Qualification des logiciels numériques. Application à un logiciel d'analyse de la combustion dans les moteurs à allumage commandé Qualification of Numerical Software. Application to a Software for Analysing Combustion in Spark-Ignition Engines

La simulation numérique est actuellement très utilisée pour étudier les systèmes physiques. Elle nécessite un programme de calcul scientifique constitué d'un modèle mathématique représentatif du problème étudié et des méthodes numériques de résolution associées. Elle fournit des résultats numériques censés représenter le phénomène physique. Pour pouvoir valider la simulation, il est absolument indispensable, d'une part, d'estimer la propagation des erreurs d'arrondi due à l'arithmétique approchée des ordinateurs et, d'autre part, d'évaluer l'influence des erreurs de données sur les résultats fournis. Nous présentons, dans cet article, le logiciel CADNA qui permet de valider les logiciels numériques. Nous l'appliquons à un logiciel de simulation d'analyse de la combustion dans les moteurs à allumage commandé et en montrons son efficacité. For analyzing physical phenomena, numerical simulation is used more and more frequently. Starting with a mathematical model describing the phenomenon being analyzed, this simulation consists in creating a scientific computing program expressing this model by implementing the numerical methods required for solving it. Simulation is considered to be valid when the results its provides are in agreement with the results issuing from experimenting with the phenomenon. However, to conclude in the possible validity of the simulation, the numerical results provided by the computer must be previously validated. Yet, these results contain a computing error resulting from the propagation of round-off errors caused by the floating-point arithmetic used by the computer. They also contain an error coming from the uncertainties concerning the data of the problem. Hence it is first indispensable to assess the influence of these errors. This article is made up of two parts. The first part concerns the validation of numerical software results. After making a brief review of the floating-point arithmetic and highlighting the serious consequences it may have on the results obtained, we describe a probabilistic approach to the analysis of round-off errors, the CESTAC (Contr le et Estimation STochastique des Arrondis de Calculs) method, from the standpoint of both its theoritical bases and its practical implementation. This method has given rise to a new arithmetic, called stochastic arithmetic, the principal properties of which are summed up. Likewise, a probabilistic approach estimating the influence of data errors is described. A software called CADNA (Control of Accuracy and Debugging for Numerical Applications) able to automaticaly imple