An accurate integral-based scheme for dispersion equation

Abstract

This paper proposes an accurate integral-based scheme for solving dispersion equation. In the newly-proposed scheme the dispersion equation is integrated over a computational element using the quadratic polynomial interpolation function. Then elements are connected by the continuity of first derivative at boundary point of adjacent elements. The newly-proposed scheme is unconditionally stable and preserves a tridiagonal system of equations which can be solved efficiently by the Thomas algorithm. Using the method of fractional steps, the newly-proposed scheme, originally developed for one-dimensional problems, can be extended straightforward to multi-dimensional problems. To investigate the computational performances of the newly-proposed scheme five numerical examples are considered : (i) dispersion of Gaussian concentration distribution in one-dimensional uniform flow, (ii)one-dimensional viscous burger's equation, (iii) pure advection of Gaussian concentration distribution in two-dimensional uniform flow, (iv) pure advection of Gaussian concentration distribution in two-dimensional rigid-body rotating flow and (v) three-dimensional diffusion in a shear flow. In comparison not only with the QUICKEST scheme, fully time-centred implicit QUICK scheme and fully time-centred implicit TCSD scheme for one-dimensional problem but also with the ADI-QUICK scheme, ADI-TCSD scheme and MOSQUITO scheme for two-dimensional problems, the newly-proposed scheme shows convincing computational performances.