Hybrid Numerical Scheme of Preissmann Slot Model for Transient Mixed Flows

Abstract

The Preissmann slot model is one of the most widely used models to conceptualize both free-surface and pressurized flows in urban drainage systems. Despite its simplicity and wide range of applications, numerical solutions of the Preissmann slot model suffer from the spurious oscillations, especially when flow conditions switch from free-surface flow to pressurized flow. To overcome this problem, a new hybrid numerical flux solver of the Preissmann slot model is proposed herein, in which the upwind flux solver is combined with the centered flux solver. Numerical experiments are conducted for multiple flow conditions such as typical filling, pipe-filling, and transition-flow conditions. The numerical results indicate that the proposed scheme generally outperforms the conventional flux schemes for various hydraulic conditions and wave velocities. The proposed scheme should be useful to further enhance integrated urban water modeling in which transient mixed flow conditions significantly impact the simulation accuracy during extreme floods.

Suppress Numerical Oscillations in Transient Mixed Flow Simulations with a Modified HLL Solver

“…In the transient mixed flow simulations, numerical oscillations are widely observed behind the filling-bore front causing unphysical transient pressure peaks and computation failures [12]. These numerical oscillations are very similar to the "post-shock oscillations" in gas dynamics which have been studied by many researchers [20][21][22].…”

“…The solution to Ui+1/2 can be obtained by solving equations (12) and (13) iteratively, although the exact solver can compute the wave structure in each Riemann problem correctly, there are serious numerical oscillations in the simulation results. A filtering process is carried out after flow sates are updated in all computational cells,:…”

“…To simplify this question, we can reduce the number of governing equations by adopting one set of governing equations for both flow conditions. Based on this idea, the Preissmann slot model (PSM) is proposed by Cunge [11] and it has been adopted by many researchers and commercial software packages for its simplicity and accuracy [12][13][14][15][16][17][18]. The gradient of piezometric head at the interface between two flow regimes are very steep which forms a discontinuity in flow, therefore the governing equations are normally discretized using the state-of-art finite volume method for it admits discontinuous solutions [19].…”

“…It needs to be noted that numerical oscillations do not only appear under the PSM, but also under other models, such as the two-component approach model and two equation model [25]. Many oscillation-suppressing methods have been proposed to solve this problem [12,23,24], however, there is no paper that evaluates the effects of these methods. In this paper, four oscillation-suppressing methods are tested on a benchmark model, their accuracy and robustness are rated, based on these approaches, a general idea to devise an oscillation-suppressing approach is revealed and then a new oscillation-suppressing method which can eliminate numerical oscillations under an acoustic wave speed of 1000ms -1 is proposed.…”

Experimental and Numerical Study on Water Filling and Air Expelling Process in a Pipe with Multiple Air Valves under Water Slow Filling Condition

“…Affected by the change of water-flow rate and pipe elevation, the water flow is unsteady with free surface flows, pressurized flows and free-surface-pressurized flows occurred concurrently or separately. Many Preissmann slot methods have been established for simulating these unsteady water flows, which are also applicable to simulate unsteady water flow during pipe filling [3][4][5][6][7]. However, for simulating the air evolution and air expelling inside the pipe, the water-air two-phase model is needed.…”