Smoothly limited finite-volume modelling of rapidly varying river flows

The Barth-Jespersen (BJ) reconstruction procedure is a well established method to provide oscillation-free, higher-order accuracy to Godunov-type schemes on general unstructured meshes. Their scalar limiter is, however, known to suffer from poor convergence to steady-state with nonsmooth solutions, such as those that occur in rapidly varying river flows. In order to improve convergence, a general smoothing procedure applicable to unstructured limiters is introduced in this paper. In essence, the reconstruction gradually reverts to unlimited gradients for small oscillations in the solution thus reducing the adverse interaction between the limiter and numerical noise. Popular limiters - minmod, superbee, van Leer and van Albada - are also brought to the same BJ formulation so as to suit them to general unstructured meshes and smoothing. The advantage of the new, smoothed BJ limiter is demonstrated by solving a steady, two-dimensional transcritical channel flow problem.