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NUMERICAL APPROXIMATION OF A 1D NONLINEAR CONVECTION-DIFFUSION EQUATION: A MOL-FV FRAMEWORK
Keywords:
method of lines (MOL), finite volume method (FVM), nonlinear convection-diffusion equation, Porous mediaDOI:
https://doi.org/10.17654/0972087126008Abstract
This work proposes a high-order numerical framework for solving one-dimensional nonlinear convection-diffusion equations, in the context of porous media flows using the method of lines (MOL). Spatial discretization is carried out using a finite volume (FV) scheme, and the resulting system of ordinary differential equations is solved by using Scilab ode routine. This strategy avoids the high-degree polynomial approximations and Newton iterations often required by discontinuous Galerkin (DG) methods.
Received: August 30, 2025
Revised: September 10, 2025
Accepted: September 16, 2025
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