NUMERICAL solution of advection-diffusion using hyperbolic equations

摘要

The conventional advection-diffusion equation representing solute migration is typically solved numerically using either a finite element or finite difference formulation. Herein an alternate solution is presented in which a tune derivative is added to the flux equation, and when coupled with the conservation of mass, produces a pair of hyperbolic differential equations. Computed results are shown to match reasonably well with analytical and alternative numerical solutions. Discrepancies that occur due to the introduction of the artificial time derivative are discussed and means to control them are presented.