Output-Based Space-Time Mesh Adaptation for Unsteady Aerodynamics

Luo, Yuxing; Fidkowski, Krzysztof J.

doi:10.2514/6.2011-491

Cited by 7 publications

(2 citation statements)

References 26 publications

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“…Within the finite volume community output-based mesh refinement has begun to be used for unsteady problems. Specifically, temporalonly adaptation and space-time adaptation in the context of aerodynamics have been explored by Mani and Mavriplis (2007) and Flynt and Mavriplis (2012) respectively, and work with the compressible Navier-Stokes equations has been done for both static domains, by Luo and Fidkowski (2011), and deforming domains, by Kast and Fidkowski (2013).…”

Section: Introductionmentioning

confidence: 99%

Adjoint Methods for Guiding Adaptive Mesh Refinement in Tsunami Modeling

Davis¹,

LeVeque²

2016

Pageoph Topical Volumes

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One difficulty in developing numerical methods for tsunami modeling is the fact that solutions contain time-varying regions where much higher resolution is required than elsewhere in the domain, particularly when tracking a tsunami propagating across the ocean. The open source GeoClaw software deals with this issue by using block-structured adaptive mesh refinement to selectively refine around propagating waves. For problems where only a target area of the total solution is of interest (e.g. one coastal community), a method that allows identifying and refining the grid only in regions that influence this target area would significantly reduce the computational cost of finding a solution.In this work, we show that solving the time-dependent adjoint equation and using a suitable inner product with the forward solution allows more precise refinement of the relevant waves. We present the adjoint methodology first in one space dimension for illustration and in a broad context since it could also be used in other adaptive software, and potentially for other tsunami applications beyond adaptive refinement. We then show how this adjoint method has been integrated into the adaptive mesh refinement strategy of the open source GeoClaw software and present tsunami modeling results showing that the accuracy of the solution is maintained and the computational time required is significantly reduced through the integration of the adjoint method into adaptive mesh refinement.

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Section: Introductionmentioning

confidence: 99%

Adjoint Methods for Guiding Adaptive Mesh Refinement in Tsunami Modeling

Davis¹,

LeVeque²

2016

Pageoph Topical Volumes

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“…The present research is a continuation of previous work in unsteady output-based adaptation on static meshes. 11,14 The discretization and error estimation extend naturally to the case of dynamic spatial order refinement, and the required modifications are discussed in Sections II and III. Error localization is also modified to increase the granularity of the adaptive indicator for driving dynamic mesh refinement, as described in Section IV.…”

Section: Introductionmentioning

confidence: 99%

An Output-Based Dynamic Order Refinement Strategy for Unsteady Aerodynamics

Fidkowski

2012

50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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An output-based dynamic order refinement strategy is presented for unsteady simulations using the discontinuous Galerkin finite element method in space and time. A discrete unsteady adjoint solution provides scalar output error estimates and drives adaptive refinement of the space-time mesh. Space-time anisotropy is measured using projection of the adjoint onto semi-refined spaces and is used to allocate degrees of freedom to additional time slabs or increased spatial order of individual space-time elements. The spatial refinement is dynamic in that the solution approximation order can change between time slabs. Results for the compressible Euler equations demonstrate benefits of the dynamic order refinement strategy in terms of total degrees of freedom: at strict error tolerances, the savings approaches two orders of magnitude compared to uniform refinement, and a factor of two to three compared to output-based refinement with a static spatial mesh.

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Adjoint Methods for Guiding Adaptive Mesh Refinement in Tsunami Modeling

Davis

LeVeque²

2016

Pure Appl. Geophys.

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One difficulty in developing numerical methods for tsunami modeling is the fact that solutions contain regions where much higher resolution is required than elsewhere in the domain, particularly since the solution may contain discontinuities or other localized features. The Clawpack software deals with this issue by using block-structured adaptive mesh refinement to selectively refine around propagating waves. For problems where only a target area of the total solution is of interest (e.g. one coastal community), a method that allows identifying and refining the grid only in regions that influence this target area would significantly reduce the computational cost of finding a solution. In this work, we show that solving the time-dependent adjoint equation and using a suitable inner product with the forward solution allows more precise refinement of the relevant waves. We present examples solving the shallow water equations in one and two dimensions. To perform these simulations, the use of the adjoint method has been integrated into the adaptive mesh refinement strategy of the open source GeoClaw software. We also present results that show that the accuracy of the solution is maintained and the computational time required is significantly reduced through the integration of the adjoint method into adaptive mesh refinement.Comment: Much of this material appeared in a previous pre-print, which can be found at arXiv:1511.03645 . Here, the material has been rewritten to focus on shallow water equations and submitted to a more application focused journa

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Output-Based Space-Time Mesh Adaptation for Unsteady Aerodynamics

Cited by 7 publications

References 26 publications

Adjoint Methods for Guiding Adaptive Mesh Refinement in Tsunami Modeling

Adjoint Methods for Guiding Adaptive Mesh Refinement in Tsunami Modeling

An Output-Based Dynamic Order Refinement Strategy for Unsteady Aerodynamics

Adjoint Methods for Guiding Adaptive Mesh Refinement in Tsunami Modeling

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