Methodology for Solving Engineering Problems of Burgers–Huxley Coupled with Symmetric Boundary Conditions by Means of the Network Simulation Method
The Burgers–Huxley equation is a partial differential equation which is based on the Burgers equation, involving diffusion, accumulation, drag, and species generation or sink phenomena. This equation is commonly used in fluid mechanics, air pollutant emissions, chloride diffusion in concrete, non-li...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/9/1740 |
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| author | Juan Francisco Sánchez-Pérez Fulgencio Marín-García Enrique Castro Gonzalo García-Ros Manuel Conesa Joaquín Solano-Ramírez |
| author_facet | Juan Francisco Sánchez-Pérez Fulgencio Marín-García Enrique Castro Gonzalo García-Ros Manuel Conesa Joaquín Solano-Ramírez |
| author_sort | Juan Francisco Sánchez-Pérez |
| collection | DOAJ |
| description | The Burgers–Huxley equation is a partial differential equation which is based on the Burgers equation, involving diffusion, accumulation, drag, and species generation or sink phenomena. This equation is commonly used in fluid mechanics, air pollutant emissions, chloride diffusion in concrete, non-linear acoustics, and other areas. A general methodology is proposed in this work to solve the mentioned equation or coupled systems formed by it using the network simulation method. Additionally, the implementation of the most common possible boundary conditions in different engineering problems is indicated, including the Neumann condition that enables symmetry to be applied to the problem, reducing computation times. The method consists mainly of establishing an analogy between the variables of the differential equations and the electrical voltage at a central node. The methodology is also explained in detail, facilitating its implementation to similar engineering problems, since the equivalence, for example, between the different types of spatial and time derivatives and its correspondence with the electrical device is detailed. As an example, several cases of both the equation and a coupled system are solved by varying the boundary conditions on one side and applying symmetry on the other. |
| first_indexed | 2024-03-10T21:54:40Z |
| format | Article |
| id | doaj.art-8e12f2e6e99c4e7c8323402e272b63b2 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T21:54:40Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-8e12f2e6e99c4e7c8323402e272b63b22023-11-19T13:11:59ZengMDPI AGSymmetry2073-89942023-09-01159174010.3390/sym15091740Methodology for Solving Engineering Problems of Burgers–Huxley Coupled with Symmetric Boundary Conditions by Means of the Network Simulation MethodJuan Francisco Sánchez-Pérez0Fulgencio Marín-García1Enrique Castro2Gonzalo García-Ros3Manuel Conesa4Joaquín Solano-Ramírez5Department of Applied Physics and Naval Technology, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, SpainDepartment of Automation Engineering, Electrical Engineering and Electronic Technology, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, SpainDepartment of Applied Physics and Naval Technology, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, SpainDepartment of Mining and Civil Engineering, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, SpainDepartment of Applied Physics and Naval Technology, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, SpainDepartment of Thermal Engineering and Fluids, Universidad Politécnica de Cartagena (UPCT), 30202 Cartagena, SpainThe Burgers–Huxley equation is a partial differential equation which is based on the Burgers equation, involving diffusion, accumulation, drag, and species generation or sink phenomena. This equation is commonly used in fluid mechanics, air pollutant emissions, chloride diffusion in concrete, non-linear acoustics, and other areas. A general methodology is proposed in this work to solve the mentioned equation or coupled systems formed by it using the network simulation method. Additionally, the implementation of the most common possible boundary conditions in different engineering problems is indicated, including the Neumann condition that enables symmetry to be applied to the problem, reducing computation times. The method consists mainly of establishing an analogy between the variables of the differential equations and the electrical voltage at a central node. The methodology is also explained in detail, facilitating its implementation to similar engineering problems, since the equivalence, for example, between the different types of spatial and time derivatives and its correspondence with the electrical device is detailed. As an example, several cases of both the equation and a coupled system are solved by varying the boundary conditions on one side and applying symmetry on the other.https://www.mdpi.com/2073-8994/15/9/1740mathematical modellingsimulationnetwork simulation methodcoupled differential equationsengineering sciencesymmetry |
| spellingShingle | Juan Francisco Sánchez-Pérez Fulgencio Marín-García Enrique Castro Gonzalo García-Ros Manuel Conesa Joaquín Solano-Ramírez Methodology for Solving Engineering Problems of Burgers–Huxley Coupled with Symmetric Boundary Conditions by Means of the Network Simulation Method Symmetry mathematical modelling simulation network simulation method coupled differential equations engineering science symmetry |
| title | Methodology for Solving Engineering Problems of Burgers–Huxley Coupled with Symmetric Boundary Conditions by Means of the Network Simulation Method |
| title_full | Methodology for Solving Engineering Problems of Burgers–Huxley Coupled with Symmetric Boundary Conditions by Means of the Network Simulation Method |
| title_fullStr | Methodology for Solving Engineering Problems of Burgers–Huxley Coupled with Symmetric Boundary Conditions by Means of the Network Simulation Method |
| title_full_unstemmed | Methodology for Solving Engineering Problems of Burgers–Huxley Coupled with Symmetric Boundary Conditions by Means of the Network Simulation Method |
| title_short | Methodology for Solving Engineering Problems of Burgers–Huxley Coupled with Symmetric Boundary Conditions by Means of the Network Simulation Method |
| title_sort | methodology for solving engineering problems of burgers huxley coupled with symmetric boundary conditions by means of the network simulation method |
| topic | mathematical modelling simulation network simulation method coupled differential equations engineering science symmetry |
| url | https://www.mdpi.com/2073-8994/15/9/1740 |
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