Abstract:
The article represents a purely algebraic (i.e., derivative-free) approach to the description of physical and chemical processes in the continuum approximation as a generalization of Godunov's scheme. This approach is based on dividing the domain into finite volumes with the continuous medium inside. The mathematical model of the studied physical and chemical processes in each volume consists of the conservation laws and phenomenological laws. According to the molecular-kinetic theory, all macroparameters (density, temperature, pressure, etc.) are constant in open finite volumes and discontinuous on their faces. The advantage of the algebraic approach (so-called computational macromechanics) is simpler and more accurate mathematical description of the modeled phenomena, which is important for black-box software. One of the problems is the formulation of phenomenological laws of the gradient type (Fourier, Fick, Newton, etc.), since all macroparameters are defined in finite volumes in the computational macromechanics, not in points. First, the article represents an expression for the specific heat flux in the ideal gas. Then, an equation for the thermal conductivity coefficient is obtained in the discontinuous approximation under the assumption that the continuous temperature changes linearly in each finite volume, and the thermal conductivity coefficient depends linearly on the temperature. The variants for constructing difference schemes of computational macromechanics are considered. In conclusion, the results of 1D computational experiment illustrating theoretical analysis are presented.
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