Investigation of the stability and convergence of difference schemes for the three-dimensional equations of the atmospheric boundary layer

Authors

  • Konrad Gromaszek Lublin University of Technology
  • Almas Temirbekov al-Farabi Kazakh National University, Almaty, Kazakhstan
  • Baydaulet Urmashev al-Farabi Kazakh National University, Almaty, Kazakhstan

Abstract

In this article we construct a finite-difference scheme for the three-dimensional equations of the atmospheric boundary layer. The solvability of the mathematical model is proved and quality properties of the solutions are studied. A priori estimates are derived for the solution of the differential equations. The mathematical questions of the difference schemes for the equations of the atmospheric boundary layer are studied. Nonlinear terms are approximated such that the integral term of the identity vanishes when it is scalar multiplied. This property of the difference scheme is formulated as a lemma. Main a priori estimates for the solution of the difference problem are derived. Approximation properties are investigated and the theorem of convergence of the difference solution to the solution of the differential problem is proved

Author Biography

Konrad Gromaszek, Lublin University of Technology

Institute of Electronics and Information Technolofy

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Published

2018-07-20

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Applications