## 2 Materials and Methods  
### Study Area  
Almaty, Kazakhstan's largest metropolis, grapples with significant air pollution challenges stemming from a confluence of factors including industrial emissions, vehicular traffic, and geographical constraints, necessitating a comprehensive and integrated approach to pollution assessment [20]. To describe the dynamics of pollutants in the atmosphere, a system of compressible Navier-Stokes equations is used, supplemented by an equation for the transport of pollutants with dispersion and reaction components. Continuity equation (conservation of mass):  
\[\frac{\partial\rho}{\partial t}+\frac{\partial(\rho u)}{\partial x}+\frac{ \partial(\rho v)}{\partial x}+\frac{\partial(\rho w)}{\partial x}=0 \tag{1}\]  
here \(\rho\) is density, \(t\) is time, \(x\), \(y\), \(z\) are coordinates in space, \(u\), \(v\), \(w\) are components of velocities. Equations of conservation of momentum:  
\[\frac{\partial(\rho u)}{\partial t}+\frac{\partial(\rho u^{2})}{\partial x}+ \frac{\partial(\rho uv)}{\partial y}+\frac{\partial(\rho uw)}{\partial z}=- \frac{\partial P}{\partial x}+\frac{\partial\tau_{xx}}{\partial x}+\frac{ \partial\tau_{xy}}{\partial y}+\frac{\partial\tau_{xz}}{\partial z}+\rho f_{ x},\]  
\[\frac{\partial(\rho v)}{\partial t}+\frac{\partial(\rho uv)}{\partial x}+ \frac{\partial(\rho v^{2})}{\partial y}+\frac{\partial(\rho vw)}{\partial z}= -\frac{\partial P}{\partial y}+\frac{\partial\tau_{xy}}{\partial x}+\frac{ \partial\tau_{yy}}{\partial y}+\frac{\partial\tau_{yz}}{\partial z}+\rho f_{ y}, \tag{2}\]  
\[\frac{\partial(\rho w)}{\partial t}+\frac{\partial(\rho uw)}{\partial x}+ \frac{\partial(\rho vw)}{\partial y}+\frac{\partial(\rho w^{2})}{\partial z}= -\frac{\partial P}{\partial z}+\frac{\partial\tau_{xz}}{\partial x}+\frac{ \partial\tau_{yz}}{\partial y}+\frac{\partial\tau_{zz}}{\partial z}+\rho f_{ z},\]  
where \(f_{x}\), \(f_{y}\), \(f_{z}\) are external forces, the components of the viscous stress tensor for a Newtonian fluid are:  
\[\tau_{xx}=\mu\left(2\frac{\partial u}{\partial x}-\frac{2}{3}\
abla\cdot \overrightarrow{u}\right),\ \tau_{yy}=\mu\left(2\frac{\partial v}{\partial y}-\frac{2}{3}\
abla\cdot \overrightarrow{u}\right),\ \tau_{zz}=\mu\left(2\frac{\partial w}{\partial z}-\frac{2}{3}\
abla\cdot \overrightarrow{u}\right),\]  
\[\tau_{xy}=\tau_{yx}=\mu\left(\frac{\partial u}{\partial y}+\frac{\partial v} {\partial x}\right),\ \tau_{xz}=\tau_{zx}=\mu\left(\frac{\partial u}{\partial z}+\frac{ \partial w}{\partial x}\right),\ \tau_{yz}=\tau_{zy}=\mu\left(\frac{\partial v}{ \partial z}+\frac{\partial w}{\partial y}\right)\]  
Energy conservation equation:  
\[\frac{\partial(\rho E)}{\partial t}+\frac{\partial(\rho uE+up)}{\partial x}+ \frac{\partial(\rho vE+up)}{\partial y}+\frac{\partial(\rho wE+wp)}{\partial z }=\frac{\partial}{\partial x}\left(k\frac{\partial T}{\partial x}\right)+ \frac{\partial}{\partial y}\left(k\frac{\partial T}{\partial y}\right)+ \frac{\partial}{\partial z}\left(k\frac{\partial T}{\partial z}\right)+\Phi+Q, \tag{3}\]  
\(E=e+\frac{1}{2}\left(u^{2}+v^{2}+w^{2}\right)\) is total energy per unit mass, \(e\) is internal energy per unit mass, \(k\) is thermal conductivity coefficient, \(\Phi\) is dissipation function (conversion of kinetic energy into thermal energy due to viscosity), \(Q\) is external heat sources. For air, the ideal gas equation can be used:  
\[P=\rho RT, \tag{4}\]  
where \(R\) is the gas constant for air. Temperature equation:  
\[\frac{\partial(\rho T)}{\partial t}+\frac{\partial(\rho uT)}{\partial x}+\frac{ \partial(\rho vT)}{\partial y}+\frac{\partial(\rho wT)}{\partial z}=\frac{ \partial}{\partial x}\bigg{(}D\frac{\partial T}{\partial x}\bigg{)}+\frac{ \partial}{\partial y}\bigg{(}D\frac{\partial T}{\partial y}\bigg{)}+\frac{ \partial}{\partial z}\bigg{(}D\frac{\partial T}{\partial z}\bigg{)}, \tag{5}\]  
where \(T\) is the temperature.