Conformal Mapping in Mathematical Modelling of Air Flows in Premises

Background/Objectives: Mathematical mapping of velocity, concentration and temperature fields is the most promising method of studying the distribution of microclimate parameters influencing health and safety and technological requirements for the indoor air of premises. Methods/Statistical Analysis: Mappings using analytical functions or conform mappings, which is actually the same, have become common in mathematical physics in solving problem of low speed aerodynamics. This method allows one to obtain an analytical solution for designing speed fields of the air which improves the accuracy of calculations. This problem takes several stages: Designing current lines of the air and determining numerical values of the air velocity. Findings: The described method of calculating the velocity fields of air flows based on the theory of conformal mapping allows one to determine the velocities at any point of a particular premises regardless of its geometric characteristics and ways of supplying and removing the air. The model is based on the use of the symmetry of the rectangular premises and elliptic integral. The implementation of this function in the symbolic math packages retains high accuracy for the numerical study of this model. Applications/Improvements: The resulting solution is analytic so in some cases it may be more accurate than the solution of the system of differential equations.