False diffusion in convection and diffusion with chemical reaction
The effect of the so-called ''false diffusion'' in problems involving diffusion and convection is discussed. The mathematical equation of the problem involves a linear diffusion equation with convection which is given in the form \(C_ t+uC_ x=DC_{xx}-kC\). Using a finite difference scheme the continuous equation is reduced to the difference equation \(C_{j,i}=C_{j-1}+u(\Delta t/\Delta x)(C_{j-1,i-1}-C_{j- 1,i})-kC_{j-1}\Delta t,\) where i and j denote the \(i^{th}\) reaction zone and \(j^{th}\) time step. The author applies the method of moments to obtain the false diffusion coefficient and its effect in unsteady state problems through the above finite difference equation.
linear diffusion equation with convection
scientific article; zbMATH DE number 3866902