Analysis and mitigation of post-bore noises in modeling mixed flows in closed conduits

In this paper, the author analyzes the post-bore noise problem in mixed pipe-flow modeling, which uses shock-capturing methods within single-equation frameworks. The study reveals that the origin of these numerical noises following pipe-filling is the sudden jump from the free-surface gravity wave speed c to a significantly higher constant pipe acoustic wave speed ac during surcharging. This abrupt transition results in an excessively large Laplacian type numerical dissipation, which overwhelms the physical fluxes, reverses their directions, and leads to significant decreases in mass and momentum, particularly at the bore front where the concavity of the conserved variable is not small in a relatively sharp bore profile, and periodically manifest at the bore front following the initial pressurization of a cell. Based on the analyses of the above origin and underlying mechanisms, the author proposes a novel noise-mitigation technique: the post-bore oscillation mitigation (PBOM) approach, which diminishes the concavity of the shock profile by allowing the ventilated cells ahead of the bore to fill more rapidly, and introduces a new smooth transient function for signal wave speed to prevent a sudden jump in the numerical viscosity coefficient. Some preliminary tests validate this proposed noise-mitigation approach.