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.
Highlights
The paper discusses some generalizations and justifications for the practical application of continualcorpuscular models of the computational hydromechanics
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
A computational experiment in hydromechanics is designed on the basis of explicit schemes on two stages of physical processes modeling and 3D tensor mathematics
Summary
The paper discusses some generalizations and justifications for the practical application of continualcorpuscular models of the computational hydromechanics. 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 This creates the necessary tools and ample mechanisms for direct algorithmic modeling of various spatio-temporal processes in the nearest environment of a computational cell. An intuitive-natural variant of a direct computational experiment constructing is represented by two stages of spatial integration of the first order These stages connect the differentials of kinematic and rheological processes into the general solution of mechanics equations by means of extrapolation of the second order in time. (2) At the corpuscular stage of the calculations, physical fields are updated in empirical gradient, direct linear and divergent dependences for volumetric and surface stresses on liquid particles, taking into account the current rheological state of the spatial flows of the continuous medium. The flows and transformation of the material medium are uniformly formalized in tensor form on the continuum and corpuscular stages of the computational experiment
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