## 4 Simulation and Integration Results  
### Spatiotemporal Characteristics of Airflow and Methane Distribution  
The established model was numerically simulated and all terms of the evolution equations, including streaming step and collision step were solved. The coupling mode is solved using Boussinesq approximation method. The detailed parameters are presented in Table 3. The simulation required around 1.6 h on workstations with four core processors and 8 GB RAM.  
The velocity field of airflow is one of the main factors which directly influence the methane distribution and mitigation. As presented in Figures 5 and 6, the predicted air velocity and methane concentration profiles were investigated at different time points with a fixed methane emission rate of 0.2 m\({}^{3}\)/s. Here, we analysed the overall spatiotemporal characteristics of velocity behaviour and methane distribution inside the laneway. The pressing air is flowing from the intake side of the laneway at high velocity, and there exists an obvious jet flow, which goes along the laneway and flows into the working face. When the airflow arrives at the working face, it is obstructed by the face and the airflow changes its flow direction and flows along the working face area, as can be  
\begin{table}
\begin{tabular}{l} \hline \hline
**Algorithm. The LBM Based Turbulent Velocity-Concentration Coupling Model Integrated with LrGIS Platform** \\ \hline Step 1: Geometric model construction with specific geospatial coordinates. \\ Step 2: Lattice attributes configuration for two different lattice (D2Q9 and D2Q5) \\ Step 3: Main loop starts \\  Parameters initialization: \(f_{i},f_{i}^{eq},C_{i},C_{i}^{eq},\Delta x,\Delta t\), maxIter \\  For (it = 0; it \(<\) maxIter; ++it) \\  If (it = 0) \\  Set static boundary conditions (fluid region, wall). \\  Else if (it = 0) \\  Set dynamic boundary conditions(inflow, outflow and methane emission rate). \\  Do collision step \\ \(\widehat{f_{i}}(x,t)=f_{i}(x,t)-1/\tau[f_{i}(x,t)-f_{i}^{eq}(x,t)]\) \\ \(\widehat{\Psi_{i}}(C)=-1/\tau_{i}[C_{i}(x,t)-C_{i}^{eq}(x,t)]+\Delta t\alpha /4\) \\  Do streaming step \\ \(f_{i}(x+c_{i}\Delta t,t+\Delta t)=\widehat{f_{i}}(x,t)\) \\ \(C_{i}(x+c_{i}\Delta t,t+\Delta t)-C_{i}(x,t)=\widehat{\Psi_{i}}(C)\) \\  Do coupling step \\ \(f_{i}(x+c_{i}\Delta t,t+\Delta t)-\widehat{f_{i}}(x,t)=-1/\tau[\widehat{f_{i} }(x,t)-f_{i}^{eq}(x,t)]+k\epsilon_{i}g_{i}(C-C_{0})/2\) \\ Step 4: Save the result data as time series grid files \\  Step 5: FluentEntity call time series grid files and display field data on LrGIS GUI integrated with various coal mine map objects \\ \hline \hline \end{tabular}
\end{table}
Table 2: Algorithm steps of the numerical model.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Setting** \\ \hline Air density (kg/m\({}^{3}\)) & 1.225 \\ Methane gas density (kg/m\({}^{3}\)) & 0.716 \\ Turbulent viscosity(m\({}^{2}\)/s) & \(1.7894\times 10^{-5}\) \\ Turbulent kinetic energy & 1.3 \\ Convergence criteria & 10e\({}^{-6}\) \\ Calculation steps & 10000 \\ Lattice size (m) & 0.1 \\ Time step size (s) & 1 \\ Rendols number & 500 \\ Initial pressure & 1/3 \\ Air velocity of inlet (m/s) & 3.17 \\ Methane volume flow at the working face (m\({}^{3}\)/s) & 0.2 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Parameters for LBM simulation.  
seen in Figure 5a-c about the airflow distribution at different times. Correspondingly, the methane gas gushes from the coal seam and disperses into the working face with the impact of airflow after about 5 min. (Figure 6a), when the airflow is distributed fully in the working face area. Then the methane gas gradually diluted and decreased to a low concentration level with the effect of airflow in the wind outtake side of the lineway and approximately becomes stable at 10 min. (Figure 6b-d).