1. NUMERICAL SIMULATION OF AIR POLLUTION TRANSFER IN URBAN AREAS P. I. Kudinov, V. A. Ericheva Dnepropetrovsk National University, Dnepropetrovsk, Ukraine e-mail: p_kudinov@ukr.net, web: http://Xoptimum.narod.ru

2. Aims: Development of numerical methods for incompressible viscid flows Better understanding of 3D vortex flows formation regularities Study of pollution transfer in elements of urban areas Development and analysis of visualization techniques for numerical simulation of 3D vortex flow

3. Governing equations The passive admixture model is used. This model is close to truth if the sizes of particles are small enough. All equations can be written in the form of conservation law of some physical variable  here  e - effective coefficient of diffusion, S  - sources of . Mass and momentum conservation of viscose incompressible fluid

4. Numerical method Discrete analogues of governing equations in curvilinear non-orthogonal coordinate system e i, e j – covariant and contravariant components of local basis. System of linear algebraic equations is solved by Gauss-Zeydel method. For pressure calculation the modification of SIMPLER algorithm on the case of curvilinear coordinates is used. Verification of developed models and numerical methods was done on test problems of lid driven flow in a square cavity, flow around circular cylinder.

5. Some typical geometry configurations of urban areas Courtyard with different wind direction Long street

6. Streamlines on the surfaces and n umerical “laser knife” visualization in vertical and horizontal cross section of the infinite trench

7. Trajectories

8. Pe=10 4 Pe=10 6 Pollution concentration in vertical cross sections

9. Pollution concentration in horizontal cross sections Pe=10 4 Pe=10 6 Pollution concentration in frontal cross sections

10. Flow in 3D cavity with moving lid

11. Pollution concentration in vertical cross sections Pollution concentration in frontal cross sections Pollution concentration in horizontal cross sections Pe=10 5

12. Streamlines on the bottom, side and a), b), c) – windward, d), e), f) – leeward walls of the trench at Re=10 3 and angles of lid motion a), d)  =5 , b), e)  =20 , c), f)  =45  a) b) c) d) e) f)

13. Streamlines on the bottom, side and a), b), c) – windward, d), e), f) – leeward walls of the trench at Re=10 3 and angles of lid motion a), d)  =60 , b), e)  =80 , c), f)  =90  a) b) c) d) e) f)

15. Pollution concentration in vertical cross sections Pollution concentration in frontal cross sections Pollution concentration in horizontal cross sections Pe=10 5

16. Conclusions and aims for future work  Developed numerical techniques permits to simulate and visualize 3D flows and mass transfer in obstructed geometry.  For better understanding of structure of 3D flows we need to use combination of different types of visualization techniques. There is no universal method of visualization of 3D flows. Using of only 2D visualization can lead to loss of important information. Actual problems are:  Development of numerical simulation and visualization methods for unsteady 3D flows and pollution transfer in obstructed geometry.  Investigation of regularities of momentum heat and mass transfer in single elements and arrays of typical urban and vegetative canopy geometry.  Development of numerical method for aeroelastic problems for flexible canopies.