Solutions of High-order Methods for Three-dimensional Compressible Viscous Flows

Wang, Li; Anderson, W. Kyle; Erwin, Jon T.

doi:10.2514/6.2012-2836

Cited by 13 publications

(6 citation statements)

References 45 publications

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“…In this method, which has been used by Wang et al, 11 the geometry of the domain to be meshed is considered as an elastic solid that obeys the isotropic linear elasticity relations. The elasticity equation can be recast in the following form…”

Section: Iva Interior Curving Strategymentioning

confidence: 99%

Higher-Order Finite Volume Solution Reconstruction on Highly Anisotropic Meshes

Jalali

Ollivier‐Gooch

2013

21st AIAA Computational Fluid Dynamics Conference

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Numerical experiments have demonstrated that the least-squares solution reconstruction suffers from poor accuracy and conditioning on highly anisotropic meshes. These issues are more severe for meshes with finite curvature that are often encountered in aerodynamic applications. This paper presents a comprehensive analysis of solution reconstruction procedure for second-and higher-order finite volume schemes on anisotropic triangular meshes. For this purpose, two families of anisotropic meshes are considered. The accuracy and conditioning of the reconstruction procedure is investigated for straight meshes, which are typically used in the wake region of viscous flows, using unweighted and weighted leastsquares techniques. We found that the unweighted least-squares system exhibits better conditioning and produces more accurate derivatives using the choice of stencil previously used for isotropic meshes. Similarly, the issues are addressed for triangular meshes varying anisotropically over a curved surface. Our results illustrates the shortcomings of the choice of stencil for this family of meshes. Hence, a new choice of stencil is proposed along with a local coordinate system consistent with the cells' anisotropy that resolves the conditioning and accuracy problems for anisotropic curved meshes.

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Section: Iva Interior Curving Strategymentioning

confidence: 99%

Higher-Order Finite Volume Solution Reconstruction on Highly Anisotropic Meshes

Jalali

Ollivier‐Gooch

2013

21st AIAA Computational Fluid Dynamics Conference

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“…The visible difference is due to the fact that the current mesh density is not sufficiently fine for the P = 1 scheme, which leads to unavoidably more dissipation and rampant spreading as the vortices travel downstream. It should also be noted that unlike a RANS approach, 5,41 in which all unsteady motions of turbulence are modeled, the turbulent eddy viscosity determined by the LES-WALE model is always non-negative. This fact indeed facilitates LES computations with high-order methods and improves the robustness since a cut-off limiting procedure as employed in RANS for the turbulent eddy viscosity is not needed in LES.…”

Section: Computationmentioning

confidence: 98%

Multiscale Large Eddy Simulation of Turbulence Using High-Order Finite Element Methods

Wang

Anderson

Taylor

2014

7th AIAA Theoretical Fluid Mechanics Conference

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In this paper, multiscale large-eddy simulation (LES) is investigated using a high-order discontinuous Galerkin (DG) finite element method to study the instantaneous and statistical features of turbulent flows. In the present LES, large structures of the flow are directly resolved and simulated, while the effects arising from scales smaller than the grid size are accounted for by means of a wall-adapting local eddy-viscosity (WALE) model. This subgrid scale model is chosen for obtaining correct eddy-viscosity near-wall behavior and ease of implementation. To enhance the accuracy of LES solutions, the high-order DG method is used in conjuction with high-order implicit temporal schemes, varying from a second-order backward difference formula to a fourth-order implicit Runge-Kutta scheme. Curved surface representations are properly modeled through a computational analysis programming interface while the interior mesh is deformed subsequently via a linear elasticity solver for allowing valid anisotropic elements. Numerical results demonstrate the capabilities of the high-order LES-WALE algorithms for capturing both dynamic and statistical properties of turbulent flows. The employment of a higher-order discretization is also shown to be beneficial to resolving both mean flow and turbulence statistics, as well as improving the solution accuracy and computational efficiency. Furthermore, the order-of-accuracy property of the present high-order finite element method is assessed using the Method of Manufactured Solutions based on the compressible LES-WALE equations.

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“…Professors, research faculty, and students at the Chattanooga campus of the University of Tennessee have been developing highorder finite element capabilities for a wide range of applications including fluid dynamics, electromagnetics, and structural analysis [1][2][3][4][5][6][7][8][9]. Here, both discontinuous-Galerkin (DG) methods and PetrovGalerkin (PG) stabilized finite element methods have been pursued, and it has been clearly demonstrated that the PG approach has significant advantages over the DG approach in terms of the amount of computational work required for the same level of accuracy for moderate orders of accuracy [1,9,10].…”

Section: Nomenclaturementioning

confidence: 99%

Finite Element Solutions for Turbulent Flow over the NACA 0012 Airfoil

2016

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A high-order Petrov-Galerkin finite element scheme is used to compute turbulent flow over a NACA 0012 airfoil at a freestream Mach number of 0.15, an angle of attack of 10 deg, and a Reynolds number based on the airfoil chord of 6 million. Results are obtained on a series of grids available on the NASA Turbulence Modeling Resource Web site and are compared with reference solutions that have been obtained using the FUN3D and CFL3D finite volume solvers on meshes with as many as 14.6 million degrees of freedom. Forces, moments, pressure distributions, skin friction, and profiles of velocity and turbulence working variable for the Spalart-Allmaras turbulence model are compared between the finite element and the finite volume solutions. It is demonstrated that the finite element scheme shows similar results as the finite volume schemes for most of the comparisons, but demonstrates significantly less dissipation of the wake profiles downstream of the airfoil. It is shown that, when the same number of degrees of freedom is used in the simulations, solutions obtained with quadratic elements are more accurate than those obtained using linear elements with only minor increases in computational cost. Finally, initial results with an adjoint-based hpadaptive methodology are obtained that further demonstrate that the high-order finite element framework can efficiently yield accurate results. NomenclatureA, B, k = flux Jacobian matrices C D = total drag coefficientviscous flux vector N = Lagrangian or hierarchical basis function p = polynomial order Q = solution variables (ρ, u, v, T) S = source term t = time x, y = Cartesian coordinates Γ = surface of control volume τ = stabilization matrix ϕ = weighting function Ω = control volume

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Solutions of High-order Methods for Three-dimensional Compressible Viscous Flows

Cited by 13 publications

References 45 publications

Higher-Order Finite Volume Solution Reconstruction on Highly Anisotropic Meshes

Higher-Order Finite Volume Solution Reconstruction on Highly Anisotropic Meshes

Multiscale Large Eddy Simulation of Turbulence Using High-Order Finite Element Methods

Finite Element Solutions for Turbulent Flow over the NACA 0012 Airfoil

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