The AIAA Code Verification Project - Test cases for CFD Code Verification

Ghia, Urmila; Bayyuk, Sami; Habchi, Sami D.; Roy, Chris; Shih, Tsan‐Hsing; Conlisk, Terrence; Hirsch, Charles; Powers, Joseph M.

doi:10.2514/6.2010-125

Cited by 10 publications

(9 citation statements)

References 25 publications

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“…A small increase in the entropy is noticed near the slip-wall boundary that defines the wedge surface. This increase in entropy is from numerical error and was observed to decrease in magnitude and extent as the mesh was refined, consistent with the results published by Ghia et al [150]. Table 5.6 presents the numerically computed shock angle, β , approximated as the angle between the x-axis and the point at which the oblique shock intersects the outflow boundary; and the post-shock Mach number M 2 , computed as an average of cell-centered values along a streamline.…”

Section: Resultssupporting

confidence: 91%

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Adjoint-based aerodynamic design optimisation in hypersonic flow

Damm¹

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The drive for improved flexibility and reusability in satellite launch systems has brought a resurgence in the popularity of scramjet-powered access-to-space launch vehicle concepts. A challenge in scramjet-powered accelerator vehicles is achieving positive thrust margins at the high-speed end of their flight envelopes. As a consequence, scramjet-powered vehicles typically rely on highly integrated airframe-engine configurations. However, due to the tight integration, the geometries and the flow physics are complex. An automated optimisation method seems an excellent candidate approach to explore the complex design space of hypersonic vehicles. This thesis focuses on the development and application of a particular optimisation method, adjoint-based optimisation, to aid in efficient aerodynamic design in hypersonic flows. Shape optimisation of scramjet-powered vehicles requires many design parameters to capture the geometric detail, and, since the flow physics is complex, the fidelity of Reynolds-Averaged Navier-Stokes (RANS) analyses is desirable. The combination of many design parameters and an expensive objective function evaluation drives the need for gradient evaluation methods that scale well with the number of design variables. An advantage of the adjoint method is that all shape sensitivities for an objective function are evaluated at the cost of only one flow solution and one adjoint solution. As a result of its efficiency, the adjoint method has become widely used for aircraft design, evolving to the design optimisation of full configurations. Despite the wide use of adjoint methods in aircraft optimisation, there has been very little application to hypersonic vehicle design. Several high-speed adjoint solvers have been reported in the literature, however, a majority of these works have only verified the adjoint sensitivities, few have followed on to demonstrate the method for use in design optimisation. The contribution of this work is the description and application of a discrete adjoint solver in high-speed compressible flow optimisation. What is unique in this work is a demonstration that complex-step differentiation works well to linearise a second-order spatially accurate unstructured RANS solver. In particular, the approach presented in this work utilises the k − ω turbulence model in high-speed ducted flow configurations. As part of this work, to provide flow analysis with a rapid turnaround , an unstructured steadystate RANS solver driven by a Jacobian-Free Newton-Krylov method was developed. Turbulence is modelled using the two-equation k − ω turbulence model. The Newton method is globalised by using the pseudo-transient approach. A restarted GMRES method is used to solve the system of linear equations arising when solving for the Newton steps. Evaluation of the matrix-vector products required in the GMRES algorithm is accomplished by Fréchet derivatives using imaginary perturbations in the complex plane. This is necessary to achieve robust convergence of the types of turbulent hypersonic flows...

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Section: Resultssupporting

confidence: 91%

“…f n is the numerical value at cell n and f ref,n is the manufactured value evaluated at cell centroid coordinates. The Method of Manufactured Solutions and it's importance to the verification of CFD codes is widely known and is a strongly recommended method for code verification by the AIAA Committee on Standards [150].…”

Section: Verificationmentioning

confidence: 99%

Adjoint-based aerodynamic design optimisation in hypersonic flow

Damm¹

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“…In this oblique shock problem, a uniform flow impinges on an impermeable wall. Following [9], we pose the two-dimensional stationary Euler equations in the domain. When the uniform horizontal flow impinges on the wedge at the bottom of the domain, a shock will form.…”

Section: Two-dimensional Systemsmentioning

confidence: 99%

“…We solve this problem setting δ = 15 • as the angle the bottom wedge makes with the horizontal. We expect the shock to make an angle of approximately 32.2 • with the horizontal, and the flow beyond the shock should have a Mach number of approximately 2.255 [9].…”

Section: Two-dimensional Systemsmentioning

confidence: 99%

Fast sweeping methods for hyperbolic systems of conservation laws at steady state II

Engquist

Froese

Tsai

2015

Journal of Computational Physics

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Abstract. The idea of using fast sweeping methods for solving stationary systems of conservation laws has previously been proposed for efficiently computing solutions with sharp shocks. We further develop these methods to allow for a more challenging class of problems including problems with sonic points, shocks originating in the interior of the domain, rarefaction waves, and two-dimensional systems. We show that fast sweeping methods can produce higher-order accuracy. Computational results validate the claims of accuracy, sharp shock curves, and optimal computational efficiency.

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“…Regression tests are limited to cases where the discretization error in the solution can be computed directly. This includes cases where the analytical solution is known, such as test cases proposed by Ghia et al 17 , and cases with analytical solutions from the High-Order Workshops 18 . The Method of Manufactured Solutions [19][20][21] is also used to broaden the spectrum of analytical solutions.…”

Section: G Regression-testingmentioning

confidence: 99%

A Verification Driven Process for Rapid Development of CFD Software

Galbraith

Allmaras

Darmofal

2015

53rd AIAA Aerospace Sciences Meeting

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Previous work by the authors has demonstrated a high-order fully-automated output-error based mesh adaptation method suitable for solving the Reynolds-Averaged Navier-Stokes equations. The high-order of accuracy is achieved with a discontinuous Galerkin discretization. While the adaptation method has proven to provide significant reduction in computational cost relative to second-order methods, the authors are currently exploring alternate high-order finite element discretizations to further reduce the computational cost. However, the previously developed software framework is not suitable for all discretizations of interest. Hence, a new software framework is being developed with enhanced maintainability and flexibility relative to the previous framework. This paper focuses on strategies employed to accelerate the development of the new software framework. A software development environment that promotes a verification driven process for software development is presented. The development environment encourages developers to incorporate the verification principles of Verification and Validation as part of the software development process to promote maintainability and collaboration. The software development is further accelerated through the use of automatic differentiation, which is used here to automatically compute the linearization of a mathematical model. This paper outlines an implementation of automatic differentiation with minimal computational overhead relative to manually written linearizations.

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The AIAA Code Verification Project - Test cases for CFD Code Verification

Cited by 10 publications

References 25 publications

Adjoint-based aerodynamic design optimisation in hypersonic flow

Adjoint-based aerodynamic design optimisation in hypersonic flow

Fast sweeping methods for hyperbolic systems of conservation laws at steady state II

A Verification Driven Process for Rapid Development of CFD Software

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