A Lagrangian Particle Model For Convection-Diffusion-Reaction Problems

Due to the continuous growth of population and the rapid development of various industries,some obvious negative impacts are arising.Various environmental problems are emerging,including air pollution,water pollution,land desertification and sand disasters,soil erosion,drought and floods,etc.,and affecting people's daily work and life.Thus,it is of great importance to solve the environmental pollution problems.The research on the behavior of pollutant transport depends on accurately solving the convection-diffusion-reaction equation.There are two main categories of numerical methods for solving the convection-diffusion-reaction equation.One is the grid-based Eulerian method and the other is the meshless Lagrangian method.This paper provided detailed introduction to both of them.For the Eulerian method,the finite volume methods with ten common fluxes are selected for numerical experiments for the autocatalytic reaction flow model.Numerical results show that the MTVDLF scheme with Superbee limiter can eliminate the numerical dissipation and numerical oscillation existed in traditional methods.It is considered to be the best one among the tested Eulerian methods for the convection-diffusion-reaction problems.For the meshless method,Smoothed Particle Hydrodynamics(SPH)is introduced in this paper.It overcomes the boundary deficiency problem by adding virtual particles.It is used to discretized the spatial derivatives in the governing equations.By comparing the calculation results of two kinds of methods in several numerical examples.It is seen that the SPH method is more effective than the grid-based methods.No numerical diffusion and unphysical oscillation are observed.At the same time,four time-integration algorithms are applied to the linear reaction flow problem with one reactant,and the comparison results show that the fourth-order Runge-Kutta method has higher accuracy than the other three algorithms.In addition,based on Web technique,an easy-to-operate,expansile,well-interacting simulation system for convection-diffusion-reaction problem is developed,which uses hybrid programming with Java and Matlab.After applying the corresponding conditions and parameters according to specific problems,the calculation data and simulation results can be obtained.This on-line system can greatly facilitate and assist researchers to carry out relevant numerical experiments with lower manpower and material resources.