Numerical Approximation of the In Situ Combustion Model Using the Nonlinear Mixed Complementarity Method
In this work, we study a numerical method to approximate the exact solution of a simple in situ combustion model. To achieve this, we use the mixed nonlinear complementarity method (MNCP), a variation of the Newton method for solving nonlinear systems, incorporating a single Hadamard product in its...
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| Format: | Article |
| Language: | English |
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MDPI AG
2025-04-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/10/4/92 |
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| author | Julio César Agustin Sangay Alexis Rodriguez Carranza Juan Carlos Ponte Bejarano José Luis Ponte Bejarano Eddy Cristiam Miranda Ramos Obidio Rubio Franco Rubio-López |
| author_facet | Julio César Agustin Sangay Alexis Rodriguez Carranza Juan Carlos Ponte Bejarano José Luis Ponte Bejarano Eddy Cristiam Miranda Ramos Obidio Rubio Franco Rubio-López |
| author_sort | Julio César Agustin Sangay |
| collection | DOAJ |
| description | In this work, we study a numerical method to approximate the exact solution of a simple in situ combustion model. To achieve this, we use the mixed nonlinear complementarity method (MNCP), a variation of the Newton method for solving nonlinear systems, incorporating a single Hadamard product in its formulation. The method is based on an implicit finite difference scheme and a mixed nonlinear complementarity algorithm (FDA-MNCP). One of its main advantages is that it ensures global convergence, unlike the finite difference method and the Newton method, which only guarantee local convergence. We apply this theory to an in situ combustion model, reformulating it in terms of mixed complementarity. Additionally, we compare it with the FDA-NCP method, demonstrating that the FDA-MNCP is computationally more efficient when the spatial discretization is refined. |
| format | Article |
| id | doaj-art-ae326cc4131a4dfa8f59c394538deee4 |
| institution | OA Journals |
| issn | 2311-5521 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj-art-ae326cc4131a4dfa8f59c394538deee42025-08-20T02:28:34ZengMDPI AGFluids2311-55212025-04-011049210.3390/fluids10040092Numerical Approximation of the In Situ Combustion Model Using the Nonlinear Mixed Complementarity MethodJulio César Agustin Sangay0Alexis Rodriguez Carranza1Juan Carlos Ponte Bejarano2José Luis Ponte Bejarano3Eddy Cristiam Miranda Ramos4Obidio Rubio5Franco Rubio-López6Departamento de Ciencias, Universidad Privada del Norte, Campus San Isidro, Trujillo 13011, PeruDepartamento de Ciencias, Universidad Privada del Norte, Campus San Isidro, Trujillo 13011, PeruDepartamento de Ciencias, Universidad Privada del Norte, Campus San Isidro, Trujillo 13011, PeruUniversidad Tecnológica del Peru, Trujillo 15046, PeruDepartamento de Matemáticas, Universidad Nacional de Trujillo, Trujillo 13011, PeruDepartamento de Matemáticas, Universidad Nacional de Trujillo, Trujillo 13011, PeruDepartamento de Matemáticas, Universidad Nacional de Trujillo, Trujillo 13011, PeruIn this work, we study a numerical method to approximate the exact solution of a simple in situ combustion model. To achieve this, we use the mixed nonlinear complementarity method (MNCP), a variation of the Newton method for solving nonlinear systems, incorporating a single Hadamard product in its formulation. The method is based on an implicit finite difference scheme and a mixed nonlinear complementarity algorithm (FDA-MNCP). One of its main advantages is that it ensures global convergence, unlike the finite difference method and the Newton method, which only guarantee local convergence. We apply this theory to an in situ combustion model, reformulating it in terms of mixed complementarity. Additionally, we compare it with the FDA-NCP method, demonstrating that the FDA-MNCP is computationally more efficient when the spatial discretization is refined.https://www.mdpi.com/2311-5521/10/4/92in situ combustion modelnonlinear mixed complementarity method |
| spellingShingle | Julio César Agustin Sangay Alexis Rodriguez Carranza Juan Carlos Ponte Bejarano José Luis Ponte Bejarano Eddy Cristiam Miranda Ramos Obidio Rubio Franco Rubio-López Numerical Approximation of the In Situ Combustion Model Using the Nonlinear Mixed Complementarity Method Fluids in situ combustion model nonlinear mixed complementarity method |
| title | Numerical Approximation of the In Situ Combustion Model Using the Nonlinear Mixed Complementarity Method |
| title_full | Numerical Approximation of the In Situ Combustion Model Using the Nonlinear Mixed Complementarity Method |
| title_fullStr | Numerical Approximation of the In Situ Combustion Model Using the Nonlinear Mixed Complementarity Method |
| title_full_unstemmed | Numerical Approximation of the In Situ Combustion Model Using the Nonlinear Mixed Complementarity Method |
| title_short | Numerical Approximation of the In Situ Combustion Model Using the Nonlinear Mixed Complementarity Method |
| title_sort | numerical approximation of the in situ combustion model using the nonlinear mixed complementarity method |
| topic | in situ combustion model nonlinear mixed complementarity method |
| url | https://www.mdpi.com/2311-5521/10/4/92 |
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