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Direct computational experiments in fluid mechanics using three-dimensional tensor mathematics

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Abstract

Architecture of a digital computing system determines the technical foundation of a unified mathematical language for exact arithmetic-logical description of phenomena and laws of continuum mechanics for applications in fluid mechanics and theoretical physics. Deep parallelization of the computing processes serves to the revival of application of functional programming at a new technological level. The efficiency of computations is provided by true reproduction of the fundamental laws of physics and continuum mechanics. Tensor formalization of numerical objects and computing operations serves to spatial interpolation of rheological state parameters and laws of the fluid mechanics as mathematical models in the local coordinates of the elementary numeric cells - large liquid particles. The proposed approach allows the use of explicit numerical scheme, which is an important condition for increasing the efficiency of the algorithms developed by numerical procedures with natural parallelism.

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Bogdanov, A., Degtyarev, A., & Khramushin, V. (2018). Direct computational experiments in fluid mechanics using three-dimensional tensor mathematics. In 11th International Conference on Computer Science and Information Technologies, CSIT 2017 (Vol. 2018-March, pp. 139–144). Institute of Electrical and Electronics Engineers Inc. https://doi.org/10.1109/CSITechnol.2017.8312158

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