Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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 akly Review 117 (1989a) 1006; Moneatry and akly Review 117 (1989b) 2633] is employed for approximating advective fluxes. A two-level time ighting 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-negativ ee volution of the scalar concentration field. Numerical experiments re 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 � /Friedrich � /Levy (CFL) stability criterion has to be met. # 2003 Elsevier Science Ltd. All rights reserved.
['Minghui Jin', 'Roseanne M. Ford', 'Peter T. Cummings']
I am writing a research paper on a idea A numerical method for solving a scalar advection-dominated transport equation with concentration-dependent sources
[{"from": "human", "value": "I am writing a research paper on a idea A numerical method for solving a scalar advection-dominated transport equation with concentration-dependent sources"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: 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\u2019s upstream-biased Eulerian advection scheme [Moneatry and akly Review 117 (1989a) 1006; Moneatry and akly Review 117 (1989b) 2633] is employed for approximating advective fluxes. A two-level time ighting 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-negativ ee volution of the scalar concentration field. Numerical experiments re 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 \ufffd /Friedrich \ufffd /Levy (CFL) stability criterion has to be met. # 2003 Elsevier Science Ltd. All rights reserved."}]