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<p>In this paper, using the example of mass balance for a continuous medium, a kinematic approach based on the concept of local volumetric flow is proposed for the transition from a discrete to a continuous description. This approach takes into account the possibility of discontinuities in the flow derivative at the boundaries of an elementary layer and allows one to derive the balance equation in differential form, eliminating the need for integral relations. It is shown that the inequality of jumps in the derivatives at the left and right boundaries is equivalent to the assumption of mass concentration at the layer boundaries. It is established that the coincidence of the sums of the left and right derivatives at both boundaries is a necessary condition for eliminating negative values of the mass density in the continuous limit.</p>

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Balance equation: local volumetric flow and surface fluxes in the theory OF continual media

  • 期刊论文

  • 发表日期：

    2026年2月12日

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  • A. Zh. Khachatrian,
  • G. P. Vardanyan,
  • O. A. Zadoyan,
  • Y. G. Virabyan

摘要

In this paper, using the example of mass balance for a continuous medium, a kinematic approach based on the concept of local volumetric flow is proposed for the transition from a discrete to a continuous description. This approach takes into account the possibility of discontinuities in the flow derivative at the boundaries of an elementary layer and allows one to derive the balance equation in differential form, eliminating the need for integral relations. It is shown that the inequality of jumps in the derivatives at the left and right boundaries is equivalent to the assumption of mass concentration at the layer boundaries. It is established that the coincidence of the sums of the left and right derivatives at both boundaries is a necessary condition for eliminating negative values of the mass density in the continuous limit.