A High-Order Finite-Volume Method with Anisotropic AMR for Ideal MHD Flows

Freret, Lucie; Ivan, Lucian; Sterck, Hans De; Groth, C. P. T.

doi:10.2514/6.2017-0845

Cited by 8 publications

(15 citation statements)

References 31 publications

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“…In the present study, a second-order limited upwind finite-volume spatial discretization scheme is used along with the anisotropic block-based AMR scheme of Freret and Groth 15 and Freret et al 27 for the solution of compressible form of Euler equations on three-dimensional multi-block body-fitted meshes consisting of hexahedral computational cells. High-order residual evaluation associated with p-refinement is carried out using the high-order central essentially non-oscillatory (CENO) finite-volume scheme of Ivan and Groth 40 that was recently extended for use with the anisotropic block-based AMR scheme.…”

Section: Scope Of Present Studymentioning

confidence: 99%

“…The evaluation of error estimates for directing the anisotropic mesh refinement based on p refinement is also considered here and, for this, the evaluation of the solution residual to high-order (i.e., p > 2) is required. High-order evaluation of the solution residual is accomplished here by using the high-order CENO finite-volume and reconstruction scheme of Ivan and Groth 40 and Freret et al 27 The CENO scheme is a hybrid approach that combines a high-order unlimited central scheme for fully resolved solution content with a low-order limited linear method for under-resolved/discontinuous content. To ensure monotonicity, switching from high-to low-order is controlled by a smoothness indicator.…”

Section: Iiid High-order Ceno Finite-volume Schemementioning

confidence: 99%

“…The range for α is −∞ < α ≤ 1 and it will approach unity as piecewise Kexact solution reconstruction within each cell yields a smooth and continuous representation of the solution between adjacent cells. Note that Freret et al 27 propose an anisotropic smoothness indicator to represent the smoothness of the solution in a particular logical or computational coordinate direction of the grid. The anisotropic smoothness indicator for a direction, γ, is evaluated using…”

Section: Iiid1 Smoothness Indicatormentioning

confidence: 99%

“…15 The latter has several advantages making it more efficient and better suited for high-order spatial discretizations. The extension of the anisotropic AMR approach for use with the high-order central essentially non-oscillatory (CENO) finite-volume scheme is considered in the recent study by Freret et al 27 In many of the aforementioned studies, physics-and/or gradient-based strategies were used to identify regions for mesh refinement by monitoring solution quantity changes over spatial ranges. These approaches are easily implementable and work well for many of the problems studied.…”

Section: Introductionmentioning

confidence: 99%

“…To avoid the shortcomings of physics-and/or gradient-based refinement strategies mentioned above, the use of adjoint-based error estimation is considered here for directing the mesh adaptation. In particular, the application of adjoint-based error estimation as proposed by a number of previous researchers [29][30][31][32][33][34][35][36][37][38][39] is examined for directing mesh refinement in the anisotropic block-based AMR approach of Freret and Groth 15 as well as Freret et al 27 The adjoint-based error estimation is used to evaluate the sensitivity of pre-defined engineering quantities or functionals of interest to corresponding local estimates of the solution error. This output-based error estimate is calculated here via two approaches: one based on mesh (or h) refinement and the other based on order (or p) refinement and these estimates are then used to direct the mesh adaptation.…”

Section: Introductionmentioning

confidence: 99%

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Comparison of h- and p-Derived Output-Based Error Estimates for Directing Anisotropic Adaptive Mesh Refinement in Three-Dimensional Inviscid Flows

Ngigi

Freret

Groth

2018

2018 AIAA Aerospace Sciences Meeting

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The use of adjoint-based error estimation in conjunction with a highly parallel and scalable, anisotropic, block-based, adaptive mesh refinement (AMR) technique is considered for the more efficient prediction of three-dimensional compressible flows. In particular, a comparison is made between the computational performances of output-based error estimates, derived via two approaches, namely one based on mesh (or h) refinement and the other based on order (or p) refinement, for directing the mesh refinement in anisotropic AMR scheme. The AMR scheme allows enhancement of local mesh resolution, with preference given to directions as dictated by the flow solution. The proposed adjoint-based error estimation technique provides a posteriori estimates of the error for an engineering functional of interest in terms of estimates of the local solution error following from the solution residual. The estimated error in the solution residual is obtained either via direct refinement of the mesh in the preferred directions (here referred to as the h-derived error indicator) or by using a higher-order spatial operator with anisotropic feature detection based on the anisotropic smoothness indicator of an appropriate solution quantity (here referred to as the p-derived error indicator). Both approaches are considered here. Additionally, two formulations of the adjoint-based error indicator are examined for directing the output-based AMR. The first is the so-called computable correction (CC), where the residual error is weighted by the corresponding adjoint solution for the functional of interest, and the second is the so-called error in the computable correction (ECC), which is comprised of a linear combination of the residual error weighted with the adjoint solution and the adjoint residual weighted with the primal solution. The resulting output error indicator is used to direct the mesh refinement, with regions of the solution domain contributing most significantly to the functional error being selected for local enrichment of the mesh. In this way, the computed accuracy of the functional is increased while potentially greatly reducing the associated computational cost of performing the simulation. For the cases of interest, both low-and high-order upwind finite-volume spatial discretization schemes are applied in conjunction with the block-based AMR scheme to the solution of the partial differential equations governing steady-state inviscid compressible flows. The potential benefits of the proposed anisotropic block-based AMR with adjoint-based error estimation are demonstrated for a range of compressible inviscid flow problems of varying complexity. Comparisons of solution accuracy and relative computational costs for results obtained using both hand p-derived error estimates of the solution residual are examined and discussed.

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Section: Scope Of Present Studymentioning

confidence: 99%

Section: Iiid High-order Ceno Finite-volume Schemementioning

confidence: 99%

Section: Iiid1 Smoothness Indicatormentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%