Keywords: conservative schemes, integrated flux concept, numerical diffusion, numerical schemes, positive definiteness, rotational and deformational tests, tracer advection
On some explicit advection schemes for dispersion modelling application
The advection scheme TRAP (Trapezium) was elaborated from the Bulgarian dispersion model EMAP (Eulerian Model for Air Pollution), which is a 3-D, PC-oriented multi-layer model. The TRAP scheme is of the Bott type; it is explicit, positively definite and conservative with limited numerical dispersion and good transportivity. Displaying the same properties as Bott's scheme, the TRAP scheme turns out to be faster. In the TRAP scheme, instead of Bott's method of integrating the polynomial fit over the neighbouring grid values, the flux area is supposed trapezoidal. The flux is determined as a product of the Courant number and a single value of the approximating polynomial referring to the middle of the passed distance. The same 4th order polynomial is used and Bott's normalisation is also applied. Some new and faster schemes built in the base of the TRAP and the Integrated Flux concepts are presented and tested here. The performance quality is determined exploiting the rotational test; instantaneous point-shaped and cone-shaped sources are rotated in a 101 X 101 grid point field. A set of criteria is used reflecting suitable characteristics of the advection algorithm. Additional demonstration tests are made over the scheme found to be the best of the set.