Comparison between MPDATA and High Order Upwind Compact Finite Difference Methods in Air Pollutants Dispersion Modeling

In this paper high order multidimensional positive definite advection transport algorithm (MPDATA) and compact finite difference methods are applied to one (1-D) and two-dimensional (2-D) advection equation. MPDATA methods are designed based on upwind scheme using anti-diffusive velocity that compensates diffusivity of upwind method. In high order compact method one implicit relation between a function and its first derivative is added to the governing equation of flow and this combination increases the accuracy of the method. In the present study, the grid study is carried out at 11, 21, 41, 81, 161, 321, and 641 grid points in 1-D case. Also, the number of grid points in 2-D case are , , , , and for MPDATA method and , , and for compact scheme. Two important characteristics of numerical schemes are investigated. First, the accuracy of two mentioned methods is compared together. It shows that in 1-D case the accuracy of MPDATA scheme at 641 grid points is approximately equal to the accuracy of compact method at 161 grid points. In 2-D case this comparison shows that the accuracy of MPDATA scheme at grid points is approximately equal to the accuracy of compact method at grid points. Second, the comparison of computational cost of two methods shows that the computational cost of compact method is 333 and 306 times of MPDATA scheme computational cost in 1-D and 2-D cases, respectively.