Refined numerical scheme for advective transport in diffusion simulation

We propose an accurate numerical scheme for calculating advection in the simulations of mass, heat, and momentum transport. The second-order spatial derivatives of the advection-diffusion equation can be discretized more accurately by the usual finite-difference approximation than the first-order spatial derivatives. By taking this feature into account, we can expect that the second-order wave equation is more available for numerical calculation of pure advection than the first-order advection equation. However, the second-order wave equation has two types of propagating wave solutions, one of which is unnecessary. To get a unique solution that shows the downstream advection only, the concept of characteristics method is applied. By minimizing truncation errors in the scheme, the parameters involved could be determined as functions of the Courant number. Comparison of this scheme with several others in model calculations proves its superior accuracy and stability. The proposed scheme uses only three grid points in space in case of one-dimensional problems. In addition, this can be easily applied to multidimensional practical problems.