Cubic-Spline Interpolation in Lagrangian Advection Computation

In the computation of advection-diffusive contaminant transport, the Holly-Preissmann characteristics scheme for the advection operator is known to be quite accurate and stable. However, these qualities are obtained at the expense of having to solve an auxiliary transport problem for the concentration derivative. This paper shows that the Holly-Preissmann Hermite cubic interpolating polynomial can be replaced by a cubic-spline interpolating polynomial, thus obviating the need to solve the auxiliary problem. Although the cubic-spline approach lacks some of the intuitively appealing features of the Holly-Preissmann approach, it is nearly as accurate while offering a computational time saving of 20%-30%, with a corresponding reduction in code size. The paper outlines the computational procedure, and presents demonstrative calculations illustrating the performance of the method for the familiar test case of advective transport of a Gaussian contaminant distribution.