François Févotte

TriScale innov

The Richards equation is ubiquitous in the modelling of flows in porous media. It serves as a model in its own right, but also as a stepping stone to more complex models of multiphase flows. Despite its relative simplicity, it features many challenges from a computational point of view due to the nonsmooth and degenerate nature of the nonlinear sta...

We consider nonsmooth partial differential equations associated with a minimization of an energy functional. We adaptively regularize the nonsmooth nonlinearity so as to be able to apply the usual Newton linearization, which is not always possible otherwise. We apply the finite element method as a discretization. We focus on the choice of the regul...

Quantifying errors and losses due to the use of Floating-point (FP) calculations in industrial scientific computing codes is an important part of the Verification, Validation, and Uncertainty Quantification process. Stochastic Arithmetic is one way to model and estimate FP losses of accuracy, which scales well to large, industrial codes. It exists...

In this paper, we propose a new non-linear technique for accelerating the solution of the discrete ordinates transport equation. The new method, called Response Matrix Acceleration (RMA), has been designed to complement the Coarse-Mesh Finite Difference method (CMFD) by offering better stability and improved performance in cases where CMFD fails. T...

Goal-based error estimation due to spatial discretization and adaptive mesh refinement (AMR) has previously been investigated for the one dimensional, diamond difference, discrete ordinate (1-D DD-SN) method for discretizing the Neutron Transport Equation (NTE). This paper investigates the challenges of extending goal-based error estimation to mult...

In this paper, we propose a new non-linear technique for accelerating the solution of the discrete ordinates transport equation. The new method, called Response Matrix Acceleration (RMA), has been designed to complement the Coarse-Mesh Finite Difference method (CMFD) by offering better stability and improved performance in cases where CMFD fails. T...

In this paper we propose a new non-linear technique for accelerating the source iterations of the discrete-ordinates transport equation. The acceleration method, called Spatially Variant Rebalancing Method (SVRM), is based on the computation of the zeroth and first order spatial variation of the neutron balance equation. The non-linear acceleration...

In this paper, we propose a new non-linear technique for accelerating the source iterations of the discrete ordinates transport equation. The new method, called Response Matrix Acceleration (RMA), has been designed to complement the Coarse-Mesh Finite Difference method (CMFD) by offering better stability and improved performance in cases where CMFD...

This paper presents an efficient parallel method for the deterministic solution of the 3D stationary Boltzmann transport equation applied to diffusive problems such as nuclear core criticality computations. Based on standard MultiGroup-Sn-DD discretization schemes, our approach combines a highly efficient nested parallelization strategy with the PD...

This paper presents an efficient parallel method for the deterministic solution of the 3D stationary Boltzmann transport equation applied to diffusive problems such as nuclear core criticality computations. Based on standard MultiGroup-Sn-DD discretization schemes, our approach combines a highly efficient nested parallelization strategy with the PD...

The type length chosen for floating-point numbers (e.g. 32 bits or 64 bits) may have an impact on the execution time, especially on SIMD (Single Instruction Multiple Data) units. Furthermore optimizing the types used in a numerical simulation causes a reduction of the data volume that is possibly transferred. In this paper we present PROMISE, a too...

In this paper we propose a new non-linear technique for accelerating the source iterations of the discrete-ordinates transport equation. The acceleration method, called Spatially Variant Rebalancing Method (SVRM), is based on the computation of the zeroth and first order spatial variation of the neutron balance equation. The non-linear acceleration...

Floating-point computations play a central role in scientific computing. Achieving high numerical stability in these computations affects not just correctness, but also computing efficiency, by accelerating the convergence of iterative methods and expanding the available choices of precision. The ACTS project aims at establishing an experiment-agno...

Quantifying errors and losses due to the use of Floating-Point (FP) calculations in industrial scientific computing codes is an important part of the Verification, Validation and Uncertainty Quantification (VVUQ) process. Stochastic Arithmetic is one way to model and estimate FP losses of accuracy, which scales well to large, industrial codes. It e...

The method of discrete ordinates (Sn) is a popular choice for the solution of the neutron transport equation. It is however well known that it suffers from slow convergence of the scattering source in optically thick and diffusive media, such as pressurized water nuclear reactors (PWR). In reactor physics applications, the Sn method is thus often a...

This paper uses local dual weighted residual (DWR) error indicators to flag cells for goal-based refinement in a 1-D diamond difference (DD) discretisation of the discrete ordinate (SN) neutron transport equations. Goal-orientated adaptive mesh refinement (GO-AMR) aims to produce a mesh that is optimal for a given goal or QoI (Quantity of Interest)...

This paper presents an efficient parallel method for the deterministic solution of the 3D stationary Boltzmann transport equation applied to diffusive problems such as nuclear core criticality computations. Based on standard MultiGroup-Sn-DD discretization schemes, our approach combines a highly efficient nested parallelization strategy with the Pi...

The method of discrete ordinates (Sn) is a popular choice for the solution of the neutron transport equation. It is however well known that it suffers from slow convergence of the scattering source in optically thick and diffusive media, such as pressurized water nuclear reactors (PWR). In reactor physics applications, the Sn method is thus often a...

We present in this paper a process which is suitable for the complete analysis of the numerical quality of a large industrial scientific computing code. Random rounding, using the Verrou diagnostics tool, is first used to evaluate the numerical stability, and locate the origin of errors in the source code. Once a small code part is identified as un...

L’outil VERROU vise à faciliter le diagnostic et la correction des erreurs de calcul dans les outils de simulation industriels. Ces erreurs, dues aux propriétés de l’arithmétique flottante, peuvent être détectées et quantifiées grâce à l’Arithmétique en Arrondi Aléatoire (AAA). VERROU utilise cette arithmétique pour instrumenter les codes de calcul...

Verrou is a tool allowing to perform the numerical verification and help debugging industrial scientific codes. The numerical quality is assessed using Random Rounding, which can be seen as a variant of Monte Carlo Arithmetic or an asynchronous CESTAC method. Verrou leverages the power of the Valgrind platform to analyze the program in binary form:...

EDF has been developping a new calculation chain, ANDROMÈDE, to replace the current one, CASSIOPEE. This work has been underway for more than 10 years now, and among the different components, there is the neutronic core code COCAGNE, which is the subject of this paper. COCAGNE has state-of-the-art fux solvers, an efficient microscopic (isotopic) de...

The quantity of interest (QoI) associated with a solution of a partial differential equation (PDE) is not, in general, the solution itself, but a functional of the solution. Dual weighted residual (DWR) error estimators are one way of providing an estimate of the error in the QoI resulting from the discretisation of the PDE. This paper aims to prov...

As an industrial facility relying on numerical simulation to improve the safety and efficiency of its electricity production units, EDF is committed to ensure that all the numerical simulation codes it develops and uses are correctly validated and verified. Within this context, the accuracy of floating-point operations has progressively become one...

EDF développe et utilise un grand nombre d’applications utilisant la simulation numérique. Dans le cadre des processus de Validation & Vérification (V&V), EDF souhaite évaluer l’impact de l’arithmétique flottante sur la qualité des résultats fournis. Parmi les outils existants, CADNA implémentant l’arithmétique stochastique discrète permet d’audite...

EDF/R&D is developing a new calculation scheme based on the simplified transport (SPn) approach. The lattice code used is the deterministic code APOLLO2, developed at CEA with the support of EDF and AREVA-NP. The core code is the code COCAGNE, developed at EDF R&D. The latter can take advantage of a microscopic depletion solver which improves the t...

Large scale tri-dimensional transport calculations in unstructured meshes are limited in scale mostly by the amountof data to process (memory space limitations), the number of operations to perform (computational time limitations), or both. A method relying on a prismatic projection of non-uniform 3-D geometries is proposed, that reduces both memor...

The past few years have been marked by a noticeable increase in the interest in 3D whole-core heterogeneous deterministic neutron transport solvers for reference calculations. Due to the extremely large problem sizes tackled by such solvers, they need to use adapted numerical methods and need to be efficiently implemented to take advantage of the f...

As part of its activity, EDF R&D is developing a new nuclear core simulation code named COCAGNE. This code relies on DIABOLO, a Simplified PN (SP N ) method to compute the neutron flux inside the core for keff eigenvalue problems. In order to complete complex simulations involving a large number of suc- cessive eigenvalue calculations within accept...

The large increase in computing power over the past few years now makes it possible to consider developing 3D full-core heterogeneous deterministic neutron transport solvers for reference calculations. Among all approaches presented in the literature, the method first introduced in [1] seems very promising. It consists in iterating over resolutions...

Possible hindering effects of impurities on the crystal growth were shown to take place because of the adsorption of impurity species on the crystal surface. Transient features of this adsorption were observed, such that the growth of a given crystal does not depend on supersaturation only, but also on the time a given particle spent in contact wit...

For obvious industrial and theoretical reasons the problem of accounting for the effect of impurities in the population balance modelling of solution crystallization processes is a very important issue, and yet it has never been reported until today. Meanwhile, several kinetic models are proposed in the literature that relate the effect of impuriti...

In this paper we present the last improvements of the recently proposed linear surface (LS) characteristics scheme for unstructured meshes. First we introduce a new numerical tracking technique, specifically adapted to the LS method, which tailors transverse integration weights to take into account the geometrical discontinuities that appear along...

In the past years, the Method of Characteristics (MOC) has become a popular tool for the numerical solution of the neutron transport equation. Among its most interesting advantages are its good precision over computing time ratio, as well as its ability to accurately describe complicated geometries using non structured meshes. In order to reduce th...

Parmi les différentes méthodes de résolution numérique de l'équation du transport des neutrons, la méthode des caractéristiques est actuellement l'une des plus employées pour les calculs industriels. Elle permet en effet d'obtenir un bon rapport entre précision et temps de calcul, tout en facilitant la description précise de géométries complexes gr...

A technique has been developed, allowing the reduction of the storage size requirements for the tracking in the method of characteristics on periodic lattices. This technique takes advantage of repetitions and symmetries in the geometry to compute and store only few minimal tracking data, which can later be fetched and recombined on-the-fly during...

A novel technique for a better computation of transmission probabilities has been developed for the method of characteristics in unstructured meshes (MOC). This technique relies on a transverse quadrature that properly accounts for discontinuities along trajectories, without penalizing the transverse step, and on the use of a Taylor expansion for t...

A systematic study of a multi-dimensional model or particle dynamics in a granulation process is detailed. The model accounts for three controlled variables: distributions in particle size, moisture composition, and porosity. Controllability insights are obtained from sensitivity studies involving the properties of the manipulated input: binder add...