Upwinding parameter

After the aussembly of elemental equations into a global set and imposition of the boundary conditions the final solution of the original differential equation with respect to various values of upwinding parameter jS can be found. The analytical solution of Equation (2.80) with a = 50 is found as... 

The finite element results obtained for various values of (3 are compared with the analytical solution in Figure 2.27. As can be seen using a value of /3 = 0.5 a stable numerical solution is obtained. However, this solution is over-damped and inaccurate. Therefore the main problem is to find a value of upwinding parameter that eliminates oscillations without generating over-damped results. To illustrate this concept let us consider the following convection-diffusion equation... 

Figure 5.4 Laser-doppler anemometer profiles of mean velocity in and above a wind tunnel model study of flow over an isolated sinusoidal two-dimensional ridge covered with a tall canopy. Profiles are located upwind (x = -2L, dot dash line) on the hilltop (solid line) and downwind (x = +2L, dotted line). The hill parameters were H/L = 0.1 hc/H = 1.0. Full details of the experiment can be obtained from the author (Finnigan and Hughes, pers. comm.)...

Both point-by-point and line-by-line overrelaxation methods were used to resolve the algebraic equations. ° An overrelaxation parameter of 1.5-1.8 was typically used. The two methods required similar computational times. An upwind scheme was used for all variables for high-Pe problems, while a central-difference scheme was used for low Pe. For some high-Pe cases, a central-difference scheme was used for the potential, but no appreciable differences in the results were observed. 

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