Analysis of the Burgers–Huxley Equation Using the Nondimensionalisation Technique: Universal Solution for Dirichlet and Symmetry Boundary Conditions

  1. Sánchez-Pérez, Juan Francisco 1
  2. Solano-Ramírez, Joaquín 1
  3. Castro, Enrique 1
  4. Conesa, Manuel 1
  5. Marín-García, Fulgencio 1
  6. García-Ros, Gonzalo 1
  1. 1 Universidad Politécnica de Cartagena
    info

    Universidad Politécnica de Cartagena

    Cartagena, España

    ROR https://ror.org/02k5kx966

Aldizkaria:
Axioms

ISSN: 2075-1680

Argitalpen urtea: 2023

Alea: 12

Zenbakia: 12

Mota: Artikulua

DOI: 10.3390/AXIOMS12121113 GOOGLE SCHOLAR lock_openSarbide irekia editor

Beste argitalpen batzuk: Axioms

Objetivos de desarrollo sostenible

Laburpena

The Burgers–Huxley equation is important because it involves the phenomena of accumulation, drag, diffusion, and the generation or decay of species, which are common in various problems in science and engineering, such as heat transmission, the diffusion of atmospheric contaminants, etc. On the other hand, the mathematical technique of nondimensionalisation has proven to be very useful in the appropriate grouping of the variables involved in a physical–chemical phenomenon and in obtaining universal solutions to different complex engineering problems. Therefore, a deep analysis using this technique of the Burgers–Huxley equation and its possible boundary conditions can facilitate a common understanding of these problems through the appropriate grouping of variables and propose common universal solutions. Thus, in this case, the technique is applied to obtain a universal solution for Dirichlet and symmetric boundary conditions. The validation of the methodology is carried out by comparing different cases, where the coefficients or the value of the boundary condition are varied, with the results obtained through a numerical simulation. Furthermore, one of the cases presented presents a boundary condition that changes at a certain time. Finally, after applying the technique, it is studied which phenomenon is predominant, concluding that from a certain value diffusion predominates, with the rest being practically negligible.

Erreferentzia bibliografikoak

  • Appadu, (2022), Front. Appl. Math. Stat., 7, pp. 1, 10.3389/fams.2021.773733
  • Hashim, (2006), Math Comput. Model, 43, pp. 11, 10.1016/j.mcm.2005.08.017
  • Wen, Y., and Chaolu, T. (2023). Study of Burgers–Huxley Equation Using Neural Network Method. Axioms, 12.
  • Hemel, (2021), J. Appl. Math. Phys., 9, pp. 1351, 10.4236/jamp.2021.96092
  • Madrid, C., and Alhama, F. (2012). Análisis Dimensional Discriminado en Mecánica de Fluidos y Transferencia de Calor, Editorial Reverté.
  • Cengel, Y.A., and Cimbala, J.M. (2018). Fluid Mechanics, Fundamentals and Applications, McGraw-Hill Education. [4th ed.]. no. 5.
  • Bejan, A. (1984). Convection Heat Transfer, Wiley-Interscience.
  • Bejan, A., and Kraus, A.D. (2003). Heat Transfer Handbook, John Wiley & Sons. no. 3.
  • Kreith, F., Manglik, R.M., and Bohn, M.S. (1999). Principles of Heat Transfer, Cengage Learning. [7th ed.].
  • Heinrich, (1987), ZAMM—J. Appl. Math. Mech./Z. Angew. Math. Mech., 67, pp. 212, 10.1002/zamm.19870670331
  • Alhama, (1998), Numeri. Heat Transf. A Appl., 33, pp. 549, 10.1080/10407789808913954
  • Nigri, (2022), Therm. Sci. Eng. Prog., 32, pp. 101333, 10.1016/j.tsep.2022.101333
  • Albani, (2015), Atmos. Environ., 118, pp. 19, 10.1016/j.atmosenv.2015.07.036
  • Ku, (1987), Atmos. Environ., 21, pp. 201, 10.1016/0004-6981(87)90287-3
  • Moradpour, (2017), Atmos. Pollut. Res., 8, pp. 253, 10.1016/j.apr.2016.09.002
  • Fenaux, M. (2013). Modelling of Chloride Transport in Non-Saturated Concrete: From Microscale to Macroscale. [Ph.D. Thesis, E.T.S.I. Caminos, Canales y Puertos (UPM)].
  • Fenaux, M.M.C., Reyes, E., Moragues, A., and Gálvez, J.C. (2013, January 10–14). Modelling of chloride transport in non-saturated concrete. From microscale to macroscale. Proceedings of the 8th International Conference on Fracture Mechanics of Concrete and Concrete Structures, FraMCoS 2013, Toledo, Spain.
  • Pradelle, (2016), Mater. Struct./Mater. Constr., 49, pp. 4497, 10.1617/s11527-016-0803-y
  • Climent, (2011), Constr. Build. Mater., 25, pp. 785, 10.1016/j.conbuildmat.2010.07.005
  • Meijers, (2005), Mater. Struct./Mater. Constr., 38, pp. 145, 10.1007/BF02479339
  • Nielsen, (2003), Cem. Concr. Res., 33, pp. 133, 10.1016/S0008-8846(02)00939-0
  • Pantazopoulou, (2001), Comput. Struct., 79, pp. 1251, 10.1016/S0045-7949(01)00018-9
  • Fang, (2017), N. J. Phys., 19, pp. 053007, 10.1088/1367-2630/aa6d49
  • Sheng, (2021), J. Sound. Vib., 492, pp. 115739, 10.1016/j.jsv.2020.115739
  • Fu, (2023), Front. Phys., 11, pp. 1108505, 10.3389/fphy.2023.1108505
  • Yasmin, H., Aljahdaly, N.H., Saeed, A.M., and Shah, R. (2023). Investigating Families of Soliton Solutions for the Complex Structured Coupled Fractional Biswas–Arshed Model in Birefringent Fibers Using a Novel Analytical Technique. Fractal Fract., 7.
  • Rodriguez, (2019), Chaos Solitons Fractals, 118, pp. 41, 10.1016/j.chaos.2018.10.031
  • Zhang, (2023), Results Phys., 50, pp. 106549, 10.1016/j.rinp.2023.106549
  • Alhama, (2020), Commun. Nonlinear Sci. Numer. Simul., 84, pp. 105201, 10.1016/j.cnsns.2020.105201
  • Sánchez-Pérez, J.F., García-Ros, G., Conesa, M., Castro, E., and Cánovas, M. (2023). Methodology to Obtain Universal Solutions for Systems of Coupled Ordinary Differential Equations. Examples of a Continuous Flow Chemical Reactor and a Coupled Oscillator. Mathematics, 11.
  • Conesa, M., Sánchez-Pérez, J.F., García-Ros, G., Castro, E., and Valenzuela, J. (2023). Normalization Method as a Potent Tool for Grasping Linear and Nonlinear Systems in Physics and Soil Mechanics. Mathematics, 11.
  • Sánchez-Pérez, J.F., Marín-García, F., Castro, E., García-Ros, G., Conesa, M., and Solano-Ramírez, J. (2023). Methodology for Solving Engineering Problems of Burgers–Huxley Coupled with Symmetric Boundary Conditions by Means of the Network Simulation Method. Symmetry, 15.
  • Sánchez-Pérez, J.F., Marín, F., Morales, J.L., Cánovas, M., and Alhama, F. (2018). Modeling and simulation of different and representative engineering problems using network simulation method. PLoS ONE, 13.
  • Castro, (2021), Alex. Eng. J., 60, pp. 4627, 10.1016/j.aej.2021.03.058
  • Alhama, (2019), Results Phys., 12, pp. 1015, 10.1016/j.rinp.2018.12.066
  • Hussin, (2016), J. Teknol., 78, pp. 13