Mathematical problems in the difference scheme for equations of the atmosphere boundary layer.

Abstract

The mathematical model for the atmospheric boundary layer equations and the transport equation and transformation of pollutants harmful substances in the air. Proved the solvability of the mathematical model and studied qualitative Properties of solutions. The finite-difference scheme for two-and three-dimensional equations of ABL. To solve the differential equations, a priori estimates. Investigated mathematical questions of difference schemes for the equations of the boundary layer of the atmosphere. We prove the lemma for the grid function. With the help of this lemma have the basic energy inequality. By the lemma and using the Cauchy-Schwarz inequality to estimate the basic size. The convergence theorem in the rules of functional spaces. Obtain the basic a priori estimates for the solution of the difference problem. Studied approximation properties and prove the convergence of a solution of the problem to the solution of the differential problem. To prove the theorem and approximation properties of the difference problem is considered in a stationary analog. Conducted methodical numerical calculations.