Laserfiche WebLink
<br />27 2 <br />N _ b"x rc~i+1/2 ( +) ex J-1/2 ] <br />FJ-1/2 - ~ t t 2 I/> J-1 I/> J - 2 (I/> J -I/> J-1 ) <br /> <br />(eq. 32) <br /> <br />ex = UA t <br />~x <br /> <br />(eq. 33) <br /> <br />"" <br /> <br />and: <br /> <br />N <br />I/>J <br /> <br />~ <br /> <br />= the conservative quantity being advected at grid <br />point J and time step N <br /> <br />U J = advection velocity at grid point J <br /> <br />b"x = grid spacing (uniform) <br /> <br />~t = ti me step <br /> <br />All quantities occurring at ~1/2 grid intervals in the above equation are determined <br /> <br />by linear interpolation as for example: <br /> <br />U J + U J+ 1 <br />U J+ 1/2 = 2 <br /> <br />(eq. 34) <br /> <br />Hydrometeor Advection Scheme <br /> <br />The above second order Crowley advection scheme was chosen due to its <br /> <br />relative low pseudo-diffusion errors as described by Crowley (1968). When attempting <br /> <br />to use this scheme for particle advection, however, it was found that negative particle <br /> <br />concentrations were sometimes generated near sharp particle gradients. This was <br /> <br />~ <br /> <br />determined to be a property of the advection scheme which of course does not occur <br /> <br />in state parameter advection since state parameter fields are not physically constrained <br /> <br />0' <br /> <br />by reflective boundary conditions at 0.0 values. For this pragmatic reason it was <br /> <br />decided to advect particles via a first order upstream differencing technique rather <br />