Improvements And Applications Of SPH Method For Simulating Solute Transport In Heterogeneous Aquifer

The migration process of contaminant in aquifer is a complex process.This is due to the complexity of natural conditions and aquifer and natural aquifers generally have strong heterogeneity.The heterogeneity of aquifer has an important effect on the transport and transformation of nitrogen in groundwater in particular.Compared with homogeneous aquifer,the migration of contaminant in heterogeneous aquifer is more complex.Accurate and efficient simulation of solute transport process in heterogeneous aquifer is the basis for prediction of site contamination and remediation of groundwater.Smoothed particle hydrodynamics(SPH)method,a Lagrangian method,has been found to often perform better than traditional Eulerian schemes for simulating advection dominated solute transport problem when solving advection-dispersion equation(ADE)due to SPH’s ability of eliminating numerical dispersion.However,SPH is subject to numerical errors in heterogeneous aquifers.To improve the accuracy of SPH method in heterogeneous aquifer,this study developed a series of new methods by using numerical solutions,analytical methods and a large number of numerical experiments,and investigated the effectiveness of improved SPH methods for simulating solute transport problems in heterogeneous aquifer.The key findings summarized from the present study include:(1)This study derived numerical model of C-SPH(Corrected SPH,C-SPH)solution for simulating solute transport problem,which has more accurate ADE solutions than SPH does for irregularly distributed particles in heterogeneous aquifer.C-SPH is similar to SPH in theory but uses a modified kernel gradient to construct a SPH approximation of concentration gradients.Performance of SPH and C-SPH with irregularly distributed particles was evaluated by using two numerical cases,including dispersion transport with an analytical solution and advection and dispersion transport with a reference for the evaluation.For each of the two cases,several numerical experiments were conducted using multiple sets of irregularly distributed particles with different levels of particle irregularity due to different levels of heterogeneity of hydraulic conductivity.Numerical results indicate that(a)C-SPH outperforms SPH to yield more accurate ADE solutions,compared with SPH,C-SPH reduces 20%-60% error;(b)the overestimation of maximum concentration at plume center problem in SPH solution is significantly alleviated in the C-SPH solution;(c)However,C-SPH solutions are still subject to numerical errors,and the errors increase when the level of heterogeneity of hydraulic conductivity increases.(2)This study developed a new approach called Interactively Corrected Smoothed Particle Hydrodynamics(IC-SPH)and derived the numerical model of IC-SPH solution for simulating solute transport problem.The new model reduces the errors of C-SPH solution in heterogeneous field of hydraulic conductivity,which is an improved version of the C-SPH model.IC-SPH uses an interactively corrected kernel gradient to construct concentration gradients used to solve ADE.This correction is made for each particle by using not only the particle’s neighbor particles within the particle’s support domain but also the particles within each neighbor particle’s support domain.This study evaluated IC-SPH performance in two numerical studies.One considers dispersion transport with an analytical solution,and the other considers advection-dispersion transport in a heterogeneous field of hydraulic conductivity.For each numerical study,several numerical experiments were conducted using multiple sets of irregularly distributed particles with different levels of particle irregularity.The numerical experiments indicate that,(a)IC-SPH produces more accurate ADE solutions,converges faster to the analytical solution.(b)based on the numerical experiments,IC-SPH reduces 30%-90% error of SPH;(c)the reduced error is obvious for maximum concentration and highly non-uniform velocity field;(d)while IC-SPH is more computationally expensive than SPH and C-SPH,since IC-SPH needs to solve additional matrix equations for correcting kernel gradient;(e)This study suggest using C-SPH and IC-SPH for a wide range of solute transport problems that need high simulation accuracy without considering computational cost.(3)This study developed the Decoupled Finite Particle Method with Normalized Kernel(DFPM-NK)and derived numerical model of DFPM-NK solution for simulating solute transport problem.The new model improves computational accuracy of DFPM model and improves computational efficiency and stability of FPM model while with similar accuracy with FPM model by using normalized kernels in DFPM.Finite particle method(FPM)is an improved SPH method with higher approximate accuracy than SPH.Therefore,FPM also obtained a more accurate ADE solution than SPH method when simulating solute transport in heterogeneous aquifers.FPM however is computationally more expensive than SPH because FPM needs to solve a correction matrix equation for each particle.While decoupled FPM(DFPM)can reduce computational cost of FPM by using diagonal terms of the matrix equation,DFPM is less accurate than FPM due to discarding off-diagonal terms of the matrix equation.This is because concentration and concentration gradient are independently modified(i.e.,the concentration gradient is modified without considering the concentration itself),while concentration and concentration gradient in FPM are simultaneously modified by solving matrix equation.This study developed the Decoupled Finite Particle Method with Normalized Kernel(DFPM-NK)to improve computational accuracy of DFPM by using normalized kernels in DFPM.This study evaluated computational performance of SPH,FPM,DFPM,and DFPM-NK by using two numerical experiments of ADE with dispersion and advection dispersion transport in a heterogeneous aquifer.Results of the two experiments indicate that,(a)among the four methods,SPH has the least computational time,but has the worst computational accuracy;(b)DFPM-NK is substantially more efficient than FPM,saves 70% ～ 87% CU time of FPM,and has similar accuracy of FPM;(c)DFPM-NK and DFPM have similar computational cost,but DFMP-NK is significantly more accurate than DFPM,especially for heterogeneous hydraulic conductivity fields;(d)This study thus recommend using DFPM-NK for computationally expensive solute transport problems without sacrificing computational accuracy(compared with FPM).(4)The proposed DFPM-NK method was applied to the nitrogen transport and transformation model in heterogeneous aquifer,and analyzed the effect of aquifer heterogeneity on nitrate transport and removal.Before applying this method to nitrogen model,simple reactive solute transport problems were used to verify DFPM-NK’s simulation accuracy for simulating reactive solute transport problems.Simple reactions include first-order chemical reactions in homogeneous aquifer and aerobic respiration bimolecular reactions in heterogeneous aquifer.The accuracy of DFPM-NK was verified by analytical solution and numerical reference solution for the two models,respectively.Then,a numerical model of nitrogen migration and transformation in heterogeneous aquifer(heterogeneous permeability and porosity)was established to analyze the effect of aquifer heterogeneity on nitrate migration and removal.The results show that(a)the removal rate of nitrate in aquifer increases with the increase of permeability heterogeneity;(b)considering the heterogeneity of porosity,the nitrate removal rate will be reduced and the time of nitrate reaching the observation point will be delayed;(c)if the heterogeneity of aquifer permeability is not considered,the nitrate removal rate will be underestimated;(d)in the case permeability heterogeneity,if the heterogeneity of porosity is not considered,the nitrate remove rate will be overestimated,and the time of nitrate reaching observation point will be early estimated if the porosity heterogeneity is not considered.The results of this thesis provide new numerical methods for simulation of pollutant migration process in groundwater and enrich the numerical models for simulating solute transport.