3.1 Eulerian Approach to Mixing
39
Fig. 3.3 Examples of two
different grids: (Top)
hexahedral grid [2] and
(bottom) tetrahedral grid [38]
is obtained for the velocity field, discrepancies may still exist for the concentration
field due to numerical (or false) diffusion, particularly at large Peclet numbers.
False diffusion can occur in the numerical solution with a poor quality grid,
resulting in overprediction of mixing. Effect of false diffusion on numerical solution was tested by Liu [19] for both tetrahedral and hexahedral grids in a micromixer
designed by Chen and Meiners [20]. It was found that false diffusion in the numerical
solution was more pronounced for tetrahedral cells compared to hexahedral cells, and
the difference was almost one order of magnitude. He recommended to avoid tetrahedral cells for mixing analysis. Also, hexahedral grids need much smaller numbers of
cells, and significantly reduce the computational burden to obtain solutions compared
to tetrahedral grids.
The governing equations are discretized to obtain the system of algebraic equations in a finite-element or finite-volume framework. Choice of discretization scheme
affects the quality of the numerical solution. More details of the discretization and
solution procedure can be found in Patankar [21] and Ferziger and Peric [22]. On the
accuracy of numerical schemes for scalar mixing, Liu [19] showed that higher-order
discretization schemes are less susceptible to numerical diffusion. Standard upwind
39
Fig. 3.3 Examples of two
different grids: (Top)
hexahedral grid [2] and
(bottom) tetrahedral grid [38]
is obtained for the velocity field, discrepancies may still exist for the concentration
field due to numerical (or false) diffusion, particularly at large Peclet numbers.
False diffusion can occur in the numerical solution with a poor quality grid,
resulting in overprediction of mixing. Effect of false diffusion on numerical solution was tested by Liu [19] for both tetrahedral and hexahedral grids in a micromixer
designed by Chen and Meiners [20]. It was found that false diffusion in the numerical
solution was more pronounced for tetrahedral cells compared to hexahedral cells, and
the difference was almost one order of magnitude. He recommended to avoid tetrahedral cells for mixing analysis. Also, hexahedral grids need much smaller numbers of
cells, and significantly reduce the computational burden to obtain solutions compared
to tetrahedral grids.
The governing equations are discretized to obtain the system of algebraic equations in a finite-element or finite-volume framework. Choice of discretization scheme
affects the quality of the numerical solution. More details of the discretization and
solution procedure can be found in Patankar [21] and Ferziger and Peric [22]. On the
accuracy of numerical schemes for scalar mixing, Liu [19] showed that higher-order
discretization schemes are less susceptible to numerical diffusion. Standard upwind