5.1 New software

6.1 Numerical simulations on GPU with the GMlib v3.0 library

Participants: Loïc Maréchal [correspondant], Julien Vanharen.

The whole library was completely rewritten to implement an automatic finite-element shader generation that converts a simple user source code into an OpenCL source that is in compiled on the GPU at run time. The library handles all meshing data structures, from file reading, renumbering and vectorizing for efficient access on the GPU, and transfer to the graphic card, all automatically and transparently. With this framework, the user can focus on the calculation part of the code, known as kernel, as all the rest is taken care of by the library. The OpenCL language was chosen as it is hardware agnostic and runs on any GPU (Intel, Nvidia and AMD) and can also use the multicore and vector capacities of modern CPUs.

Julien Vanharen developed a basic heat solver using the v3.0 as a test case so we could validate the software with various boundary conditions, calculation scheme, unstructured meshes and different memory access patterns with success. Even with basic calculation which does not stress the full GPU's power, we achieved two orders of magnitude greater speed against a single CPU core and one order of magnitude compared to a multithreaded implementation.

6.2 High Order Meshing: from a straight mesh to a curved one

Participants: Loïc Maréchal [correspondant].

Works continued on P1toPk, a software that transform any first order hybrid mesh (triangles, quads, tets, pyramids, prisms and hexes) into a second order one while respecting a prescribe surface curvature. Efforts were made on boundary layers curving, which was challenging because jacobian validity is harder to guarantee as the elements get highly stretched, and a lot effort were also made to speed up the code by optimizing mathematical operations and parallelizing them. The code is now mature enough to be sent to industrial users for real life usage and we are waiting for valuable feedback in the present year.

6.3 Pixel-exact rendering for high-order meshes and solutions

Participants: Matthieu Maunoury [correspondant], Adrien Loseille.

We are developing ViZiR 4, a visualization software with pixel exact rendering to address the high-order visualization challenges 25, 15. ViZiR 4 is bundled as a light, simple and interactive high-order meshes and solutions visualization software. It is based on OpenGL 4 core graphic pipeline. The use of OpenGL Shading Language (GLSL) allows to perform pixel exact rendering of high order solutions on straight elements (without extra subdivision or ray casting) and almost pixel exact rendering on curved elements (high-order meshes). ViZiR 4 enables the representation of high order meshes (up to degree 4) and high order solutions (up to degree 10) with pixel exact rendering. Unlike other visualization software (ParaView 33, TecPlot 34, FieldView 35, Ensight 32, Medit 27, Vizir (OpenGL legacy based version) 37, Gmsh 31), there is no subdivision process that is expensive nor visualization error that has to be controlled. Moreover, the subdivision of the curved entities is done on the fly on GPU which leaves the RAM memory footprint at the size of the loaded mesh. Furthermore, in comparison with standard rendering techniques based on legacy OpenGL, the use of OpenGL 4 core version improves the speed of rendering, reduces the memory footprint and increases the flexibility. Many post-processing tools, such as picking, hidding surfaces, isolines, clipping, capping, are integrated to enable on the fly the analysis of the numerical results.

6.4 Fast high-order tetrahedral mesh correction and metric-based curving for P2 cavity remeshing

Participants: Lucien Rochery [correspondant], Adrien Loseille.

We aim to deal with three main topics around high-order mesh adaptation with applications to classic a posteriori curving.

One, a new method to untangle high-order Bézier meshes is introduced. It maximizes directly the minimum control coefficient over the mesh. Under some conditions, the $maxmin$ problem can be recast as a linear program, solvable exactly by specialized algorithms. The best possible position of an edge control point is obtained in as long as to compute and differentiate dependent control coefficients five times.

Two, Riemannian edge length minimization is used to prescribe metric-based mesh-interior curvature. This generalizes weakly the unit mesh definition on linear meshes, and is very fast as only edge scale problems are solved. Through metric gradation on surface metrics, surface curvature is naturally propagated to the interior by length minimization. Similarly, the mesh-intrinsic metric can be used to curve boundary layers. In realistic settings, a so-called back mesh holding the discrete metric field is kept unchanged throughout remeshing. This prevents anisotropy loss through repeated interpolation. It also leads to the metric at a point $P$ within an element $K$ being the result of two interpolations. First, at the control points of $K$ using the back mesh. Then, at $P$ using those. This metric at $P$ is differentiated, in order to provide derivatives of anisotropic geometric quantities.

Three, the cavity operator if extended to $P^2$ meshes. It rewrites topological changes (insertions, collapses, generalized swaps) as element deletions followed by point starring. The $P^2$ cavity operator is modular and distinguishes between two types of curvature: prescribed and necessary. Here, CAD/$P^3$ surrogate projection and Riemannian length minimization are used for the surface and interior respectively.

Necessary curvature results from subsequent high-order untangling, as prescribed curvature is not expected to yield valid cavities.

Numerical results focus on a posteriori curving of difficult cases. Boundary control points are projected. Metric-based curvature is used to propagate surface curvature, curve boundary layers, and follow natural curvature of a metric field resulting from CFD adaptation. The simplex-based Jacobian smoother corrects the resulting meshes. Examples are based on 3D real-world geometries encountered in Computational Fluid Dynamics (CFD). This framework allow us to curve highly anisotropic meshes with around 10 million elements within minutes.

6.5 Unstructured anisotropic mesh adaptation for 3D RANS turbomachinery applications

Participants: Frédéric Alauzet [correspondant], Adrien Loseille, Julien Vanharen.

We aim to demonstrate the viability and efficiency of unstructured anisotropic mesh adaptation techniques to turbomachinery applications. The main difficulty in turbomachinery is the periodicity of the domain that must be taken into account inthe solution mesh-adaptive process. The periodicity is strongly enforced in the flow solver using ghost cells to minimize the impact on the source code. For the mesh adaptation, the local remeshing is done in two steps. First, the inner domain is remeshed with frozen periodic frontiers, and, second, the periodic surfaces are remeshed after moving geometric entities from one side of the domain to the other. One of the main goal of this work is to demonstrate how mesh adaptation, thanks to its automation, is able to generate meshes that are extremely difficult to envision and almost impossible to generate manually. This study only considers feature-based error estimate based on the standard multi-scale Lp-interpolation error estimate. We presents all the specific modifications that have been introduced in the adaptive process to deal with periodic simulations used for turbomachinery applications. The periodic mesh adaptation strategy is then tested and validated on the LS89 high pressure axial turbine vane and the NASA Rotor 37 test cases.

6.6 Mixed-element mesh adaptation for CFD simulations

Participants: Frédéric Alauzet [correspondant], Julien Vanharen, Adrien Loseille, Cosimo Tarsia Morisco.

Due to their various nature, physical phenomena that we seek to capture in CFD simulations may have specific specific mesh requirements. For example, to solve the boundary layer, some numerical schemes favor structured meshes respecting alignment with the boundary of the domain, while these constraints are not necessary elsewhere. Our approach is to use the techniques of metric-based mesh adaptation to generate a mixed-element mesh that can fulfill these different mesh requirements. This approach is based on the metric-orthogonal point-placement, creating some structured parts from the intrinsic directional information bore by the metric-field. Some unstructured areas may remain where structure is not needed. The main goals of this work are to improve the orthogonality of the output mesh and its alignment with the metric field. This work has three main axes. First, we have improved the preprocessing gradation step to smooth the metric field and improve the orthogonality of the final mesh. Then, we have studied two methods to obtain quadrilaterals: one using an a priori quadrilaterals recombination, the other detecting straightforwardly the orthogonal patterns during the re-meshing step. Finally, the work on the solver Wolf has been carried on and corrected to perform robust and accurate simulations on mixed-element meshes. These three developments were embodied in a mixed-element adaptation loop. The first two topics are detailed in what follows.

6.7 Coupled flow and adjoint solver

Participants: Francesco Clerici [correspondant], Frédéric Alauzet.

When solving the RANS equations, usually one decouples the equations relative to the mean-flow and the equations relative to turbulence. This division provides two separated systems to be solved at each time step, one relative to the mean-flow and the other relative to the turbulence. This presents two main drawbacks: in the flow solver, the Jacobian of the system lacks of the terms bounding the mean-flow and the turbulence, and this can slow down the residual convergence. The second drawback regards the adjoint problem, which consists into a linear system assembled with the transpose of the Jacobian matrix of the residuals and, on the right-hand side, the derivative of an aeronautical coefficient with respect to the flow variables. A Jacobian missing the coupling terms between the mean-flow and the turbulence provides a null adjoint turbulent viscosity, and this is a limitation in the development of more complex discretization error estimates. We have therefore developed a 2D version of the coupled flow and adjoint solver which includes in the Jacobian the coupling terms between the mean-flow and the turbulence. When have tested this method on the 2D geometry provided for the 4th CFD AIAA High Lift Prediction Workshop, and the result provided several features to emerge, such as a high mesh refinement inside the boundary layer of the leading edges, and inside the regions of high turbulence destruction. The work is pursued in collaboration with Philippe Spalart (Boeing), and is presented in 24.

6.8 Turbulent error estimate

Participants: Francesco Clerici [correspondant], Frédéric Alauzet.

Goal-oriented mesh adaptation is a methodology used to adapt the mesh in order to minimize the discretization error commited on a functional depending on the solution. As an intermediate step, one finds an upper bound to such discretization error taking the form of a weighted sum of the interpolation errors of the solution, and such upper bound is called error estimate. Regarding Wolf and the RANS equations, up to now we have focused only on the mean-flow part of such an error estimate, meaning that the terms coming from turbulence have been neglected. The scope of this work is to enrich the error estimate with the information coming from the turbulence. In particular, the methodology has been tested on the 2D geometry provided for the 4th CFD AIAA High Lift Prediction Workshop, providing high mesh refinements on the boundaries of the turbulent regions. Also this work is pursued in collaboration with Philippe Spalart (Boeing), and is presented in 24.

7.1 Bilateral contracts with industry

Participants: Frédéric Alauzet [correspondant], Adrien Loseille.

• Safran Tech
• Ariane Group
• Lemma

8.1 European initiatives

9.1 Major publications

• 1 articleF.Frédéric Alauzet and A.Adrien Loseille. High Order Sonic Boom Modeling by Adaptive Methods.Journal Of Computational Physics2292010, 561-593URL: http://dx.doi.org/10.1016/j.jcp.2009.09.020
• 2 articleT.Tahar Amari, A.Aurélien Canou, J.-J.Jean-Jacques Aly, F.Francois Delyon and F.Frédéric Alauzet. Magnetic cage and rope as the key for solar eruptions.Nature5547691February 2018, 211 - 215
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• 3 unpublishedA.A. Belme, F.F. Alauzet and A.A. Dervieux. An a priori anisotropic Goal-Oriented Error Estimate for Viscous Compressible Flow and Application to Mesh Adaptation.November 2018, working paper or preprint
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• 4 bookH.Houman Borouchaki and P.-L.Paul-Louis George. Meshing, Geometric Modeling and Numerical Simulation 1.John Wiley & Sons, Inc.October 2017
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• 5 articleS.Stéphanie Chaillat, S. P.Samuel P Groth and A.Adrien Loseille. Metric-based anisotropic mesh adaptation for 3D acoustic boundary element methods.Journal of Computational Physics372November 2018, 473 - 499
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• 6 articleR.Rémi Feuillet, M.Matthieu Maunoury and A.Adrien Loseille. On pixel-exact rendering for high-order mesh and solution.Journal of Computational Physics424January 2021, 109860
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• 7 bookP. L.Paul Louis George, F.Frédéric Alauzet, A.Adrien Loseille and L.Loïc Maréchal. Meshing, Geometric Modeling and Numerical Simulation 3.1Wiley; WileyNovember 2020
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• 8 inbookP.-L.Paul-Louis George, H.Houman Borouchaki, P.-J.P.-J. Frey, P.Patrick Laug and E.E. Saltel. Mesh Generation and Mesh Adaptivity: Theories and Techniques.Encyclopedia of Computational Mechanics, Volume 1: FundamentalsISBN 0-470-84699-2, E. Stein, R. de Borst and T.J.R. Hughes ed., 2nd edition 2008Wiley InterScience2004, 17497-523
• 9 inproceedingsA.Adrien Loseille and F.Frédéric Alauzet. Optimal 3D Highly Anisotropic Mesh Adaptation based on the Continuous Mesh Framework.18th International meshing roundtableSalt-Lake City, UT, USASpringer2009, URL: http://dx.doi.org/10.1007/978-3-642-04319-2_20
• 10 articleA.Adrien Loseille, A.A. Dervieux and F.Frédéric Alauzet. Fully anisotropic goal-oriented mesh adaptation for 3D steady Euler equations.Journal Of Computational Physics2292010, 2866-2897URL: http://dx.doi.org/10.1016/j.jcp.2009.12.021
• 11 inproceedingsA.Adrien Loseille and R.Rémi Feuillet. Vizir: High-order mesh and solution visualization using OpenGL 4.0 graphic pipeline.2018 - AIAA Aerospace Sciences Meeting, AIAA SciTech Forumkissimmee, United StatesJanuary 2018, 1-13
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• 12 incollectionA.Adrien Loseille and R.Rainald Löhner. Robust Boundary Layer Mesh Generation.Proceedings of the 21st International Meshing RoundtableSpringer Berlin Heidelberg2012, 493-511
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• 13 inproceedingsE.Emmanuel Montreuil, W.Weeded Ghedhaifi, V.Vivien Chmielarski, V.Vuillot François, F.Fabien Gand and A.Adrien Loseille. Numerical Simulation of contrail formation on the Common Research Model wing/body/engine configuration.AIAA Aviation and Aeronautics Forum and Exposition 2018Atlanta, United StatesJune 2018
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9.2 Publications of the year

9.3 Cited publications

• 20 articleF.F. Alauzet and A.A. Loseille. A decade of progress on anisotropic mesh adaptation for Computational Fluid Dynamics.722016, 13-39
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• 21 articleF.F. Alauzet and A.A. Loseille. High Order Sonic Boom Modeling by Adaptive Methods.2292010, 561-593
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• 22 articleN.N. Barral, G.G. Olivier and F.F. Alauzet. Metric-based anisotropic mesh adaptation for three-dimensional time-dependent problems involving moving geometries.3312017, 157-187
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• 23 articleH.H. Borouchaki, P.P. Laug and P.P.L. George. Parametric surface meshing using a combined advancing-front -- generalized-Delaunay approach.International Journal for Numerical Methods in Engineering491-22000, 233-259
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• 24 articleF.F. Clerici, P.P. Spalart and F.F. Alauzet. Coupled adjoint solver and turbulent error estimate for anisotropic mesh adaptation in high-fidelity RANS simulations..AIAA J.2022
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• 25 articleR.Rémi Feuillet, M.Matthieu Maunoury and A.Adrien Loseille. On pixel-exact rendering for high-order mesh and solution.Journal of Computational Physics424January 2021, 109860
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• 26 inproceedingsP.P.J. Frey. About surface remeshing.Proceedings of the 9th international meshing roundtableNew Orleans, LO, USA2000, 123-136
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• 27 miscP. J.P. J. Frey. Medit: An interactive mesh visualization software, INRIA Technical Report RT0253.2001
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• 28 articleP. ..P .L. George and H.H. Borouchaki. Construction of tetrahedral meshes of degree two.International Journal for Numerical Methods in Engineering9092012, 1156,1182
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• 29 articleP.P.L. George and H.H. Borouchaki. ``Ultimate'' robustness in meshing an arbitrary polyhedron.5872003, 1061-1089
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• 30 articleP.P.L. George, F.F. Hecht and E.E. Saltel. Automatic mesh generator with specified boundary.921991, 269-288
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• 31 articleC.C. Geuzaine and J.-F.J.-F. Remacle. Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities.International Journal for Numerical Methods in Engineering79112009, 1309-1331
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• 32 miscA.Ansys Inc.. Ensight.
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• 33 miscK.KitWare Inc.. ParaView.
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• 34 miscT.TecPlot Inc.. TecPlot.
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• 35 miscI.Intelligent Light. FieldView.
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• 36 articleA.Adrien Loseille, F.Frédéric Alauzet and V.Victorien Menier. Unique cavity-based operator and hierarchical domain partitioning for fast parallel generation of anisotropic meshes.Computer-Aided Design852017, 53-67
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• 37 miscA.A. Loseille, H.H. Guillard and A.A. Loyer. An introduction to Vizir: an interactive mesh visualization and modification software.2016
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• 38 inproceedingsL.L. Maréchal. A new approach to octree-based hexahedral meshing.2001, 209--221
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• 39 inproceedingsL.L. Maréchal. Advances in Octree-Based All-Hexahedral Mesh Generation: Handling Sharp Features.18Salt Lake City, UT, USA2009, 65-84
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• 40 inproceedingsD.D.J. Mavriplis. Results from the 3rd Drag Prediction Workshop using NSU3D unstructured mesh solver.45AIAA-2007-0256, Reno, NV, USAJan 2007
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• 41 inproceedingsM.M. Park, J.J. Krakos, T.T.R. Michal, A.A. Loseille and J.J. Alonso. Unstructured Grid Adaptation: Status, Potential Impacts, and Recommended Investments Toward CFD Vision 2030.462016-3323, Washington, D.C., USA2016
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• 42 articleG.Guillaume Puigt, V.Valerie Auffray and J.-D.J-D Müller. Discretisation of diffusive fluxes on hybrid grids.Journal of Computational Physics22952010, 1425--1447
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• 43 articleC.C.L. Rumsey, J.J.P. Slotnick, M.M. Long, R.R.A. Stuever and T.T.R. Wayman. Summary of the first AIAA CFD High-Lift Prediction Workshop.Journal of Aircraft4862011, 2068-2079
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• 44 articleC.C.L. Rumsey and J.J.P. Slotnick. Overview and Summary of the Second AIAA High Lift Prediction Workshop.Journal of Aircraft5242015, 1006-1025
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• 45 techreportJ.J. Slotnick, A.A. Khodadoust, J.J. Alonso, D.D. Darmofal, W.W. Gropp, E.E. Lurie and D.D. Mavriplis. CFD Vision 2030 Study: A path to revolutionary computational aerosciences.NASAMarch 2014
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• 46 inproceedingsC.Cosimo Tarsia Morisco, L.-M.Lucille-Marie Tenkes and F.Frederic Alauzet. Extension of the Vertex-Centered Mixed-Element-Volume MUSCL scheme to mixed-element meshes.AIAA SCITECH 2023 Forum2023, 0832
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• 47 incollectionL.-M.Lucille-Marie Tenkes and F.Frédéric Alauzet. Size Gradation Control for Anisotropic Hybrid Meshes.Numerical Geometry, Grid Generation and Scientific Computing143Lecture Notes in Computational Science and EngineeringSpringer International PublishingMay 2021, 127-139
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• 48 inproceedingsL.-M.Lucille-Marie Tenkes, F.Frédéric Alauzet and J.Julien Vanharen. Hybrid anisotropic mesh adaptation using metric-orthogonal approach.AIAA Scitech 2021 ForumVirtual, United StatesAmerican Institute of Aeronautics and AstronauticsJanuary 2021
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