A hybrid multilevel method for high-order discretization of the Euler equations on unstructured meshes

May, Georg; Iacono, Francesca; Jameson, Antony

doi:10.1016/j.jcp.2010.01.036

Cited by 10 publications

(9 citation statements)

References 29 publications

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“…Explicit methods for time integration suffer yet a stronger limitation of the time step value allowed for stability and, together with stretched high-order mesh cells, even current implicit schemes are typically not robust enough. 1 There is an active research community working on high-order methods for unstructured meshes. The international workshops on high-order CFD methods 2 have gathered several research groups to discuss and propose solutions for the difficulties encountered in high-order simulations for practical aerospace applications.…”

Section: Introductionmentioning

confidence: 99%

High-Order Compressible Flow Simulations with the Unstructured Spectral Difference Method

Moreira

Breviglieri

Azevedo

2015

22nd AIAA Computational Fluid Dynamics Conference

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The spectral difference (SD) method is applied to the spatial discretization of the 2-D Euler equations on several compressible flow simulations. An order of accuracy study is performed for schemes from 2nd to 6th order. The work also evaluates a high order hierarchical limiting technique for the SD method. The numerical method results are compared with other high-order methods, such as spectral finite volume and weighted essentially non-oscillatory schemes. Unsteady flow problems with strong shock waves and other discontinuities typical of compressible flows are also analyzed in order to allow for an assessment of the resolution capability and computational cost of the SD scheme along with the applied nonlinear stability technique.

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Section: Introductionmentioning

confidence: 99%

High-Order Compressible Flow Simulations with the Unstructured Spectral Difference Method

Moreira

Breviglieri

Azevedo

2015

22nd AIAA Computational Fluid Dynamics Conference

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“…This behavior is expected due to the limited CFD value required for numerical stability of higher-order schemes. 1 In accordance with the previous test case, future studies will consider the analysis of an implicit time-marching scheme coupled to the SD method, which should considerably improve the convergence rate for the higher-order simulations. Figure 15: NACA 0012 convergence history for the SD method.…”

Section: Viib Naca 0012 Airfoilmentioning

confidence: 80%

“…Explicit methods for time integration suffer yet a stronger limitation of the time step value allowed for stability and, together with stretched high-order mesh elements, even current implicit schemes are not robust enough. 1 There is an active research community working on high-order methods for unstructured meshes. The international workshop on high-order CFD methods 2 has gathered several research groups to discuss and propose solutions for the difficulties encountered in high-order simulations for practical aerospace applications.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study of Discontinuous High Order Methods for Compressible Flows

Breviglieri

Paula

Wolf

et al. 2014

32nd AIAA Applied Aerodynamics Conference

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A comparative study of three numerical formulations for discontinuous high-order reconstruction on unstructured grids is performed. The Weighted Essentially Non-Oscillatory (WENO), the Spectral Finite Volume (SFV) and the Spectral Difference (SD) methods are considered for the spatial discretization of the 2-D Euler equations. The study compares, in particular, results for linear, quadratic and cubic reconstructions. The test cases include problems with strong shock waves and other discontinuities which provide a comparative assessment of the resolution capability of the tested schemes. This work explores the high-order method capabilities to solve literature test cases and it is expected that such results provide valuable guidelines for future developments regarding high-order methods for aerospace applications.

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“…• hybridized DG schemes, including target-based adaptation via adjoint equation [6,7,8] • Stable high-order Spectral Difference method for hyperbolic conservation laws on triangules [1] • Multilevel methods for solution of the Euler equations [5];…”

Section: Discussionmentioning

confidence: 99%

“…• Matrix-free solution methods for implicit relaxation schemes in response to the extreme storage requirement of implicit relaxation methods for high-order discretization [5,3,2];…”

Section: Discussionmentioning

confidence: 99%

High Order Methods for Compressible Viscous Flow on Unstructured Meshes: New Discretization Techniques and Algorithms

May¹

2014

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A hybrid multilevel method for high-order discretization of the Euler equations on unstructured meshes

Cited by 10 publications

References 29 publications

High-Order Compressible Flow Simulations with the Unstructured Spectral Difference Method

High-Order Compressible Flow Simulations with the Unstructured Spectral Difference Method

A Comparative Study of Discontinuous High Order Methods for Compressible Flows

High Order Methods for Compressible Viscous Flow on Unstructured Meshes: New Discretization Techniques and Algorithms

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