A linearization technique for multi-species transport problems

Abstract

We study a one-dimensional multi-species system of dispersive-advective contaminant transport equations coupled by nonlinear biological (kinetic reactions) and physical (adsorption) processes. To deal with the nonlinearities and the coupling, and to avoid additional computational costs, we propose a linearization technique based on first-order Taylor's series expansions. A stabilized finite element in space, combined with an Euler implicit finite difference discretization in time, is used to approximate the dispersive-advective transport problem. Three computational tests are performed with different boundary conditions, retardation factors and kinetic parameters for a nonlinear reactive multi-species transport model. The proposed methodology is shown to be accurate and decrease computational costs in the numerical implementation of nonlinear reactive transport problems.

Numerical simulation of BOD5 dynamics in Igapó I lake, Londrina, Paraná, Brazil: Experimental measurement and mathematical modeling

“…represents the BOD 5 concentration, u and v are the speed obtained by the hydrodynamic model, The Semi-Discrete Stabilized Finite Element, a method that combines finite differences in time and finite elements in space (ROMEIRO et al, 2007;MALTA;CASTRO, 2010, LADEIA, C. A. et al, 2013, was used to resolve the model presented in eq. (4) under a null initial condition and a frontier condition given by…”

“…In the context of Lake Igapo, we consider a mathematical modeling in which the hydrodynamic model is decoupled from the transport model. Thus, the BOD 5 transport simulation was carried out by an advection-dispersionreaction two-dimensional model given by The Semi-Discrete Stabilized Finite Element, a method that combines finite differences in time and finite elements in space (ROMEIRO et al, 2007;MALTA;CASTRO, 2010, LADEIA, C. A. et al, 2013, was used to resolve the model presented in eq. ( 4) under a null initial condition and a frontier condition given by…”

“…The MAC (Marker-and-Cell) Method was the technique used to solve the system of equations (AMSDEN;HARLOW, 1970). To transport model, the Semi-Discrete Stabilized Finite Element (SDSFE), a method that combines finite differences in time and finite elements in space (DONEA;HUERTA, 2003;ROMEIRO et al, 2007;MALTA;CASTRO, 2010), was used. The Navier-Stokes velocity field was used as entry data in the transport model.…”

Formulações Semi-Discretas para a Equação 1D de Burgers

“…Devidoà vasta aplicabilidade destas pesquisas em problemas que envolvem processos convectivos e difusivos [7,9,10,13,20,21], interessa-nos as formulações numéricas que possam ser aplicadas a estes problemas, em especialà equação de Burgers [5,6,7,8,15,16,24,25].…”

Avaliação de Três Formas de Soluções de Sistemas de Equações de Transporte Advectivo-difusivo com Decaimento

“…Existem diversos modelos analíticos cujos sistemas de ETAD com decaimento empregam uma cinética simplificada de primeira ordem [7,15,16,5,17]. Romeiro (2003) utilizou a primeira ordem da expansão em série de Taylor nos termos não lineares de um modelo unidimensional de ETAD de tal forma a lineariza-los [11], comparou as soluções numéricas dos modelos usando coeficientes de decaimento não lineares e linearizados e utilizou uma generalização da solução analítica para verificar a aplicabilidade do modelo linearizado [12,13,14]. Desta forma, os termos dos processos de reações no sistema de ETAD com decaimento podem ser descritos com coeficientes lineares de primeira ordem ou não lineares do tipo Monod.…”