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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Main Authors: Julio César Agustin Sangay, Alexis Rodriguez Carranza, Juan Carlos Ponte Bejarano, José Luis Ponte Bejarano, Eddy Cristiam Miranda Ramos, Obidio Rubio, Franco Rubio-López
Format: Article
Language:English
Published: MDPI AG 2025-04-01
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.
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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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