A Modified Shock Tracking–Capturing Finite-Volume Approach for Transient Mixed Flows in Stormwater Systems

Abstract

This paper proposes a modification to a previous shock tracking-capturing approach used for simulating transient flows in stormwater systems. Based on the Godunov-type finite-volume (FV) method, this modified approach uses two governing equations for free-surface and pressurized flows discretized. The free-surface flow is simulated using an explicit FV method. However, the pressurized flow is discretized on one control volume and simulated using an implicit FV method. Different examples will be solved to examine the abilities of the proposed modified approach. The examples are pressurized and partially pressurized flows, including the water hammer, the pipe-filling bore advancement, and air pocket entrapment problems. The partially pressurized flow following air pocket entrapment is analyzed under different conditions including various ranges of driving pressure, air and water lengths, as well as dry-bed and with and without air-release conditions. It will be shown that the proposed modification can result in improving the overestimated peak values and the underestimated attenuation of pressure distribution. In addition, it will be shown that the proposed modified approach exhibits less oscillatory behavior, particularly in simulating pipe-filling bore advancement.