Specifying the Link Type for Mass Flux Links

There are three types of mass flux links in GoldSim. A mass flux link between two pathways can be defined as a normal link, a previous value link, or a coupled link. When you create a mass flux link, a drop list is available to allow you to select the type of link.

• In a coupled link, the equations for the pathways and their fluxes are solved simultaneously (since they are solved as a system of coupled differential equations as part of a cell net). Only links between Cells can be coupled. The influence representing a coupled link takes on a special shape:

Coupled links can be identified by the small circle at the beginning of the influence.

• In a normal link, at each timestep the “upstream” pathway’s output is computed and then applied to the “downstream” pathway. That is, the mass is propagated asynchronously (i.e., the “upstream” pathway is solved first, followed by the “downstream” one).

• In a previous value link, at each timestep the “upstream” pathway’s output from the previous timestep is applied to the “downstream” pathway. So, like a normal link, the mass is propagated asynchronously (but with a timestep delay).

Mass flux links to or from other types of pathways are defaulted to normal links (and cannot be coupled). Note that only flux links between Cells can be coupled links. Diffusive mass flux links between Cells must be coupled (i.e., the other options are not available in this case).

Note: For advection, solving pathway equations asynchronously (rather than in a coupled manner) is mathematically feasible, since the advective mass flux from one pathway to another is only a function of the concentration in the upstream pathway (i.e., it is not necessary to reference the downstream pathway to compute the mass flux). Although we can model advection by solving the Cells asynchronously (rather than in a coupled manner), doing so can in fact reduce the accuracy of the solution. This is related to the fact that GoldSim effectively subdivides the computational timestep (into fractional timesteps) when solving a cell net to improve accuracy (when the Medium or High Precision setting is selected). “Breaking” a Cell Net and computing fluxes between cells asynchronously effectively reduces the effectiveness of the fractional timesteps, and hence reduces the accuracy somewhat (in the same manner that using the Low Precision setting does). For most systems, using Normal links in a model in several locations (as opposed to throughout the entire model) would be unlikely to affect the results significantly. Using Previous-value links would introduce a more noticeable error (effectively delaying results by a timestep for each Previous-value link in the sequence of Cells). Again, however, for most realistic situations, using Previous-value links a model in several locations is also not likely to affect the results significantly.

There are some special cases, however, when it may be necessary to modify the type of link connecting pathways:

• Changing a coupled or normal mass flux link to a previous value mass flux link: This may be necessary if you are building a looping pathway network.

• Changing a coupled mass flux link to a normal mass flux link: This change is necessary if you wish to "filter" an incoming flux (using a treatment flux link).

• Changing a coupled mass flux link to a normal mass flux link: The computational effort to solve the coupled equations of a large number of Cells increases rapidly (i.e., not linearly) with the number of Cells. In most models, this is not a problem, but for extremely large models (hundreds of Cells), it may be worthwhile to break a very large set of coupled Cells (a Cell Net) into several smaller Cell Nets (by using a Normal link).