SOLUTION OF ADVECtION-DOMINATED TRANSPORT

We provide a s:lfstemat.1c analysts of thl:: consistency. stability. convergence and accuracy of the numerical solution of the transport equation by a general Eulerian-Lagrangian Method (ELM). Tbe method involves three basic steps: the backwards trackln~ of characteristIc lines follo\1ing the flow. the interpolation of concentrations at the feet of these lines. and the solution of dispersion takirag su.:::h concentrations as ini tial conditions. The first two steps constitute the Backwards Method of Characteristics (BMC): the third step In'folves a time-discretization along the characteristic l{nes, and a spatial c.'lscret1zation of the dispersion. operator. both based on conventional techn~queF (e.g~. Euler or CrankNicholson for t~me: finite-elements or finite-differences for space). The choice of the spatial interpolator is shown to impact the consistency, ~tab111ty and converg~nce. as well as the accuracy of the BMC. Most interpolators ensure consistency. but only a few ensure stability. hence convergence: stability criteria are derived from a newly developed generalized Fourier analysis, which can account for non-linearities introduced by quadratic grids. The comparison or formally derived propagation and truncation errors, complemented by numerical experimentation, provides a rererence for the choice of t~e interpolator, given a specific transport problem characterized by prevailing concentration gradients. The BMC potentiates the use of large time-steps, well above Courant number of order one. In the limiting case or pure advection. optimal accuracy would be obtained Cor a At close to the total time of interest; the presence of dispersion constrains, however, the !Size of At. especially in the case of non-uniform flows. The comparison of the truncation errors for the three bastc steps of ELM prOVides a reference to select At. as a function ofAx Cl or the spatial l;tterpolators and time....dlscretizat1on schemes. and of the gradients of flow and concentrations. Thesis Supervisor: Dr. Keith D. Stolzenbach Title: Associate ProCessor of Civil Engineering Thesis Supervisor: Dr. E. Eric Adams Title: Principal Research Engineer and Lecturer