A dynamic numerical method for models of renal tubules.
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.
Layton
H E
HE
Department of Mathematics, Duke University, Durham, NC 27708-0320.
Pitman
E B
EB
D001834:Body Water / Q000378:metabolism; D002137:Calculi; D002463:Cell Membrane Permeability; D003198:Computer Simulation; D004231:Diuresis; D007684:Kidney Tubules / Q000502:physiology*; D008954:Models, Biological; D012212:Rheology