Improved Modeling of Flows in Sewer Pipes with a Novel, Well-Balanced MUSCL Scheme

The numerical study in this paper aims at obtaining exact well-balance and improving the computational accuracy, efficiency, and the performance at wet–dry fronts, especially for the flows in ventilated sewer pipes. To this end, a novel numerical model for mixed flows in a circular-shaped sewer is proposed. The major contributions of this study are: (1) a MUSCL scheme (monotonic upstream-centered scheme for conservation laws) is designed so that second-order accuracy is achieved, which leads to accurate solutions even over coarse meshes; (2) a special reconstruction technique and novel source term discretization are proposed for pipe flows to guarantee the exact well-balance in the framework of a MUSCL scheme, thus numerical oscillations at stationary steady states are avoided; (3) the proposed new scheme produces reasonable solutions for kinetic flows in underresolved finite-volume grids with very low water volumes; and (4) it guarantees the positivity of the computed water volume without forcing a minimum wetted area value or reducing the global time step size. The performance and superiorities of the proposed new scheme for sewer flows are verified against previously reported well-balanced numerical models on a number of experiments.