Application of symmetry analysis to viscoelastic fluid model

Shagolshem, Sumanta; Bira, B.; Sil, Swarnendu

doi:10.1016/j.cnsns.2023.107417

Cited by 6 publications

(1 citation statement)

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“…However, it can be easily noted that there are not many studies devoted to multicomponent systems of PDEs because essential technical difficulties occur if one intends to find exact solutions for such systems by applying Lie symmetries. Taking into account the above observation, we refer the reader to recent works [18][19][20][21][22][23], devoted to applications of the classical Lie method to the nonlinear three-component systems of PDEs.…”

Section: Introductionmentioning

confidence: 99%

New Lie Symmetries and Exact Solutions of a Mathematical Model Describing Solute Transport in Poroelastic Materials

Cherniha,

Davydovych,

Vorobyova

2024

MCA

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A one-dimensional model for fluid and solute transport in poroelastic materials (PEMs) is studied. Although the model was recently derived and some exact solutions, in particular steady-state solutions and their applications, were studied, special cases occurring when some parameters vanish were not analysed earlier. Since the governing equations are nonintegrable in nonstationary cases, the Lie symmetry method and modern tools for solving ODE systems are applied in order to construct time-dependent exact solutions. Depending on parameters arising in the governing equations, several special cases with new Lie symmetries are identified. Some of them have a highly nontrivial structure that cannot be predicted from a physical point of view or using Lie symmetries of other real-world models. Applying the symmetries obtained, multiparameter families of exact solutions are constructed, including those in terms of elementary and special functions (hypergeometric, Whittaker, Bessel and modified Bessel functions). A possible application of the solutions obtained is demonstrated, and it is shown that some exact solutions can describe (at least qualitatively) the solute transport in PEM. The obtained exact solutions can also be used as test problems for estimating the accuracy of approximate analytical and numerical methods for solving relevant boundary value problems.

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