# Parallel Implementation of the Algorithm to Compute Forest Fire Impact on Infrastructure Facilities of JSC Russian Railways

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}+ 2K) is presented. The program is implemented in Python 3.x using the NumPy and Concurrent libraries. Calculations were carried out on a multiprocessor cluster in the Sirius University of Science and Technology. The results of calculations and the acceleration coefficient for operating modes for 1, 2, 4, 8, 16, 32, 48 and 64 processes are presented. The developed algorithm can be applied to assess the fire safety of infrastructure facilities of Russian Railways. The main merit of the new development should be noted, which is explained by the ability to use large computational domains with a large number of computational grid nodes in space and time. The use of caching intermediate data in files made it possible to distribute a large number of computational nodes among the processors of a computing multiprocessor system. However, one should also note a drawback; namely, a decrease in the acceleration of computational operations with a large number of involved nodes of a multiprocessor computing system, which is explained by the write and read cycles in cache files.

## 1. Introduction

## 2. Initial Data

## 3. Mathematical Statement and Methodology

- In the enclosing structures, heat exchange is carried out by the heat conduction mechanism;
- Two-dimensional setting;
- The shape of the fire front is a parabola;
- Thermophysical properties of building materials do not depend on temperature;
- A catastrophic scenario of fire weather is assumed when there is no moisture in the surface layer of the wall;
- Disregard wood pyrolysis;
- The main mechanism of heat transfer from the line of fire to the building is heat radiation;
- The temperature of the forest fire front is taken into account using the Stefan-Boltzmann law;
- The impact of the forest fire front on the wall is determined by q
_{ff}and T_{ff}.

_{ff}. On the surface of the fence exposed to the heat flow from the forest fire front, the material itself becomes a radiation source.

_{w}is the heat source inside the decision area; t is the temporal coordinate; x, y, z are the spatial coordinates.

_{1}, T

_{2}are the temperature in computational mesh nodes number 1 and 2; α

_{1}is the first running coefficient number 1; β

_{1}is the second running coefficient number 1.

_{N}(K). The boundary conditions have been discredited to the first order of approximation. It is assumed that a forest fire front is approaching the structure from the left side. Convection-radiation heat transfer at the boundary of the enclosing structure is calculated as an approximation on the left and right boundaries.

_{1}is the temperature in the first node of computational mesh; T

_{ff}is the temperature in the fire front; λ

_{1}is heat conduction coefficient of first layer of the enclosing construction of the wall; α is the heat transfer coefficient; ε is the emissivity factor; σ is the Stefan–Boltzmann constant; q

_{ff}is the heat flux from fire line; x is the spatial coordinate.

_{1}is the first running coefficient; β

_{1}is the second running coefficient; λ

_{1}is the heat conduction coefficient of the first layer of enclosing construction of the wall; α is the heat transfer coefficient; ε is the emissivity factor; σ is the Stefan–Boltzmann constant; q

_{ff}is the heat flux from fire line; T

_{1}is the temperature in the first node of computational mesh; T

_{ff}is the temperature in the fire front; h is the spatial step in x-direction.

_{2}is the temperature in the second layer of the enclosing construction of the wall; T

_{e}is the temperature of the indoor environment of the object; x

_{N}is the thickness of the wall; λ

_{2}is the heat conduction coefficient of the second layer of enclosing construction of the wall; α is the heat transfer coefficient; x is the spatial coordinate.

_{i}, c

_{i}, λ

_{i}, T

_{i}are the density, heat capacity, heat conduction coefficient and temperatures in the first and second layers of the enclosing construction of wall; T

_{e}is the indoor environment temperature; q

_{ff}is the resulting heat flux from fire front; q

_{fd}is the heat flux component depending on distance from wall to fire front; q

_{fh}is the heat flux component depending on fire front height; k is the coefficient for law that similar to Bouguer–Lambert–Beer law; ε is the emissivity factor; σ is the Stefan–Boltzmann constant; α is the heat transfer coefficient; xf is the current distance from wall to fire front until the end of exposure; d is the initial distance from wall to fire front; x, y are the spatial coordinates; t is the temporal coordinate; t

_{exp}is the exposure time from fire front.

## 4. Parallel Implementation

_{1}and β

_{1}are also calculated, arrays of initial values of the temperature field and coordinate axes are created and filled. After that, the nodes are evenly divided into sections along the X and Z axes. After dividing the computational grid, the start and end points of the process are set for each process. The processes are launched within the specified ranges along the Z axis with accuracy L (Figure 2). During the process, locally one-dimensional problems are solved for each L(n) included in the range L(start, end).

_{M}can be defined using relationship T

_{0}to T

_{M}and, as a result, obtain

_{0}is the calculation time in sequential mode, T

_{M}is the calculation time using M processes. This ratio allows you to calculate the efficiency factor without taking into account losses.

_{M}parameter. Efficiency is calculated using the formula [67]:

- 2 Intel Xeon Gold 6140 processors, 2.3 GHz, 18 cores/36 threads, 10.4 GT/s, 24.75 MB cache, Turbo, HT (140 W), DDR4 2666 MHz.
- 8 memory modules RDIMM 32 GB, 2666 MT/s.
- Mellanox Technologies MT27800 ConnectX-5 Single Port Infiniband Adapter, EDR (name ib0 within host or cn-X-ib0 within cluster).
- Dual Port Ethernet NIC—Intel Corporation Ethernet Controller X710 for 10GbE SFP + (eth0).
- SATA 200 GB.

- 2 Intel Xeon Gold 5118 processors, 2.3 GHz, 18 cores/36 threads, 10.4 GT/s, 24.75 MB cache, Turbo, HT (140 W), DDR4 2666 MHz.
- 8 memory modules RDIMM 32 GB, 2666 MT/s.
- Mellanox Technologies MT27800 ConnectX-5 Single Port Adapter Infiniband, EDR (name ib0 within the host or nodeXXX-ib0 within the cluster).
- Dual Port Ethernet NIC—Intel Corporation Ethernet Controller X710 for 10GbE SFP + (em0).
- Dual Port Ethernet NIC—I350 Gigabit Network Connection (em3).
- 4 SAS disks 1.8 TB, 10,000 rpm

## 5. Results and Discussion

^{3}. Temperatures reach critical values, while the falling heat flux is not large.

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 10.**Impact of a surface forest fire (low intensity) on plywood from a distance of 20 m—temperature distribution along the wall thickness.

**Figure 11.**Impact of a surface forest fire (high intensity) on plywood from a distance of 20 m—temperature distribution along the wall thickness.

**Figure 12.**Impact of a crown forest fire on plywood from a distance of 20 m for different facade heights (from 1 to 10 m).

**Figure 13.**Impact of surface forest fires (low intensity) on various materials from a distance of 20 m in 425 s of exposure—temperature distribution over the wall thickness.

**Figure 14.**Impact of surface forest fires (high intensity) on various materials from a distance of 20 m for 350 s of exposure—temperature distribution along the wall thickness.

**Table 1.**Thermophysical characteristics of materials [62].

Material | $\mathit{\lambda},\frac{\mathbf{W}}{\mathbf{m}\cdot \mathbf{K}}$ | $\mathit{c},\frac{\mathbf{J}}{\mathbf{k}\mathbf{g}\cdot \mathbf{K}}$ | $\mathit{\rho},\frac{\mathbf{k}\mathbf{g}}{{\mathbf{m}}^{3}}$ |
---|---|---|---|

Pine wood | 0.12 | 1670 | 500 |

Birch wood | 0.28 | 2200 | 440 |

Glued plywood | 0.12 | 2300 | 600 |

Cardboard | 0.18 | 2300 | 1000 |

Fiberboard (1000) | 0.15 | 2300 | 1000 |

Fiberboard (800) | 0.13 | 2300 | 800 |

**Table 2.**Experimental data on wood ignition by radiant heat flux [63].

Ignition Delay, s | Heat Flux to the Surface, kW/m^{2} | Surface Temperature, K |
---|---|---|

63.5 | 12.5 | 658 |

45.0 | 21 | 700 |

11.1 | 42 | 726 |

2.6 | 84 | 773 |

0.4 | 210 | 867 |

**Table 3.**Absorption coefficients for different types of paint [62].

Paint | Absorption Coefficient |
---|---|

Pure wood | 0.6 |

Gray | 0.7 |

White | 0.3 |

Blue | 0.6 |

Straw-colored | 0.45 |

**Table 4.**Comparative analysis of the results of numerical modeling (deviation of the numerical results from the sequential version [61], average difference).

Scenario | Series 1 | Series 2 | Series 3 |
---|---|---|---|

1 (surface temperature) | 10% | 15% | 210% |

1 (in-depth temperature) | 13% | 18% | 212% |

2 (surface temperature) | 12% | 14% | 12% |

2 (in-depth temperature) | 17% | 19% | 22% |

3 (surface temperature) | 13% | 15% | 27% |

3 (in-depth temperature) | 15% | 17% | 29% |

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**MDPI and ACS Style**

Baranovskiy, N.V.; Podorovskiy, A.; Malinin, A.
Parallel Implementation of the Algorithm to Compute Forest Fire Impact on Infrastructure Facilities of JSC Russian Railways. *Algorithms* **2021**, *14*, 333.
https://doi.org/10.3390/a14110333

**AMA Style**

Baranovskiy NV, Podorovskiy A, Malinin A.
Parallel Implementation of the Algorithm to Compute Forest Fire Impact on Infrastructure Facilities of JSC Russian Railways. *Algorithms*. 2021; 14(11):333.
https://doi.org/10.3390/a14110333

**Chicago/Turabian Style**

Baranovskiy, Nikolay Viktorovich, Aleksey Podorovskiy, and Aleksey Malinin.
2021. "Parallel Implementation of the Algorithm to Compute Forest Fire Impact on Infrastructure Facilities of JSC Russian Railways" *Algorithms* 14, no. 11: 333.
https://doi.org/10.3390/a14110333