arxiv: 2604.18899 · v1 · submitted 2026-04-20 · ⚛️ physics.flu-dyn

Recognition: unknown

Application of Metric-Based Mesh Adaptation to Hypersonic Aerothermal Simulations Using US3D

Dirk Ekelschot

Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:00 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn

keywords mesh adaptationhypersonic aerothermalunstructured meshreal gas flowsphere cone capsuleRCS jetssurface heatingUS3D

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The pith

Metric-based mesh adaptation using the temperature Hessian matches structured heating predictions for hypersonic capsule flows with RCS jets.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates metric-based mesh adaptation guided by the Hessian of the temperature solution for real-gas hypersonic aerothermal problems. In simulations of supersonic flow over a hemisphere and hypersonic CO2-N2 flow over a 70-degree sphere-cone capsule, the adapted unstructured meshes produce surface heating predictions comparable to conventional block-structured DPLR results. The approach incorporates detailed geometry for eight RCS jets on the capsule back shell, a feature difficult for structured meshes. Readers would care because it shows unstructured methods can handle realistic spacecraft complexity without sacrificing accuracy in critical heating data.

Core claim

Metric-based mesh adaptation driven by the Hessian of the temperature solution enables unstructured meshes to deliver surface heating predictions comparable to block-structured DPLR simulations for hypersonic real-gas flows, while readily incorporating complex geometric features such as the eight RCS jets on a 70-degree sphere-cone entry capsule that are typically out of reach for structured approaches.

What carries the argument

Metric-based mesh adaptation algorithm that uses the Hessian of the temperature solution to dictate local refinement and coarsening of the unstructured mesh.

If this is right

Comparable surface heating is obtained for the hemisphere test case whether prisms or hexahedra are used in the boundary layer mesh.
Similar surface heating predictions are achieved for the hypersonic sphere-cone capsule compared to block-structured DPLR simulations.
The adapted meshes successfully include the full geometries of the eight RCS jets on the back shell.
The method provides flexibility for complex geometries that block-structured approaches cannot easily accommodate.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The temperature-Hessian indicator could be combined with other sensors to further improve shock and heating resolution in future applications.
This adaptation strategy may reduce manual mesh design effort for vehicles with protrusions or control jets.
The approach might extend to other real-gas or multi-species flows where structured meshing becomes impractical.

Load-bearing premise

The Hessian of the temperature solution is a sufficient and reliable indicator for mesh adaptation that captures shocks, boundary layers, and other features without degrading surface heating accuracy in hypersonic real-gas flows.

What would settle it

If an adapted unstructured simulation produces surface heating values that differ substantially from DPLR references or fails to resolve the bow shock and boundary layer on the sphere-cone case, the central claim would be falsified.

read the original abstract

The main goal of this paper is to demonstrate the application of metric-based mesh adaptation to real gas problems and highlight the benefits particularly when complex geometries are considered. We use the Hessian of the temperature solution as an indicator to dictate where the mesh needs refinement or coarsening. In the context of hypersonic flow simulations, these methods are not widely adopted since unstructured meshes often result in poor surface heating predictions. The present work aims to demonstrate the great flexibility metric-based mesh adaptation provides when it comes to predicting complex flow features while still maintaining comparable surface heating predictions. We consider two test cases: (a) a supersonic flow over a hemisphere and show that comparable surface heating is obtained by applying mesh adaptation and by employing hexahedra instead of prisms in the boundary layer mesh; (b) we consider a more realistic test case of a hypersonic flow of a C02-N2 mixture past a 70 degree sphere cone atmospheric entry capsule. For the second test case, similar surface heating predictions are obtained compared to more conventional block structured DPLR simulations. Furthermore, for the adapted unstructured simulations, the geometries of the eight Reaction Control System (RCS) jet on the back shell were taken into account. This highlights the ability of these methods to deal with complex geometries that are typically out of reach for block structured approaches.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper shows temperature-Hessian adaptation can match DPLR heating rates on a sphere-cone with RCS jets, but the indicator choice leaves open whether shocks and species layers are properly resolved.

read the letter

The central point is that metric adaptation driven by the temperature Hessian produced surface heating predictions comparable to block-structured DPLR runs on the 70-degree sphere-cone in CO2-N2 flow, and it did so while incorporating the eight RCS jet geometries that structured meshes handle poorly. That demonstration is the useful part. The hemisphere case adds a smaller check that hexahedral boundary-layer elements help keep heating accurate under adaptation. Both results are presented as direct numerical comparisons rather than theory, which keeps the claim grounded. The work is not inventing a new adaptation scheme; it is applying an existing one to real-gas hypersonic conditions with realistic backshell features. That specific combination has not been shown in the cited literature, so the demonstration itself counts as new. The flexibility for complex geometry is the clearest practical gain. Structured approaches often require manual blocking or simplifications around jets, while the adapted unstructured mesh sidesteps that. If the quantitative heating numbers hold up in the full figures, this is the kind of result that could encourage more groups to try adaptation on entry vehicles. The soft spot is the choice of indicator. Temperature Hessian can miss or under-refine strong shocks and species interfaces where temperature gradients are milder than density or pressure jumps. The abstract claims the adapted meshes still gave similar heating, but without reported error norms, grid-convergence plots, or a side-by-side multi-sensor comparison it is hard to judge how close the match really is or whether critical flow features were captured by accident. The free parameters for threshold and scaling are also left implicit. This is a minor concern if the paper supplies the missing mesh statistics and heating profiles, but it is the part that needs the most scrutiny in review. The paper is aimed at hypersonic CFD users who already run US3D or similar unstructured codes and want to reduce manual meshing time on vehicles with jets or other protrusions. Readers who care about practical aerothermal accuracy on complex shapes will get the most out of it. It is not a methods breakthrough, but the demonstration is concrete enough that a serious referee should see it. I would send it for peer review.

Referee Report

2 major / 1 minor

Summary. The manuscript demonstrates metric-based mesh adaptation driven by the temperature Hessian within the US3D unstructured solver for hypersonic real-gas aerothermal flows. It applies the method to two cases: (1) supersonic flow over a hemisphere, comparing adapted meshes using hexahedra versus prisms in the boundary layer; (2) hypersonic CO2-N2 flow over a 70° sphere-cone capsule, claiming surface heating predictions comparable to block-structured DPLR results while incorporating eight RCS jets on the backshell to show handling of complex geometry.

Significance. If the quantitative comparisons hold, the work is significant because it addresses a known limitation of unstructured meshes in hypersonic aerothermodynamics—namely, accurate surface heat-flux prediction—while demonstrating geometric flexibility that structured codes struggle to match. The direct numerical comparison to DPLR and the inclusion of RCS jets constitute concrete strengths; the paper supplies a falsifiable demonstration rather than a purely theoretical argument.

major comments (2)

[Abstract / sphere-cone results] Abstract and results for the sphere-cone case: the central claim that 'similar surface heating predictions are obtained' compared to DPLR is asserted without any reported quantitative metrics (e.g., peak heating rate differences, L2 error norms, or grid-convergence indices). This is load-bearing for the main result; the manuscript must supply tabulated values or explicit error measures to allow assessment of whether adaptation preserves accuracy.
[Method / adaptation indicator] Adaptation strategy (temperature Hessian only): the choice of the temperature Hessian as the sole metric driver is not shown to guarantee adequate resolution of shock standoff, post-shock entropy layers, or species gradients that control wall heat flux in real-gas flows. The manuscript should either provide a multi-sensor comparison or demonstrate that temperature-based anisotropy captures the relevant discontinuities; otherwise the claim that heating predictions remain comparable rests on an unverified assumption.

minor comments (1)

[Abstract] The abstract would be clearer if it stated the specific freestream conditions (Mach number, angle of attack, mixture composition) for both test cases.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of the significance of our work and for the constructive major comments. We address each point below and will revise the manuscript accordingly to strengthen the quantitative comparisons and clarify the adaptation strategy.

read point-by-point responses

Referee: [Abstract / sphere-cone results] Abstract and results for the sphere-cone case: the central claim that 'similar surface heating predictions are obtained' compared to DPLR is asserted without any reported quantitative metrics (e.g., peak heating rate differences, L2 error norms, or grid-convergence indices). This is load-bearing for the main result; the manuscript must supply tabulated values or explicit error measures to allow assessment of whether adaptation preserves accuracy.

Authors: We agree that providing quantitative metrics is important for substantiating the claim. Upon re-examination of our results, we can extract peak heating rates from the simulations. In the revised manuscript, we will add a table in the sphere-cone section reporting the peak surface heating rate from the adapted mesh simulation and the corresponding DPLR value, along with the percentage difference. If grid convergence data is available from our studies, we will also include a grid convergence index or note the observed convergence. This will make the comparison more rigorous and falsifiable. revision: yes
Referee: [Method / adaptation indicator] Adaptation strategy (temperature Hessian only): the choice of the temperature Hessian as the sole metric driver is not shown to guarantee adequate resolution of shock standoff, post-shock entropy layers, or species gradients that control wall heat flux in real-gas flows. The manuscript should either provide a multi-sensor comparison or demonstrate that temperature-based anisotropy captures the relevant discontinuities; otherwise the claim that heating predictions remain comparable rests on an unverified assumption.

Authors: The temperature Hessian is selected as it effectively captures the strong temperature gradients associated with the bow shock and the thermal boundary layer, which are primary drivers of aerothermal heating in hypersonic flows. In the hemisphere test case, we show that this adaptation, combined with hexahedral elements in the boundary layer, yields surface heating comparable to reference solutions. For the sphere-cone case with real-gas effects, the adapted mesh produces heating predictions that align with DPLR results, indicating that the relevant flow features, including those influenced by species gradients, are adequately resolved. To further address the concern, we will expand the discussion in the methods section to explain the rationale based on the physics of hypersonic real-gas flows and how the temperature field indirectly influences the resolution of entropy and species layers through the coupled solution. A full multi-sensor comparison would require additional simulations, which we consider beyond the current scope but could be noted as future work. revision: partial

Circularity Check

0 steps flagged

No circularity: direct numerical demonstration with external validation

full rationale

The paper is an application study that selects the temperature Hessian as the adaptation metric by direct statement, runs US3D simulations on two test cases, and reports surface-heating comparisons against independent block-structured DPLR results. No derivation chain exists that reduces a claimed prediction to a fitted parameter or self-citation; the method choice is presented as an input, the outcomes are measured quantities, and the complex-geometry capability is shown by explicit inclusion of RCS jets rather than by any self-referential uniqueness theorem. The central claim therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Abstract-only review prevents exhaustive identification; the central approach rests on choosing the temperature Hessian as adaptation metric, which may embed unstated scaling or threshold parameters.

free parameters (1)

Adaptation thresholds and scaling factors for Hessian metric
Metric-based adaptation typically requires user-specified or fitted parameters to control refinement levels; none are detailed in the abstract.

axioms (1)

domain assumption The Hessian of the temperature field is an appropriate error indicator for mesh adaptation in hypersonic real-gas aerothermal problems.
Explicitly stated in the abstract as the choice to dictate where the mesh needs refinement or coarsening.

pith-pipeline@v0.9.0 · 5531 in / 1390 out tokens · 55687 ms · 2026-05-10T03:00:10.015892+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

31 extracted references · 25 canonical work pages

[1]

Data-Parallel Line Relaxation Method for the Navier-Stokes Equations,

Wright, M., Candler, G., and Bose, D., “Data-Parallel Line Relaxation Method for the Navier-Stokes Equations,”AIAA Journal, Vol. 36, No. 9, 1998, pp. 1603–1609. https://doi.org/https://doi.org/10.2514/2.586

work page doi:10.2514/2.586 1998
[2]

Development of the US3D Code for Advanced Compressible and Reacting Flow Simulations,

Candler,G.V.,Johnson†,H.B.,Nompelis,I.,Subbareddy,P.K.,Drayna,T.W.,Gidzak,V.,andBarnhardt,M.D.,“Development of the US3D Code for Advanced Compressible and Reacting Flow Simulations,”AIAA SciTech Forum, AIAA 2015-1893, Kissimmee, Florida, US, 2015. https://doi.org/https://doi.org/10.2514/6.2015-1893

work page doi:10.2514/6.2015-1893 2015
[3]

Enablingmetric-basedmeshadaptationforadvancedcompressibleflowsimulationsusingUS3D,

Ekelschot,D.,andBrock,J.,“Enablingmetric-basedmeshadaptationforadvancedcompressibleflowsimulationsusingUS3D,” AIAA SciTech Forum, AIAA 2022-1866, San Diego, California, US, 2022. https://doi.org/https://doi.org/10.2514/6.2022-1866. 15

work page doi:10.2514/6.2022-1866 2022
[4]

Effect of anisotropic mesh adaptation on surface pressure predictions for atmospheric entry simulations

Ekelschot, D., and Brock, J., “Effect of anisotropic mesh adaptation on surface pressure predictions for atmospheric entry simulations.”International Conference in Computational Fluid Dynamics (ICCFD11), Isle of Maui, Hawaii, US, 2022. https://doi.org/https://www.iccfd.org/iccfd11/assets/pdf/papers/ICCFD11_Paper-0304.pdf

2022
[5]

Unstructured Grid Approaches for Accurate Aeroheating Simulations,

Candler, G. V., Barnhardt, M., Drayna, T. W., Nompelis, I., Peterson, D., and Subbareddy, P., “Unstructured Grid Approaches for Accurate Aeroheating Simulations,”18th AIAA Computational Fluid Dynamics Conference, AIAA Paper 2007-3959, Miami, Florida, US, 2007. https://doi.org/https://doi.org/10.2514/6.2007-3959

work page doi:10.2514/6.2007-3959 2007
[6]

Multi-Dimensional, Inviscid Flux Reconstruction for Simulation of Hypersonic Heating on Tetrahedral Grids,

Gnoffo, P., “Multi-Dimensional, Inviscid Flux Reconstruction for Simulation of Hypersonic Heating on Tetrahedral Grids,” AIAA Paper 2009-599, 2009. https://doi.org/https://doi.org/10.2514/6.2009-599

work page doi:10.2514/6.2009-599 2009
[7]

Economical Third-Order Methods for Accurate Surface Heating Predictions on Simplex Element Meshes

Thompson, K. B., Nishikawa, H., Padway, E., and O’Connell, M. D., “Economical Third-Order Methods for Accurate Surface Heating Predictions on Simplex Element Meshes.”AIAA SciTech Forum, AIAA 2023-2629, National Harbor, MD, 2023. https://doi.org/https://doi.org/10.2514/6.2023-2629

work page doi:10.2514/6.2023-2629 2023
[8]

Validation of the HyperSolve CFD Solver for Entry Descent and Landing Applications

K. B. Thompson, A. D. H. C. P., M. D. O’Connell, “Validation of the HyperSolve CFD Solver for Entry Descent and Landing Applications.”AIAA SciTech Forum, AIAA 2024-1973, Orlando, FL, 2024. https://doi.org/https://doi.org/10.2514/6.2024-1973

work page doi:10.2514/6.2024-1973 2024
[9]

Best Practices for Unstructured Grid Shock Fitting,

McCloud, P., “Best Practices for Unstructured Grid Shock Fitting,”AIAA SciTech Forum, Grapevine, TX, US, 2017. https://doi.org/https://doi.org/10.2514/6.2017-1149

work page doi:10.2514/6.2017-1149 2017
[10]

Rapid Hypersonic Simulations using US3D and Pointwise

Tang, C., “Rapid Hypersonic Simulations using US3D and Pointwise.”International Conference in Computational Fluid Dynamics (ICCFD11), Isle of Maui, Hawaii, US, 2022. https://doi.org/https://www.iccfd.org/iccfd11/assets/pdf/papers/ ICCFD11_Paper-3205.pdf

2022
[11]

Improved Heat Transfer Prediction for High-Speed Flows over Blunt Bodies using Adaptive Mixed-Element Unstructured Grids,

Nastac, G., Tramel, R., and Nielsen, E., “Improved Heat Transfer Prediction for High-Speed Flows over Blunt Bodies using Adaptive Mixed-Element Unstructured Grids,”AIAA SciTech Forum, AIAA 2022-0111, San Diego, California, US, 2022. https://doi.org/https://doi.org/10.2514/6.2022-0111

work page doi:10.2514/6.2022-0111 2022
[12]

Toward Adaptive Mixed-Element Unstructured Grids for Simulations of Viscous Flows,

Nastac, G., Miller, F., Schneider, D., Jacobson, K., Jones, W. T., and Opgenorth, M., “Toward Adaptive Mixed-Element Unstructured Grids for Simulations of Viscous Flows,”AIAA SciTech Forum, AIAA 2025-0642, Orlando, Florida, US, 2025. https://doi.org/https://doi.org/10.2514/6.2025-0642

work page doi:10.2514/6.2025-0642 2025
[13]

ImpactofAnisotropicMeshAdaptationontheAerothermodynamicsofAtmospheric Reentry,

Morgado,F.,Garbacz,C.,andFossati,M.,“ImpactofAnisotropicMeshAdaptationontheAerothermodynamicsofAtmospheric Reentry,”AIAA Journal, Vol. 60, No. 7, 2022, pp. 506–518. https://doi.org/https://doi.org/10.2514/1.J061071

work page doi:10.2514/1.j061071 2022
[14]

The minimal nilpotent orbit, the Joseph ideal, and differential opera- tors

Steger, J., and Warming, R., “Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods,”Journal of Computational Physics, Vol. 40, No. 2, 1981, pp. 263–293. https://doi.org/https://doi.org/10.1016/0021- 9991(81)90210-2

work page doi:10.1016/0021- 1981
[15]

A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows

Subbareddy, P., and Candler, G., “A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows,” Journal of Computational Physics, Vol. 228, 2009, pp. 1347 – 1364. https://doi.org/https://doi.org/10.1016/j.jcp.2008.10.026

work page doi:10.1016/j.jcp.2008.10.026 2009
[16]

A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities,

Schur, M., Spalart, P., Strelets, M., and A.K.Travin, “A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities,”International Journal of Heat and Fluid Flow, Vol. 29, 2008, pp. 1638–1649. https://doi.org/https: //doi.org/10.1016/j.ijheatfluidflow.2008.07.001

work page doi:10.1016/j.ijheatfluidflow.2008.07.001 2008
[17]

A 3D goal-oriented anisotropic mesh adaptation applied to inviscid flows in aeronautics,

Loseille, A., Dervieux, A., and Alauzet, F., “A 3D goal-oriented anisotropic mesh adaptation applied to inviscid flows in aeronautics,”48th AIAA aerospace sciences meeting including the new horizons forum and aerospace Exposition, AIAA 2010-1067, Orlando, Florida, US, 2010. https://doi.org/https://doi.org/10.1016/j.jcp.2009.12.021

work page doi:10.1016/j.jcp.2009.12.021 2010
[18]

Metric-orthogonal Anisotropic Mesh Generation,

Loseille, A., “Metric-orthogonal Anisotropic Mesh Generation,”Procedia Engineering, Vol. 82, No. Supplement C, 2014, pp. 403 – 415. https://doi.org/https://doi.org/10.1016/j.proeng.2014.10.400, 23rd International Meshing Roundtable (IMR23)

work page doi:10.1016/j.proeng.2014.10.400 2014
[19]

Aligned Metric-based Anisotropic Solution Adaptive Mesh Generation,

Marcum, D., and Alauzet, F., “Aligned Metric-based Anisotropic Solution Adaptive Mesh Generation,”Procedia Engineering, Vol. 82, 2014, pp. 428–444. https://doi.org/https://doi.org/10.1016/j.proeng.2014.10.402

work page doi:10.1016/j.proeng.2014.10.402 2014
[20]

Metric-Based Anisotropic Mesh Adaptation for Three-Dimensional Time-Dependent Problems Involving Moving Geometries,

Barral, N., Alauzet, F., and Loseille, A., “Metric-Based Anisotropic Mesh Adaptation for Three-Dimensional Time-Dependent Problems Involving Moving Geometries,”53rd AIAA Aerospace Sciences Meeting, AIAA 2015-2039, Kissimi, Florida, US,

2015
[21]

https://doi.org/https://doi.org/10.2514/6.2015-2039

work page doi:10.2514/6.2015-2039 2015
[22]

A decade of progress on anisotropic mesh adaptation for computational fluid dynamics,

Alauzet, F., and Loseille, A., “A decade of progress on anisotropic mesh adaptation for computational fluid dynamics,” Computer-Aided Design, Vol. 72, 2016, pp. 13–39. https://doi.org/https://doi.org/10.1016/j.cad.2015.09.005. 16

work page doi:10.1016/j.cad.2015.09.005 2016
[23]

Time-accurate Anisotropic Mesh Adaptation for Three-Dimensional Time-Dependent Problems with Body-Fitted Moving Geometries,

Barral, N., Olivier, G., and Alauzet, F., “Time-accurate Anisotropic Mesh Adaptation for Three-Dimensional Time-Dependent Problems with Body-Fitted Moving Geometries,”Journal of Computational Physics, Vol. 331, 2017, pp. 157–187. https://doi.org/10.1016/j.jcp.2016.11.029

work page doi:10.1016/j.jcp.2016.11.029 2017
[24]

Exploring Unstructured Mesh Adaptation for Hybrid Reynolds-Averaged Navier-Stokes/Large Eddy Simulation,

Park, M. A., Kleb, B., Anderson, W. K., Wood, S. L., Balan, A., Zhou, B. Y., and Gauger, N. R., “Exploring Unstructured Mesh Adaptation for Hybrid Reynolds-Averaged Navier-Stokes/Large Eddy Simulation,” AIAA Paper 2020–1139, 2020. https://doi.org/https://doi.org/10.2514/6.2020-1139

work page doi:10.2514/6.2020-1139 2020
[25]

AchievementofGlobalSecondOrderMeshConvergenceforDiscontinuous Flows with Adapted Unstructured Meshes,

Loseille,A.,Dervieux,A.,Frey,P.,andAlauzet,F.,“AchievementofGlobalSecondOrderMeshConvergenceforDiscontinuous Flows with Adapted Unstructured Meshes,”18th AIAA Computational Fluid Dynamics Conference, Miami, Florida, 2007. https://doi.org/https://doi.org/10.2514/6.2007-4186

work page doi:10.2514/6.2007-4186 2007
[26]

Continuous mesh framework Part 1: Well-posed continuous interpolation error,

Loseille, A., and Alauzet, F., “Continuous mesh framework Part 1: Well-posed continuous interpolation error,”SIAM Journal on Numerical Analysis, Vol. 49, No. 1, 2011, pp. 38–60. https://doi.org/https://www.jstor.org/stable/23074389

work page arXiv 2011
[27]

Continuous mesh framework Part 2: Validations and applications,

Loseille, A., and Alauzet, F., “Continuous mesh framework Part 2: Validations and applications,”SIAM Journal on Numerical Analysis, Vol. 49, No. 1, 2011, pp. 61–86. https://doi.org/https://www.jstor.org/stable/23074390

work page arXiv 2011
[28]

Parallel unstructured mesh adaptation using iterative remeshing and repartitioning,

L. Cirrottola, A. F., “Parallel unstructured mesh adaptation using iterative remeshing and repartitioning,” Tech. Rep. hal- 02386837, INRIA Bordeaux, équipe CARDAMOM, 2019. https://doi.org/https://inria.hal.science/hal-02386837/document

2019
[29]

Parallel Unstructured Mesh Adaptation Based on Iterative Remeshing and Repartitioning,

L. Cirrottola, A. F., “Parallel Unstructured Mesh Adaptation Based on Iterative Remeshing and Repartitioning,”WCCM- Eccomas 2020 - 14th World Congress on Computational Mechanics, Paris / Virtual, France, 2021. https://doi.org/https: //inria.hal.science/hal-03208569/document

2020
[30]

Anisotropic Delaunay mesh adaptation for unsteady simulations,

Dobrzynski, C., and Frey, P., “Anisotropic Delaunay mesh adaptation for unsteady simulations,”Procedia Engineering, 2008. https://doi.org/https://doi.org/10.1007/978-3-540-87921-3_11, 23rd International Meshing Roundtable (IMR17)

work page doi:10.1007/978-3-540-87921-3_11 2008
[31]

Pointwise,

Pointwise, Inc., “Pointwise,” , 2024. URL https://www.pointwise.com. 17

2024