A Tikhonov Regularisation Approach to the Numerical Solution of Pipe Flows

Pipe flow problems deal with flows within tubes and are studied through Fluid Dynamics models. When considering pipe flow problems, turbulence often needs to be taken into account. Unfortunately, turbulence gives rise to difficulties in the computation of the approximated solution to such pipe flow problems, due to ill-conditioning. We propose an original stabilisation strategy based on Tikhonov regularisation for ill-posed problems. Some analytical insights on the applicability of this strategy are given, and its effectiveness is shown by a numerical experiment where the results of the proposed method are compared with the ones of a well-known solving strategy and an empirical solution for the axial velocity.