# CFD Assessment of Car Park Ventilation System in Case of Fire Event
## 2 Materials and Methods
### Simulation Setup in OpenFOAM
#### 2.3.5 Configuration of Linear Solvers, Preconditioners, Smoothers, and Application Solvers  
Linear Solvers  
In OpenFOAM, the discretized equations in the simulation are solved using linear solvers. It is important to note that the term _\"linear solver\"_ refers to the method used to solve a set of linear equations, while the \"_application solver_\" describes the set of equations and algorithms used to solve a specific problem.  
During Phase 01, the generalized geometric-algebraic multigrid (GAMG) method is employed as the linear solver to calculate the pressure field \(p\). The multigrid linear solvers utilize a coarse grid with fast solution times to generate an initial solution for the fine grid, effectively reducing errors with high frequency. GAMG utilizes either a geometric or algebraic pairing agglomeration procedure, gradually coarsening the mesh [37]. GAMG is suitable for complex geometries and delivers accurate solutions for the pressure field. To calculate other properties, such as \(U\), \(\varepsilon\), and \(k\), the smoothSolver is used in an iterative manner. This solver employs a chosen smoother at runtime to solve symmetric and asymmetric matrices. For Phase 02, the preconditioned bi-conjugate gradient (PBiCGStab) linear solver is selected due to its favorable parallel scaling and efficient utilization of computational resources. As Phase 02 involves modeling the propagation of smoke as a scalar quantity \(T\), which typically entails solving asymmetric matrices, the PBiCGStab solver is well-suited for this task. These configurations pertaining to the linear solvers are adjusted in the fvSolution dictionary.  
Preconditioners play a crucial role in improving the convergence speed of linear equation solvers compared to the original equations [37]. In Phase 01, when calculating pressure field \(p\), the diagonal-based incomplete Cholesky (DIC) preconditioner is employed. This preconditioner involves reorganizing the linear equations and computing the reciprocal diagonal matrix, which is then determined and stored for symmetric matrices. To derive the smoke concentration \(T\) in Phase 02, and for the calculation of other properties, such as \(U\), \(\varepsilon\), and \(k\) in Phase 01, the diagonal-based incomplete LU (DILU) preconditioner is utilized. DILU is similar to DIC, but it is specifically designed for handling asymmetric matrices. These configurations pertaining to the preconditioners are adjusted in the fvSolution dictionary.  
Smoothers Preconditioners are utilized to reduce the number of iterations required to solve linear equations, but they do not directly impact the number of iterations associated with mesh-related calculations. To address this issue, smoothers are employed in conjunction with solvers. Smoothers play a role in modifying the mesh shape while preserving its topology, leading to improved quality of the volume mesh. During Phase 01, for all properties of the flow field, the Gauss-Seidel method is selected as the smoother. This choice is motivated by the large number of meshing elements. The Gauss-Seidel method is known for its cost-effectiveness in terms of memory usage. It is an iterative method that aims to solve algebraic equations by iteratively approaching the desired accuracy with an approximate solution. However, it should be noted that smoothers are not implemented during the simulations in Phase 02. These configurations regarding the smoothers are adjusted in the fvSolution dictionary, ensuring their appropriate settings for the simulations.