ABSTRACT
IJu(x, t) IJu(x,, t) _ 0 8t +v 8x - (4.8)
Equations (4.2), (4.6), (4.7) and (4.8) constitute a complete convective diffusion problem, and a solution can be computed by the method of lines; for example, the convective derivative, 8ufi:Jx, can be computed by the five-point biased upwind approximations in DSS020, and the diffusive derivative, lfZujlJx2, can be computed by the five-point centered approximations in DSS044. In fact this has been done [Silebi et al. (1992)] for a more general form of equation (4.2)
8u 8u lfZu lJt + v I:Jx = D IJxl - r(u,x, t) (4.9)
Equations (4.2), (4.6), (4.7) and (4.8) are all linear, and therefore in principle, can be solved analytically. In practice this could prove to be difficult, but a numerical solution is straightforward. If r(u,x,t) is nonlinear in u, which is often the case for chemical reactions, equations (4.6), (4.7), (4.8) and (4.9) are essentially impossible to
Figure 4.1 Incremental Volume of Fluid in Cartesian Coordinates.
