Tensor methodology and computational geometry in direct computational experiments in fluid mechanics

Degtyarev, Anatoli; Khramushin, Vasily; Shichkina, Julia

doi:10.1063/1.4992291

Cited by 4 publications

(5 citation statements)

References 4 publications

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“…A specially synthesized functionalalgorithmic apparatus with a strict and definite representation of mechanics and physics laws in architecture and programming languages of modern computers is used [4].…”

Section: Direct Continual-corpuscular Computational Experimentsmentioning

confidence: 99%

“…Tensor mathematics in the simulation of processes in continuous medium mechanics synthesizes two-stage computational experiments with the help of the principal (linear) components of the hydromechanics laws in the vicinity of adjacent fluid particles at controlled time intervals [1]. The use of the classical apparatus of the tensor calculus allows one to formalize the key approximations of hydromechanics in the three-dimensional space and the absolute time.…”

Section: Introductionmentioning

confidence: 99%

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Interpolation Environment of Tensor Mathematics at the Corpuscular Stage of Computational Experiments in Hydromechanics

et al. 2018

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Abstract. Stages of direct computational experiments in hydromechanics based on tensor mathematics tools are represented by conditionally independent mathematical models for calculations separation in accordance with physical processes. Continual stage of numerical modeling is constructed on a small time interval in a stationary grid space. Here coordination of continuity conditions and energy conservation is carried out. Then, at the subsequent corpuscular stage of the computational experiment, kinematic parameters of mass centers and surface stresses at the boundaries of the grid cells are used in modeling of free unsteady motions of volume cells that are considered as independent particles. These particles can be subject to vortex and discontinuous interactions, when restructuring of free boundaries and internal rheological states has place. Transition from one stage to another is provided by interpolation operations of tensor mathematics. Such interpolation environment formalizes the use of physical laws for mechanics of continuous media modeling, provides control of rheological state and conditions for existence of discontinuous solutions: rigid and free boundaries, vortex layers, their turbulent or empirical generalizations.

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Section: Direct Continual-corpuscular Computational Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interpolation Environment of Tensor Mathematics at the Corpuscular Stage of Computational Experiments in Hydromechanics

et al. 2018

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“…The algorithmic realization of direct numerical simulations using explicit schemes has a beautiful historical analogy [2] in the form of calculus of fluxions by Isaac Newton. In the up-to-date algorithms, such implementation is represented as three-dimensional space numeric objects.…”

Section: The Subject Of Applicationmentioning

confidence: 99%

“…As shown, it can be represented in the form of the recalculation from the local coordinates of the point into the global reference system in accordance with the time interval t. 1 fluens, fluentis are functions x, y, z on the argument of time t; fluxioẋ,ẏ,ż are time derivatitives x, y, z. 2 In scalar notation: 3 Tensor object without indices here and later are marked by bold.…”

Section: The Subject Of Applicationmentioning

confidence: 99%

“…We know that it is a price to pay for the stability of the numerical scheme. However, the attractiveness of the explicit schemes has led to the development of an approach based on the description of the behavior of many large liquid particles [2]. Problems of numerical schemes instability in this case are avoided by providing a large particle with additional degrees of freedom.…”

Section: Introductionmentioning

confidence: 99%

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Coordinate Systems, Numerical Objects and Algorithmic Operations of Computational Experiment in Fluid Mechanics

Degtyarev

Khramushin

2016

EPJ Web of Conferences

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Abstract. The paper deals with the computer implementation of direct computational experiments in fluid mechanics, constructed on the basis of the approach developed by the authors. 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. The paper examines the main objects and operations that let you manage computational experiments and monitor the status of the computation process. Special attention is given to a) realization of tensor representations of numerical schemes for direct simulation; b) realization of representation of large particles of a continuous medium motion in two coordinate systems (global and mobile); c) computing operations in the projections of coordinate systems, direct and inverse transformation in these systems. Particular attention is paid to the use of hardware and software of modern computer systems.

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Virtual Testbed: Concept and Applications

Bogdanov

Degtyarev

Gankevich

et al. 2020

Lecture Notes in Computer Science

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In this paper the virtual testbed as a problem-solving environment is considered in different aspects. Fundamental questions for virtual testbed development are (1) characteristics of mathematical models and their interaction; (2) computational aspects and mapping of algorithms onto hardware; (3) information streams and data smanagement. The authors propose the concept of a virtual private supercomputer as a tool for virtual testbed computer environment. Examples of the implementation of the virtual testbed in different areas are given. The article summarizes achievements of the authors in the field of virtual testbed during last years.

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Tensor methodology and computational geometry in direct computational experiments in fluid mechanics

Cited by 4 publications

References 4 publications

Interpolation Environment of Tensor Mathematics at the Corpuscular Stage of Computational Experiments in Hydromechanics

Interpolation Environment of Tensor Mathematics at the Corpuscular Stage of Computational Experiments in Hydromechanics

Coordinate Systems, Numerical Objects and Algorithmic Operations of Computational Experiment in Fluid Mechanics

Virtual Testbed: Concept and Applications

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