Symmetry analysis, invariant subspace and conservation laws of the equation for fluid flow in porous media

Abdullahi Yusuf

2020International Journal of Geometric Methods in Modern Physics24 citationsDOI

Abstract

The equation for fluid flow in porous media is analyzed in this paper with the aid of Lie symmetry method (LSM) and invariant subspace method (ISM). Infinitesimal generators, the entire geometric fields of the vectors and the symmetry groups of the equation being considered are given. One-dimensional optimal systems of sub-algebra are reported with corresponding reduced nonlinear ordinary differential equations. By means of ISM, we determine the exact solutions and invariant subspaces (ISs) for the equation under consideration. Moreover, with the aid of the new theorem of conservation, we establish the conservation laws (CLs) for the governing equation. The construction of the conserved vectors reveals the integrability and existence of soliton solutions of the equation for fluid flow in porous media.

Topics & Concepts

Conservation lawPartial differential equationInvariant (physics)MathematicsInvariant subspaceInfinitesimalFluid dynamicsLinear subspaceOrdinary differential equationDifferential equationMathematical analysisFlow (mathematics)Porous mediumMathematical physicsPure mathematicsPhysicsGeometryQuantum mechanicsPorosityGeotechnical engineeringEngineeringNonlinear Waves and SolitonsFractional Differential Equations SolutionsNumerical methods for differential equations