The numerical solution of the flow in a general bifurcating channel at moderately high Reynolds number using boundary‐fitted co‐ordinates, primitive variables and Newton iteration

Abstract

AbstractA numerical code has been implemented for the numerical solution of the steady, incompressible Navier–Stokes equations using primitive variables in a bifurcating channel. A boundary‐fitted, numerically generated grid is placed onto the domain of the channel which is transformed into either a rectilinear C‐ or T‐shaped region. The differenced equations are solved using Newton's iteration which makes upwinding at high Reynolds number unnecessary. Practical implications of inverting the huge Jacobian matrix of Newton's method are discussed. The results have relative error of 2–3 × 10−3 at Reynolds number 100, with T‐geometry being marginally but significantly more accurate than C‐geometry. Results have been obtained for Reynolds numbers up to 1000 for three bifurcations one of which models the carotid arterial bifurcation in the human head. For this latter bifurcation the wall shear stress is calculated in connection with the onset of atherosclerosis. Finally, the results of flows having different daughter tube end pressures are presented.