Some fast variants of TRAP scheme for solving advection equation — comparison with other schemes

The advection scheme TRAP was elaborated for the Bulgarian three-dimensional PC-oriented Eulerian air pollution model. The TRAP scheme uses polynomial fit of concentration profile as the BOTT scheme but differs from it in calculating fluxes. Instead of integrating the polynomial fit over the neighboring grid values as in the BOTT scheme, the flux area is supposed to be trapezoidal and is determined as a product of the Courant number and a single value of the approximation polynomial referring the middle of the passed distance. The obtained scheme is explicit, positively definite and conservative with limited numerical dispersion and good transport ability. Displaying the same properties as the BOTT scheme, the TRAP scheme turns out to be several times faster. Following the TRAP approach some schemes are developed and presented. Some of them are obtained by optimization of the so-called “normalization” procedure. Second- and third-order polynomials are used for fitting concentration profile around each grid point. The performance quality of these as well as of some other well-known schemes is determined by exploiting the rotation and deformation tests. Recommendations for the proper usage of different schemes are made. Finally, an approach for treating non-homogeneous grids with advection schemes developed for the homogeneous ones is described and demonstrated on the TRAP scheme.