A numerical method for solving a scalar advection-dominated transport equation with concentration-dependent sources

Minghui Jin, Roseanne M. Ford, Peter T. Cummings
2003 Computers and Chemical Engineering  
A numerical scheme, upstream biased Eulerian algorithm for transport equations with sources (UpBEATES), is developed for solving a scalar advective-dominated transport equation with concentration-independent and -dependent source terms. A controlvolume method is used for spatial discretization. Time integration is invoked to yield a discrete system of integrated-flux-integratedsource form equations. The Bott's upstream-biased Eulerian advection scheme [Moneatry and Weakly Review 117 (1989a)
more » ... ; Moneatry and Weakly Review 117 (1989b) 2633] is employed for approximating advective fluxes. A two-level time weighting scheme is employed for the dispersive fluxes. An upstream-biased Eulerian algorithm is proposed for the concentration-dependent source term. Flux and source limiters are developed to ensure non-negative evolution of the scalar concentration field. Numerical experiments were presented to illustrate its performance in comparison with theoretical solutions and those of conventional methods. The proposed scheme is mass-conservative, produces non-negative concentration values, exhibits low numerical dispersion, and is efficient for advection-dominated problems with concentration-dependent source terms. Like other Eulerian schemes, the Courant Á/Friedrich Á/Levy (CFL) stability criterion has to be met. #
doi:10.1016/s0098-1354(03)00008-5 fatcat:arnsnkkauna4latar6wyn5s4ty