A dynamic numerical method for models of renal tubules |
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Authors: | H. E. Layton E. Bruce Pitman |
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Affiliation: | (1) Department of Mathematics, Duke University, Box 90320, 27708-0320 Durham, NC, U.S.A.;(2) Department of Mathematics, State University of New York, 14214-3093 Buffalo, NY, U.S.A. |
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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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