has characteristic modelling and simulation algorithm spatial description deterministic system behaviour continuous variable progression with fixed time step approximate solution Lagrangian sliding fluid element algorithm 2011-05-11 http://identifiers.org/biosimulators/jsim http://identifiers.org/pubmed/1449234 AZ BTEX Because the analytic solutions to the partial differential equations require convolution integration, solutions are obtained relatively efficiently by a fast numerical method. Our approach centers on the use of a sliding fluid element algorithm for capillary convection, with the time step set equal to the length step divided by the fluid velocity. Radial fluxes by permeation between plasma, interstitial fluid, and cells and axial diffusion exchanges within each time step are calculated analytically. The method enforces mass conservation unless there is regional consumption. LSFEA blood-tissue exchange method partial differential equation problem