Verification of a Compressible CFD Code Using the Method of Manufactured Solutions

Roy, Chris; Ober, Curt; Smith, Tony G.

doi:10.2514/6.2002-3110

Cited by 43 publications

(37 citation statements)

References 11 publications

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“…The manufactured solution technique can be used to determine the ability of an error estimation method, see Roy et al [42]. This technique requires forcing terms to drive the differential partial equations to a predetermined solution.…”

Section: Euler Equations: Manufactured Solution Test Casementioning

confidence: 99%

See 1 more Smart Citation

Adaptation strategies for high order discontinuous Galerkin methods based on Tau-estimation

Kompenhans

Rubio

Ferrer

et al. 2016

Journal of Computational Physics

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In this paper three p-adaptation strategies based on the minimization of the truncation error are presented for high order discontinuous Galerkin methods. The truncation error is approximated by means of a r-estimation procedure and enables the identification of mesh regions that require adaptation. Three adaptation strategies are developed and termed a posteriori, quasi-a priori and quasi-a priori corrected. All strategies require fine solutions, which are obtained by enriching the polynomial order, but while the former needs time converged solutions, the last two rely on non-converged solutions, which lead to faster computations. In addition, the high order method permits the spatial decoupling for the estimated errors and enables anisotropic p-adaptation. These strategies are verified and compared in terms of accuracy and computational cost for the Euler and the compressible Navier-Stokes equations. It is shown that the two quasia priori methods achieve a significant reduction in computational cost when compared to a uniform polynomial enrichment. Namely, for a viscous boundary layer flow, we obtain a speedup of 6.6 and 7.6 for the quasi-a priori and quasi-a priori corrected approaches, respectively.

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Section: Euler Equations: Manufactured Solution Test Casementioning

confidence: 99%

“…Based on Roy [42], the six steps to implement the method of manufactured solutions are: 1. Choose the form of the governing equations; 2.…”

Section: Euler Equations: Manufactured Solution Test Casementioning

confidence: 99%

Adaptation strategies for high order discontinuous Galerkin methods based on Tau-estimation

Kompenhans

Rubio

Ferrer

et al. 2016

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…As the first output-based re-meshing example the cube case with 3D manufactured solution by Roy [9] is used. Although the case is physically meaningless it is challenging for the solver as it uses highly nonlinear manufactured solution.…”

Section: Cube With 3d Manufactured Solutionmentioning

confidence: 99%

Towards an Output-Based Re-Meshing for Turbomachinery Applications

Gugala¹,

Meyer²,

Müeller³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. A methodology for estimating the truncation error between a fine computational grid and topologically inconsistent coarse grid from a multi-grid sequence is presented. This sensor is then weighted with the adjoint solution to obtain a goal-based refinement sensor which provides local scales for a re-meshing procedure. The truncation-based sensor, as well as an output-based indicator, were implemented in the proprietary Rolls-Royce code Hydra. The output-based re-meshing refinement is first applied to the simple cube case with an inviscid flow. The truncation-based sensor and the output-based sensor are then evaluated for a turbine stator case as a first step towards the turbomachinery application of the re-meshing refinement methodology. The results are presented and discussed.

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“…The manufactured solution technique can be used to determine the ability of an error estimation method, see Roy et al [Roy 2002]. This technique requires forcing terms to drive the differential partial equations to a predetermined solution.…”

Section: Manufactured Solution Test Casementioning

confidence: 99%

“…Based on Roy [Roy 2002], the six steps to implement the method of manufactured solutions are: 1. Choose the form of the governing equations, 2.…”

Section: Manufactured Solution Test Casementioning

confidence: 99%

Adaptation Strategies for Discontinuous Galerkin Spectral Element Methods by means of Truncation Error Estimations

Kompenhans¹

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Verification of a Compressible CFD Code Using the Method of Manufactured Solutions

Cited by 43 publications

References 11 publications

Adaptation strategies for high order discontinuous Galerkin methods based on Tau-estimation

Adaptation strategies for high order discontinuous Galerkin methods based on Tau-estimation

Towards an Output-Based Re-Meshing for Turbomachinery Applications

Adaptation Strategies for Discontinuous Galerkin Spectral Element Methods by means of Truncation Error Estimations

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