Wildfires Quasi-Implicit Alternative-Direction Simulations using Isogeometric Finite Element Method
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arXiv
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| Autori principali: | , , , , , , , , , |
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| Natura: | Preprint |
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2026
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| _version_ | 1866917425901993984 |
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| author | Wasieleski, Juliusz Służalec, Tomasz Woźniak, Maciej Łoś, Marcin Medina, Andres Sepulveda, Paulina Serra, Albert Oliver Valseth, Eirik Paszyńska, Anna Paszyński, Maciej |
| author_facet | Wasieleski, Juliusz Służalec, Tomasz Woźniak, Maciej Łoś, Marcin Medina, Andres Sepulveda, Paulina Serra, Albert Oliver Valseth, Eirik Paszyńska, Anna Paszyński, Maciej |
| contents | We develop a wildfire simulation model that evolves the temperature scalar field using an energy balance equation accounting for heat generation, transport, and loss. For these equations, we develop quasi-implicit time integration schemes using direction splitting of the differential operators. We use the Peaceman-Rachford and Strang splitting methods, including the Crank-Nicolson method. Based on these discretizations, we derive variational formulations and explore the Kronecker product structure of the matrices. In the wildfire model, there are some non-linear terms that we treat explicitly. We perform a detailed analysis of how treating these terms affects the stability of the time integration scheme. Namely, we show that a quasi-implicit time integration scheme achieves 10 times higher simulation accuracy. We present two wildfire simulations. The first is a simulation of the 2024 wildfire disaster in the Valparaíso region of Chile. The second one is a simulation of the 2019 wildfire disaster in Las Palmas de Gran Canaria, Spain. We discuss the numerical results and compare them against satellite images and measurement records. We also present a numerical experiment for comparison with the state-of-the-art wildfire simulation model FARSITE. Our sequential code has a linear computational cost of ${\cal O}(N)$. We also present the parallel scalability of the WILDFIRE-IGA-ADS code to illustrate the possibility of running the code on a local workstation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_19370 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Wildfires Quasi-Implicit Alternative-Direction Simulations using Isogeometric Finite Element Method Wasieleski, Juliusz Służalec, Tomasz Woźniak, Maciej Łoś, Marcin Medina, Andres Sepulveda, Paulina Serra, Albert Oliver Valseth, Eirik Paszyńska, Anna Paszyński, Maciej Computational Engineering, Finance, and Science 65, 35, 68 G.1.8; G.4; I.6.7 We develop a wildfire simulation model that evolves the temperature scalar field using an energy balance equation accounting for heat generation, transport, and loss. For these equations, we develop quasi-implicit time integration schemes using direction splitting of the differential operators. We use the Peaceman-Rachford and Strang splitting methods, including the Crank-Nicolson method. Based on these discretizations, we derive variational formulations and explore the Kronecker product structure of the matrices. In the wildfire model, there are some non-linear terms that we treat explicitly. We perform a detailed analysis of how treating these terms affects the stability of the time integration scheme. Namely, we show that a quasi-implicit time integration scheme achieves 10 times higher simulation accuracy. We present two wildfire simulations. The first is a simulation of the 2024 wildfire disaster in the Valparaíso region of Chile. The second one is a simulation of the 2019 wildfire disaster in Las Palmas de Gran Canaria, Spain. We discuss the numerical results and compare them against satellite images and measurement records. We also present a numerical experiment for comparison with the state-of-the-art wildfire simulation model FARSITE. Our sequential code has a linear computational cost of ${\cal O}(N)$. We also present the parallel scalability of the WILDFIRE-IGA-ADS code to illustrate the possibility of running the code on a local workstation. |
| title | Wildfires Quasi-Implicit Alternative-Direction Simulations using Isogeometric Finite Element Method |
| topic | Computational Engineering, Finance, and Science 65, 35, 68 G.1.8; G.4; I.6.7 |
| url | https://arxiv.org/abs/2604.19370 |