correction methods in conjunction with structured finite difference schemes is extended to low Mach and incompressible flows on strand grids. Flux correction achieves high-order by explicitly canceling low-order truncation error terms in the finite volume cell. The flux correction method is applied in unstructured layers of the strand grid. The layers are then coupled together using a source term containing the derivatives in the strand direction. Proper source term discretization is verified. Strand-direction derivatives are obtained by using summation-by-parts operators for the first and second derivatives. A preconditioner is used to extend the method to low Mach and incompressible flows. We further extend the method to turbulent flows with the Spalart Allmaras model. We verify high-order accuracy via the method of manufactured solutions, method of exact solutions, and physical problems. Results obtained compare well to analytical solutions, numerical studies, and experimental data. It is foreseen that future application in the Naval field will be possible

Verification and Validation of the Spalart-Allmaras Turbulence Model for Strand Grids

The strand-Cartesian grid approach is a unique method of generating and computing fluid dynamic simulations. The strand-Cartesian approach provides highly desirable qualities of fully-automatic grid generation and high-order accuracy. This thesis focuses on the implementation of the Spalart-Allmaras turbulence model to the strand-Cartesian grid framework. Verification and validation is required to ensure correct implementation of the turbulence model.Mathematical code verification is used to ensure correct implementation of new algorithms within the code framework. The Spalart-Allmaras model is verified with the Method of Manufactured Solutions (MMS). MMS shows second-order convergence, which implies that the new algorithms are correctly implemented.Validation of the strand-Cartesian solver is completed by simulating certain cases for comparison against the results of two independent compressible codes; CFL3D and FUN3D. The NASA-Langley turbulence resource provided the inputs and conditions required to run the cases, as well as the case results for these two codes. The strand solver showed excellent agreement with both NASA resource codes for a zero-pressure gradient flat plate and bump- in-channel. The treatment of the sharp corner on a NACA 0012 airfoil is investigated, resulting in an optimal external sharp corner configuration of strand vector smoothing with a base Cartesian grid and telescoping Cartesian refinement around the trailing edge. Results from the case agree well with those from CFL3D and FUN3D. Additionally, a NACA 4412 airfoil case is examined, and shows good agreement with CFL3D and FUN3D, resulting in validation for this case

Large-eddy simulation and wall modelling of turbulent channel flow

We report large-eddy simulation (LES) of turbulent channel flow. This LES neither resolves nor partially resolves the near-wall region. Instead, we develop a special near-wall subgrid-scale (SGS) model based on wall-parallel filtering and wall-normal averaging of the streamwise momentum equation, with an assumption of local inner scaling used to reduce the unsteady term. This gives an ordinary differential equation (ODE) for the wall shear stress at every wall location that is coupled with the LES. An extended form of the stretched-vortex SGS model, which incorporates the production of near-wall Reynolds shear stress due to the winding of streamwise momentum by near-wall attached SGS vortices, then provides a log relation for the streamwise velocity at the top boundary of the near-wall averaged domain. This allows calculation of an instantaneous slip velocity that is then used as a ‘virtual-wall’ boundary condition for the LES. A Kármán-like constant is calculated dynamically as part of the LES. With this closure we perform LES of turbulent channel flow for Reynolds numbers Re_τ based on the friction velocity u_τ and the channel half-width δ in the range 2 × 10^3 to 2 × 10^7. Results, including SGS-extended longitudinal spectra, compare favourably with the direct numerical simulation (DNS) data of Hoyas & Jiménez (2006) at Re_τ = 2003 and maintain an O(1) grid dependence on Re_τ

Development of a Three-Dimensional High-Order Strand-Grids Approach

Development of a novel high-order flux correction method on strand grids is presented. The method uses a combination of flux correction in the unstructured plane and summation-by-parts operators in the strand direction to achieve high-fidelity solutions. Low-order truncation errors are cancelled with accurate flux and solution gradients in the flux correction method, thereby achieving a formal order of accuracy of 3, although higher orders are often obtained, especially for highly viscous flows. In this work, the scheme is extended to high-Reynolds number computations in both two and three dimensions. Turbulence closure is achieved with a robust version of the Spalart-Allmaras turbulence model that accommodates negative values of the turbulence working variable, and the Menter SST turbulence model, which blends the k-ε and k-ω turbulence models for better accuracy. A major advantage of this high-order formulation is the ability to implement traditional finite volume-like limiters to cleanly capture shocked and discontinuous flow. In this work, this approach is explored via a symmetric limited positive (SLIP) limiter. Extensive verification and validation is conducted in two and three dimensions to determine the accuracy and fidelity of the scheme for a number of different cases. Verification studies show that the scheme achieves better than third order accuracy for low and high-Reynolds number flow. Cost studies show that in three-dimensions, the third-order flux correction scheme requires only 30% more walltime than a traditional second-order scheme on strand grids to achieve the same level of convergence. In order to overcome meshing issues at sharp corners and other small-scale features, a unique approach to traditional geometry, coined asymptotic geometry, is explored. Asymptotic geometry is achieved by filtering out small-scale features in a level set domain through min/max flow. This approach is combined with a curvature based strand shortening strategy in order to qualitatively improve strand grid mesh quality

Numerical simulation with low artificial dissipation of transitional flow over a delta wing

A low-dissipation simulation method is used to perform simulations of transitional aerodynamic flow over a delta wing. For an accurate simulation of such a flow, numerical conservation of important physical quantities is desirable. In particular, the discretization of the convective terms of the Navier-Stokes equations should not spuriously generate or dissipate kinetic energy, because this can interfere with the transition to turbulent flow. Conservation of discrete kinetic energy by the discretized convective terms can be achieved by writing the Navier--Stokes equations in square-root variables, which results in a skew-symmetric convective term. In the paper, simulations with such a low-dissipation method are presented at chord Reynolds numbers around 200,000. The results show good agreement with experimental measurements