Exponential Interpolation in Characteristic Based Scheme for Solving the Advective-diiusion Equation

This paper demonstrates the use of shape-preserving exponential interpolation in a characteristic based numerical scheme for the solution of the linear advective-diiusion equation. The results from this scheme are compared with results from a number of numerical schemes in current use using test problems in one-and two-dimensions. These test cases are used to assess the merits of using shape-preserving interpolation in a characteristic based scheme. The evaluation of the schemes is based on accuracy, eeciency and complexity. The use of the shape-preserving interpolation in a characteristic based scheme is accurate, captures discontinuities, does not introduce spurious oscillations and preserves the monotonicity and positivity properties of the exact solution. However, tting exponential interpolants to the nodal concentrations is computationally expensive. Exponential interpolants were also tted to the integral of the concentration proole. The integral of the concentration proole is a smoother function than the concentration proole. It requires less computational eeort to t an exponential interpolant to the integral than the nodal concentrations. By diierentiating the interpolant, the nodal concentrations are obtained. This results in a more eecient and more accurate numerical scheme.