International audiencePossible 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 with impurities present in the mother liquor. Meanwhile, few kinetic models describe the effect of impurities on the growth of crystals in solution, and published models are usually derived from data obtained, thanks to specific experiments based on the evaluation of the growth rate of single crystals. Such models are obviously questionable because, in the industrial practice, distributed properties of crystals are actually involved. Considering the “time of contamination” of particles as a new internal variable is thus made necessary. This is the reason why a specific PBE resolution algorithm is presented in this paper. The numerical scheme for the resolution of PBEs is based on the method of characteristics and shown to allow fast and accurate simulation of transient features of the crystal size distribution in the particular case when the growth or nucleation rates are assumed to exhibit unsteady-state dynamics. The algorithm is finally used to simulate the isothermal desupersaturation crystallization of citric acid in water

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 tool that makes it possible to optimize the numerical types in a program by taking into account the requested accuracy on the computed results. With PROMISE the numerical quality of results is verified using DSA (Discrete Stochastic Arithmetic) that enables one to estimate roundoff errors. The search for a suitable type configuration is performed with a reasonable complexity thanks to the delta debugging algorithm. The PROMISE tool has been successfully tested on programs implementing several numerical algorithms including linear system solving and also on an industrial code that solves the neutron transport equations.

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