Numerical Approximation of a 1d Nonlinear Convection-Diffusion Equation: A Mol-Fv Framework

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.