An investigation of Eulerian-Lagrangian methods for solving heterogeneous advection-dominated transport problems

Numerical simulation of solute transport in heterogeneous porous media is g reatly complicated by the large velocity and concentration gradients induce d by spatial variations in hydraulic conductivity. Eulerian-Lagrangian meth ods for solving the transport equation can give accurate solutions to heter ogeneous problems if their interpolation algorithms are properly selected. This paper compares the performance of four Eulerian-Lagrangian solvers tha t rely on linear, quadratic, cubic spline, and taut spline interpolators, I n each case a tensor product decomposition is used to reduce the general n- dimensional interpolation problem to a sequence of none-dimensional problem s. Comparisons of a set of test problems indicate that the linear and taut spline interpolators are dispersive while the quadratic and cubic spline in terpolators are oscillatory. The cubic and taut spline interpolators give c onsistently better accuracy than the more conventional linear and quadratic alternatives. Simulation experiments in two- and three-dimensional heterog eneous media indicate that the taut spline interpolator, which is applied h ere for the first time to a solute transport problem, is able to yield accu rate essentially nonoscillatory solutions for high grid Peclet numbers. The cubic spline interpolator requires significantly less computational effort to achieve performance comparable to the other methods.