Abstract
We show that an explicit method for solving hyperbolic partial differential equations can be applied to a model of a renal tubule to obtain both dynamic and steady-state solutions. Appropriate implementation of this method eliminates numerical instability arising from reversal of intratubular flow direction. To obtain second-order convergence in space and time, we employ the recently developed ENO (Essentially Non-Oscillatory) methodology. We present examples of computed flows and concentration profiles in representative model contexts. Finally, we indicate briefly how model tubules may be coupled to construct large-scale simulations of the renal counterflow system.
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Layton, H.E., Pitman, E.B. A dynamic numerical method for models of renal tubules. Bltn Mathcal Biology 56, 547–565 (1994). https://doi.org/10.1007/BF02460470
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DOI: https://doi.org/10.1007/BF02460470