Estimating Scheme Viscosity for Small-Scale Circulation with Implicit Finite-Difference Schemes

Abstract

The article proposes a formula for calculating scheme viscosity, which manifests itself in calculations using implicit schemes for calculating the transfer of matter and momentum. The study aims to substantiate the structure of the formula for calculating the scheme viscosity using implicit schemes for calculating the mass and momentum transfer equation. As a result of the study, the structure of the formula for calculating the scheme viscosity for implicit schemes for solving the transfer equation was determined. The accuracy of the formula was checked on a test example. It is substantiated that by all possible means, it is necessary to avoid using implicit schemes when solving problems of small-scale circulation within urban areas. The manifestation of scheme viscosity in calculations of small-scale circulation, in which small pressure drops provide air movement, is unacceptable due to the many times the greater effect of scheme viscosity over natural viscosity.