An updated list of publications can be found on my Google Scholar page.
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Papers
[1] J. Wallwork, N. Barral, D. Ham and M. Piggott,
Goal-Oriented Error Estimation and Mesh Adaptation for Tracer Transport Modelling ,
Computer-Aided Design, 2022.
Abstract>
This paper applies metric-based mesh adaptation methods to advection-dominated tracer transport modelling problems in two and three dimensions, using the finite element package Firedrake. In particular, the mesh adaptation methods considered are built upon goal-oriented estimates for the error incurred in evaluating a diagnostic quantity of interest (QoI). In the motivating example of modelling to support desalination plant outfall design, such a QoI could be the salinity at the plant inlet, which could be negatively impacted by the transport of brine from the plant’s outfall. Four approaches are considered, one of which yields isotropic meshes. The focus on advection-dominated problems means that flows are often anisotropic; thus, three anisotropic approaches are also considered. Meshes resulting from each of the four approaches yield solutions to the tracer transport problem which give better approximations to QoI values than uniform meshing, for a given mesh size. The methodology is validated using an existing 2D tracer transport test case with a known analytical solution. Goal-oriented meshes for an idealised time-dependent desalination outfall scenario are also presented.
[2] J. Wallwork, N. Barral, S. Kramer, D. Ham, M. Piggott,
Goal-oriented error estimation and mesh adaptation for shallow water modelling,
SN Applied Science, 2020.
[PDF]
Abstract>
This study presents a novel goal-oriented error estimate for the nonlinear shallow water equations solved using a mixed discontinuous/continuous Galerkin approach. This error estimator takes account of the discontinuities in the discrete solution and is used to drive two metric-based mesh adaptation algorithms: one which yields isotropic meshes and another which yields anisotropic meshes. An implementation of these goal-oriented mesh adaptation algorithms is described, including a method for approximating the adjoint error term which arises in the error estimate. Results are presented for simulations of two model tidal farm configurations computed using the Thetis coastal ocean model (Kärnä et al. in Geosci Model Dev 11(11):4359–4382, 2018). Convergence analysis indicates that meshes resulting from the goal-oriented adaptation strategies permit accurate QoI estimation using fewer computational resources than uniform refinement.
[3] M. Galbraith, P. Caplan, H. Carson, M. Park, A. Balan, W. Anderson, T. Michal, J. Krakos, D. Kamenetskiy, A. Loseille, F. Alauzet, L. Frazza, N. Barral
Verification of Unstructured Grid Adaptation Components,
AIAA Journal, 2020.
[PDF]
Abstract>
Unstructured grid techniques have the potential of minimizing discretization errors for production analysis workflows where the control of errors is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Here, the interoperability of several separately developed unstructured grid adaptation tools is verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. While optimal asymptotic error convergence rates are achieved with many grid adaptation tool combinations for the scalar problems, the scalar problems also illustrate known differences in grid adaptation component implementations and a previously unknown interaction between components. Laminar flow over a delta wing is verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and pitching moment. These verification efforts form the nucleus of a benchmark to verify the integration of unstructured grad adaptation components and support production analysis workflows.
[4] N. Barral and F. Alauzet,
Three-dimensional CFD simulations with large displacement of the geometries using a connectivity-change moving mesh approach, Engineering with Computers, 2018.
[PDF]
Abstract>
This paper deals with three-dimensional (3D) numerical simulations involving 3D moving geometries with large displacements on unstructured meshes. Such simulations are of great value to industry, but remain very time-consuming. A robust moving mesh algorithm coupling an elasticity-like mesh deformation solution and mesh optimizations was proposed in previous works, which removes the need for global remeshing when performing large displacements. The optimizations, and in particular generalized edge/face swapping, preserve the initial quality of the mesh throughout the simulation. We propose to integrate an Arbitrary Lagrangian Eulerian compressible flow solver into this process to demonstrate its capabilities in a full CFD computation context. This solver relies on a local enforcement of the discrete geometric conservation law to preserve the order of accuracy of the time integration. The displacement of the geometries is either imposed, or driven by fluid–structure interaction (FSI). In the latter case, the six degrees of freedom approach for rigid bodies is considered. Finally, several 3D imposed-motion and FSI examples are given to validate the proposed approach, both in academic and industrial configurations.
[5] N. Barral, G. Olivier and F. Alauzet,
Time-accurate anisotropic mesh adaptation for three-dimensional time-dependent problems with body-fitted moving geometries, Journal of Computational Physics, 2017.
[PDF]
Abstract>
Anisotropic metric-based mesh adaptation has proved its efficiency to reduce the CPU time of steady and unsteady simulations while improving their accuracy. However, its extension to time-dependent problems with body-fitted moving geometries is far from straightforward. This paper establishes a well-founded framework for multiscale mesh adaptation of unsteady problems with moving boundaries. This framework is based on a novel space–time analysis of the interpolation error, within the continuous mesh theory. An optimal metric field, called ALE metric field, is derived, which takes into account the movement of the mesh during the adaptation. Based on this analysis, the global fixed-point adaptation algorithm for time-dependent simulations is extended to moving boundary problems, within the range of body-fitted moving meshes and ALE simulations. Finally, three dimensional adaptive simulations with moving boundaries are presented to validate the proposed approach.
[6] P.L. George, H. Borouchaki and N. Barral,
Geometric validity (positive jacobian) of high-order Lagrange finite elements, theory and practical guidance
Engineering with computers, 2016.
[PDF]
Abstract>
Finite elements of degree two or more are needed to solve various P.D.E. problems. This paper discusses a method to validate such meshes for the case of the usual Lagrange elements of various degrees. The first section of this paper comes back to Bézier curve and Bézier patches of arbitrary degree. The way in which a Bézier patch and a finite element are related is recalled. The usual Lagrange finite elements of various degrees are discussed, including simplices (triangle and tetrahedron), quads, prisms (pentahedron), pyramids and hexes together with some low-degree Serendipity elements. A validity condition, the positivity of the jacobian, is exhibited for these elements. Elements of various degrees are envisaged also including some “linear” elements (therefore straight-sided elements of degree 1) because the jacobian (polynomial) of some of them is not totally trivial.
Preprints
[1] J. Wallwork, A. Angeloudis, N. Barral, L. Mackie, S. Kramer and M. Piggott,
Tidal Turbine Array Modelling using Goal-Oriented Mesh Adaptation,
submitted to Journal of Ocean Engineering and Marine Energy.
[PDF]
Abstract>
Purpose: To examine the accuracy and sensitivity of tidal array performance assessment by numerical techniques applying goal-oriented mesh adaptation.
Methods: The goal-oriented framework is designed to give rise to adaptive meshes upon which a given diagnostic quantity of interest (QoI) can be accurately captured, whilst maintaining a low overall computational cost. We seek to improve the accuracy of the discontinuous Galerkin method applied to a depth-averaged shallow water model of a tidal energy farm, where turbines are represented using a drag parametrisation and the energy output is specified as the QoI. Two goal-oriented adaptation strategies are considered, which give rise to meshes with isotropic and anisotropic elements.
Results: We present both fixed mesh and goal-oriented adaptive mesh simulations for an established test case involving an idealised tidal turbine array positioned in a channel. With both the fixed meshes and the goal-oriented methodologies, we reproduce results from the literature which demonstrate how a staggered array configuration extracts more energy than an aligned array. We also make detailed qualitative and quantitative comparisons between the fixed mesh and adaptive outputs.
Conclusion: The proposed goal-oriented mesh adaptation strategies are validated for the purposes of tidal energy resource assessment. Using 10% as many degrees of freedom as a high resolution fixed mesh benchmark, they are shown to enable energy output differences smaller than 10%. Applied to a tidal array with aligned rows of turbines, the anisotropic adaptation scheme is shown to yield differences smaller than 1%.
[2] J. Wallwork, L. Mackie, S. Kramer, N. Barral, A. Angeloudis and M. Piggott,
Goal-Oriented Metric-Based Mesh Adaptive Tidal Farm Modelling,
IX Conference on Computational Methods in Marine Engineering
(MARINE 2021), 2021.
[PDF]
Abstract>
The modelling of a tidal array farm is an inherently multi-scale endeavour. It requires the simultaneous resolution of tidal processes across tens or hundreds of kilometres of coastal ocean (including estuaries, or even entire seas), the hydrodynamics in the neighbourhood of the farm (hundreds of metres), the wakes of individual turbines (metres, or tens of metres) and device hydrodynamics (sub-metre). As such, the construction of an accurate, computationally efficient numerical model requires careful consideration of the underlying discretisation. In this paper, we apply time-dependent mesh adaptation techniques based on the Riemannian metric framework to an idealised tidal array and assess the quality of the resulting approximations. Whilst classical hierarchical mesh adaptation methods modify mesh element/cell size in order to improve resolution locally, the metric-based approach also allows for control of element shape and orientation, which can be especially advantageous for advection-dominated problems. Metrics are normalised in such a way that the resulting discretisation is multi-scale in both space and time as per Alauzet and Olivier (2010). Typically, metrics are constructed from recovered derivatives of solution fields, such as fluid vorticity. Alternatively, metrics may be derived from goal-oriented error estimates, enabling accurate estimation of a diagnostic quantity of interest (QoI). In the context of tidal farm modelling, one clear QoI is the power output. Building upon the idealised steady-state test case considered in Wallwork et al. (2020), which represents turbines using a drag parametrisation in a depth-averaged shallow water model, we demonstrate here that goal-oriented mesh adaptation can be used to obtain an accurate approximation of tidal farm power output using relatively few overall degrees of freedom.
[3] N. Barral, M.G. Knepley, M. Lange, M.D. Piggott and G.J. Gorman,
Anisotropic mesh adaptation in Firedrake with PETSc DMPlex,
25th International Meshing Roundtable, Washington DC, USA, September 2016.
[PDF]
Abstract>
Despite decades of research in this area, mesh adaptation capabilities are still rarely found in numerical simulation software. Wepostulate that the primary reason for this is lack of usability. Integrating mesh adaptation into existing software is difficult as non-trivial operators, such as error metrics and interpolation operators, are required, and integrating available adaptive remeshers is notstraightforward. Our approach presented here is to first integrate Pragmatic, an anisotropic mesh adaptation library, into DMPlex, aPETSc object that manages unstructured meshes and their interactions with PETSc’s solvers and I/O routines. As PETSc is alreadywidely used, this will make anisotropic mesh adaptation available to a much larger community. As a demonstration of this wedescribe the integration of anisotropic mesh adaptation into Firedrake, an automated Finite Element based system for the portablesolution of partial differential equations which already uses PETSc solvers and I/O via DMPlex. We present a proof of concept ofthis integration with a three-dimensional advection test case.
[4] P.L. George, H. Borouchaki and N. Barral,
Construction and geometric validity (positive Jacobian) of serendipity Lagrange finite elements, theory and practical guidance,
to be published.
[preprint]
Abstract>
Finite elements of degree two or more are needed to solve various P.D.E. problems. This paper discusses a method to validate such meshes for the case of the serendipity Lagrange elements of various degree. The first section of this paper comes back to Bézier curve and Bézier patches of arbitrary degree. The way in which a Bézier patch and a complete finite element are related is recalled. The construction of serendipity or reduced Lagrange finite elements of various degree is discussed, including simplices (triangle and tetrahedron), quads, prisms (pentahedron), pyramids and hexes. The validity condition, the positivity of the jacobian, exhibited for the classical (complete) elements is used to validate their serendipity counterparts after having invented a complete element equivalent to the reduced element under analyse.
Proceedings with peer-review
[1] M. Park, A. Balan, W. Anderson, M. Galbraith, P. Caplan, H. Carson, T. Michal, J. Krakos, D. Kamenetskiy, A. Loseille, F. Alauzet, L. Frazza, and N. Barral,
Verification of Unstructured Grid Adaptation Components,
AIAA Scitech 2019 Forum, AIAA Paper 2019-1723, San Diego, CA, USA, Jan 2019.
[PDF]
Abstract>
Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. Laminar flow over a delta wing and turbulent flow over an ONERA M6 wing are verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and a moment. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. The wing adaptation cases in the current study document a clear improvement to existing grid adaptation procedures. The stage is set for the infusion of verified grid adaptation into production fluid flow simulations.
[2] M. Park, N. Barral, D. Ibanez, D. Kamenetskiy, J. Krakos, T. Michal and A. Loseille,
Unstructured Grid Adaptation and Solver Technology for Turbulent Flows,
56th AIAA Aerospace Sciences Meeting, AIAA Paper 2018-1103, Kissimmee, FL, USA, Jan 2018.
[PDF]
Abstract>
Unstructured grid adaptation is a tool to control Computational Fluid Dynamics (CFD) discretization error. However, adaptive grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Issues that prevent the use of adaptive grid methods are identified by applying unstructured grid adaptation methods to a series of benchmark cases. Once identified, these challenges to existing adaptive workflows can be addressed. Unstructured grid adaptation is evaluated for test cases described on the Turbulence Modeling Resource (TMR) website, which documents uniform grid refinement of multiple schemes. The cases are turbulent flow over a Hemisphere Cylinder and an ONERA M6 Wing. Adaptive grid force and moment trajectories are shown for three integrated grid adaptation processes with Mach interpolation control and output error based metrics. The integrated grid adaptation process with a finite element (FE) discretization produced results consistent with uniform grid refinement of fixed grids. The integrated grid adaptation processes with finite volume schemes were slower to converge to the reference solution than the FE method. Metric conformity is documented on grid/metric snapshots for five grid adaptation mechanics implementations. These tools produce anisotropic boundary conforming grids requested by the adaptation process.
[3] D. Ibanez, N. Barral, J. Krakos, A. Loseille, T. Michal and M. Park,
First Benchmark of the Unstructured Grid Adaptation Working Group,
Proc. of the 26th International Meshing Roundtable, Procedia Engineering, vol 203, pp. 154-166, Washington DC, USA, 2017.
[PDF]
Abstract>
Unstructured grid adaptation is a technology that holds the potential to improve the automation and accuracy of computational fluid dynamics and other computational disciplines. Difficulty producing the highly anisotropic elements necessary for simulation on complex curved geometries that satisfies a resolution request has limited this technology’s widespread adoption. The Unstructured Grid Adaptation Working Group is an open gathering of researchers working on adapting simplicial meshes to conform to a metric field. Current members span a wide range of institutions including academia, industry, and national laboratories. The purpose of this group is to create a common basis for understanding and improving mesh adaptation. We present our first major contribution: a common set of benchmark cases, including input meshes and analytic metric specifications, that are publicly available to be used for evaluating any mesh adaptation code. We also present the results of several existing codes on these benchmark cases, to illustrate their utility in identifying key challenges common to all codes and important differences between available codes. Future directions are defined to expand this benchmark to mature the technology necessary to impact practical simulation workflows.
[4] N. Barral,F. Alauzet and A. Loseille,
Metric-Based Anisotropic Mesh Adaptation for Three-Dimensional Time-Dependent Problems Involving Moving Geometries,
AIAA SciTech 2015, Kissimee, FL, USA, January 2015.
Abstract>
Anisotropic metric based mesh adaptation has proved its efficiency to reduce the CPU time of
steady simulations while improving their accuracy. However its extension to time-dependent
problems is far from straightforward, and the introduction of moving meshes adds new problems.
This paper presents updates regarding mesh adaptation for unsteady problems with moving boundaries.
A new space-time analysis of the interpolation error in the continuous mesh framework is proposed,
which enables enhancements of the fixed- point unsteady mesh adaptation algorithm. The analysis is
then extended to the case of moving geometries, within the range of body-fitted moving meshes and
ALE simulations, and the appropriate modifications are made to the adaptation algorithm. Finally,
three dimensional adaptative simulations with moving boundaries are exhibited to validate our
approach.
[5] N. Barral, E. Luke and F. Alauzet,
Two mesh deformation methods coupled with a changing-connectivity moving mesh method for CFD Applications,
23th International Meshing Roundtable, London, October 2014.
[PDF]
Abstract>
Three-dimensional real-life simulations are generally unsteady and involve moving geometries.
Industry is currently very far from performing such body-fitted simulations on a daily basis,
mainly due to the robustness of the moving mesh algorithm and their extensive computational
cost. A moving mesh algorithm coupled to local mesh optimizations has proved its efficiency
in dealing with large deformation of the mesh without re-meshing. In this paper, the coupling
of this algorithm with two mesh deformation techniques is studied: an elasticity PDE-based one
and an explicit Inverse Distance Weighted interpolation one, and both techniques are compared.
The efficiency of this method is demonstrated on challenging test cases, involving large body
deformations, boundary layers and large displacements with shearing. Finally, the moving mesh
algorithm is coupled to a CFD flow solver.
[6] N. Barral and F. Alauzet,
Large displacement body-fitted FSI simulations using a mesh-connectivity-change moving mesh strategy,
AIAA Aviation 2014, Atlanta, GA, USA, June 2014.
Abstract>
This paper deals with numerical simulations involving three-dimensional moving
geometries with large displacements. Such simulations are much valued by industries,
but remain very time-consuming. A robust moving mesh algorithm coupling an elasticity-like
mesh deformation solution and mesh optimizations is proposed, that allows to avoid
remeshing while performing large displacements. However, this is done at the cost of
relaxing the fixed-topology constraint imposed by the classical
Arbitrary-Lagrangian-Eulerian (ALE) framework. An ALE compressible flow solver is
integrated to this process. This solver lies on the strict interpretation of the
Discrete Geometrical Conservation Law to preserve the order of accuracy of the time
integration. For fluid-structure interaction (FSI) simulations, the
six degrees of freedom (6-DOF) approach for rigid bodies is considered. Finally,
3D imposed-motion and FSI examples are given, to validate the proposed approach.
Communications
[1] N. Barral, A. Angeloudis, S. Kramer, G. Gorman and M. Piggott,
Tidal power plant modelling using anisotropic mesh adaptation in Thetis,
Firedrake '18: The Firedrake user and developer workshop, London, UK, 2018.
[2] N. Barral, A. Angeloudis, S. Kramer, G. Gorman and M. Piggott,
An anisotropic mesh adaptation approach for regional tidal energy hydrodynamics modelling,
EGU, Vienna, Austria, 2018.
[3] N. Barral, M.G. Knepley, M. Lange, M.D. Piggott and G.J. Gorman,
Anisotropic mesh adaptation in Firedrake,
Firedrake '17: The Firedrake user and developer workshop, London, UK, 2017.
[4] N. Barral, M. Knepley, M. Lange, M. Piggott and G. Gorman,
Parallel anisotropic mesh adaptation with DMPlex and Pragmatic
ADMOS 2017, Verbania, Italy, June 2017.
[5] N. Barral and M. Knepley,
Anisotropic mesh adaptation in DMPlex,
PETSc users meeting, Boulder, CO, USA, 2017.
[6] N. Barral, M.G. Knepley, M. Lange, M.D. Piggott and G.J. Gorman,
Anisotropic mesh adaptation in Firedrake with PETSc DMPlex,
25th International Meshing Roundtable, Washington DC, USA, September 2016.
[7] N. Barral and F. Alauzet,
Anisotropic error estimates for adapted dynamic meshes,
ADMOS 2015, Nantes, France, June 2015.
[8] N. Barral,F. Alauzet and A. Loseille,
Metric-Based Anisotropic Mesh Adaptation for Three-Dimensional Time-Dependent Problems Involving Moving Geometries,
AIAA SciTech 2015, Kissimee, FL, USA, January 2015.
[9] N. Barral, E. Luke and F. Alauzet,
Two mesh deformation methods coupled with a changing-connectivity moving mesh method for CFD Applications,
23th International Meshing Roundtable, London, UK, October 2014.
[10] N. Barral and F. Alauzet,
Large displacement simulations with an efficient mesh-connectivity-change moving mesh strategy,
ECCOMAS 2014, Barcelona, Spain, July 2014.
[11] N. Barral and F. Alauzet,
Parallel time-accurate anisotropic mesh adaptation for time-dependent problems,
ECCOMAS 2014, Barcelona, Spain, July 2014.
[12] N. Barral and F. Alauzet,
Large displacement body-fitted FSI simulations using a mesh-connectivity-change moving mesh strategy,
AIAA Aviation 2014, Atlanta, GA, USA, June 2014.
Research reports
[1] T. McManus, J. Percival, B. Yeager, N. Barral G. Gorman and M. Piggott
Moving mesh methods in Fluidity and Firedrake,
Archer report eCSE06-1, 2017.
[PDF]
[2] P.L George, H. Borouchaki and N. Barral, Construction et validation des éléments Serendip associés à un carreau de degré arbitraire, INRIA RR-8572, 2014.
[PDF]
[3] P.L George, H. Borouchaki and N. Barral, Construction et validation des éléments réduits associés à un carreau simplicial de degré arbitraire, INRIA RR-8571, 2014.
[PDF]
Talks and seminars
[1] Framework pour des simulations côtières avec adaptation de maillage anisotrope,
Rencontres MathOcéan, Bordeaux, Janvier 2019
[2] Adaptation de maillage anisotrope pour simulations instationnaires,
Séminaire Calcul Scientifique et Modélisation, Institut Mathématique de Bordeaux, Bordeaux, Octobre 2018
[3] Time-accurate anisotropic mesh adaptation for three-dimensional moving mesh problems,
AMCG Seminar, Imperial College, London, December 2015.
[4] Adaptation de maillages non structurés pour des problèmes instationnaires, et maillage en géométrie mobile,
Groupe de travail "Analyse Numérique et EDP", Ecole Centrale Paris, November 2014
Vulgarisation
[1] P.L. George and N. Barral,
Du réel au numérique : la science des maillages,
Pint of Science, Paris, May 2015
Theses
[1] N. Barral,
Time-accurate anisotropic mesh adaptation for three-dimensional moving mesh problems,
PhD Thesis, Université Pierre et Marie Curie, 2015.
[pdf]
Abstract>
Time dependent simulations are still a challenge for industry, notably due to prob- lems raised by moving boundaries, both in terms of CPU cost and accuracy. This thesis presents contributions to several aspects of simulations with moving meshes. A moving-mesh algorithm based on a large deformation time step and connectivity changes (swaps) is studied. An elastic- ity method and an Inverse Distance Weighted interpolation method are compared on many 3D examples, demonstrating the efficiency of the algorithm in handling large geometry displace- ment without remeshing. This algorithm is coupled with an Arbitrary-Lagrangian-Eulerian (ALE) solver, whose schemes and implementation in 3D are described in details. A linear in- terpolation scheme is used to handle swaps. Validation test cases showed that the use of swaps does not impact notably the accuracy of the solution, while several other complex 3D examples demonstrate the capabilities of the approach both with imposed motion and Fluid-Structure Interaction problems. Metric-based mesh adaptation has proved its efficiency in improving the accuracy of steady simulation at a reasonable cost. We consider the extension of these methods to unsteady problems, updating the previous fixed-point algorithm thanks to a new space-time error analysis based on the continuous mesh model. An efficient p-thread parallelization enables running 3D unsteady adaptative simulations with a new level of accuracy. This algorithm is extended to moving mesh problems, notably by correcting the optimal unsteady metric. Fi- nally several 3D examples of adaptative moving mesh simulations are exhibited, that prove our concept by improving notably the accuracy of the solution for a reasonable time cost.
[2] N. Barral,
Adaptation de maillages en régime instationnaire (Mesh adaptation for unsteady flows),
Masters Thesis, Ecole Centrale Paris, 2012.
[pdf]
Abstract>
Numerical simulation is currently broadly used in the world of engineering. Computation power and time
remain one of the main problematics, that limitate the scope of the simulations. Mesh adaptation aims
at answering this problem, thanks to a hudge increase of the precision of a com- putation, for a fixed
number of mesh vertices. Mesh adaptation for steady problems has become mature, however mesh adapation
for unsteady flows remains a challenge, from a theoretical point of view as well as practical. The
objective of this internship was the analysis of several variants of the unsteady mesh adaptation
algorithm designed in the Gamma team, at INRIA. This algorithm is based on the splitting of a simulation
interval into several sub-intervals, on which the solution does not evolve "too much", so that the same
adapted mesh can be considered on each sub-interval. The metric field, on which the generation of the
adapted meshes is based, is computed as an average of the instant metric fields along the sub-interval.
We have studied the several state-of-the art variants of the algorithm, re-doing the calculations that
lead to them. Then we have numerically compared two of these versions, in which the average metric fields
are computed differently, running a lot of simulations a several reprensentative test cases. We have
concluded that the l1 provides better results.
In parallel to this work, we have carried out a pre-study on the moving mesh of an engine, for the INP
Énergies Nouvelles. We have prepared a mesh IFP had transmitted to us, and validated the movement of its
surface.
We also have carried on the implementatio on GPU of our home CFD solver. We have improved our previous
implementation, and multiplied our acceleration factor by 5.
Awards
[1] IMR Meshing Contest Award,
23th International Meshing Roundtable, London, October 2014.
