111Equation Chapter 1 Section 1 CompuCell3d reference Manual Version 4
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- AdvectionDiffusionSolver.
DiffusionSolverFEDiffusionSolverFE is new solver in 3.6.2 and is intended to fully replace FlexibleDiffusuionSolverFE. It eliminates several limitations and inconveniences of FlexibleDiffusionSolverFE and provides new features such as GPU implementation or cell type dependent diffusion/decay coeeficcients. In addition it also eliminates the need to rescale diffusion/decay/secretion constants. It checks stability condition of the PDE and then rescales appropriately all coeeficients and computs how many extra times per MCS the solver has to be called. It makes those extra calls automatically. One of the key differences FlexibleDiffusionSolverFE and DiffusionSolverFE is the way in which secretion is treated. In FlexibleDiffusionSolverFE all secretion amount is done once followed by possibly multiple diffusion calls to diffusion (to avoid numerical instabilities). In DiffusionSolverFE the default mode of operation is such that multiple secretion and diffusion calls are interleaved. Meaning that instead of secreting full amount for a given MCS and diffusing it, the DiffusionSolverFE secretes substance gradually so that there is equal amount of secretion before each call of the diffusion. One can change this behavior by adding … With such definition the DiffusionSolverFE will behave like FlexibleDiffusionSolverFE as far as computation. Remark: DiffusionSolverFE autoscales diffusion discretization depending on the lattice so that This may result in slow performance so users have to be aware that those extra calls to the solver may be the cause. Typical syntax for the DiffusionSolverFE may look like example below: The syntax resembles the syntax for FlexibleDiffusionSolverFE. We specify global diffusion constant by using Similar principles apply to decay constant and we use to override global definition for regions occupied by Red cells. We do not support with
AdvectionDiffusionSolver.Remark: This is an experimental module and was not fully curated. This steppable solves advection diffusion equation on a cell field as opposed to grid. Of course, the inaccuracies are bigger than in the case of PDE being solved on the grid but on the other hand solving the PDE on a cell field means that we associate cocentration with a given cell (not just with a lattice point). This means that as cells move so does the concentration. In other words we get advection for free. The mathematical treatment of this kind of approximation was spelled out in Phys. Rev. E 72, 041909 (2005) paper by D.Dan et al. The equation solved by this steppable is of the type:
where denotes concentration , is diffusion constant, decay constant, is velocity field. In addition to just solving advection-diffusion equation this module allows users to specify secretion rates of the cells as well as different secretion modes. The syntax for this module follows same apttern as FlexibleDiffusionSolverFE. Example syntax: Download 0.81 Mb. Share with your friends:
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