Numerical stability problems in hydrodynamic modelling of confluences with small junction angles

Abstract

The paper addresses problems which arise from the use of 3D grids with quadrilateral faces on the horizontal planes in hydrodynamic modelling of discordant beds asymmetrical confluences with small junction angles. There are two sources of instabilities: a) steep gradients that develop near the backward facing step at the tributary entrance to the confluence and b) skewness of the cell faces on the horizontal planes. In previous studies of the concordant beds confluences the junction-angle of 45 was reported as the angle which still provides stable solution. In this paper, the limit value is redefined, and the minimal percentages of the post-confluence channel widening, necessary for obtaining stable solution, are defined for the set of small junction angles. Additionally, the practical consequences of artificial channel widening are discussed in detail. An attempt is made to reconstruct the profiles of the: a) minimal and maximal u-, v- and w- velocity values and b) non-dimensional bed shear stress for the case with no post-confluence channel widening.