A fast universal solver for 1D continuous and discontinuous steady flows in rivers and pipes

Abstract

IntroductionOne dimensional numerical simulation of free-surface and pressurized flows is a useful engineering tool for a wide range of practical applications in civil engineering. The method can be used as long as no 2D and 3D hydraulic effects are predominant and must be thus taken into account. For instance, large rivers networks are often managed and developed by means of 1D models [1,2]. Similarly, simulation of pressurized flow in pipes networks such as water supply or sewer systems relies traditionally on such models [3,4]. Finally, 1D models can be reliably considered in the design process of many hydraulic structures such as water intake, bottom outlet tailrace tunnel, flushing galleries in dams [5]. On account of the large number of practical applications concerned, an efficient prediction of 1D flow features is an obvious need. Developing a unified 1D model for all the situations of interest in civil engineering remains however challenging. Various flow patterns may indeed coexist in actual situations:1. Free surface flows, where supercritical, subcritical and transcritical conditions could co-exist [2], are usually modelled, including the discontinuities (hydraulic jump), on the basis of the conservative Saint-Venant equations [6,7]. 2. Pressurized flows are traditionally described by the water hammer equations [4]. 3. Mixed flows, characterized by a simultaneous occurrence of free-surface and pressurized flow, are still nowadays an issue of research [8][9][10][11] for its mathematical description and its numerical solution. To achieve our purpose to develop a universal solver handling free-surface, pressurized and mixed flow, it is then required 1. to establish a unified mathematical model which overcomes the dissimilarity between the sets of equations describing pressurized and free-surface flows; 2. to set an efficient resolution scheme for this model. As previously mentioned, different mathematical approaches to describe free-surface, pressurized and mixed flow in a unified framework have been developed to date and are still subject to many research. Shock-tracking methods consists in solving separately free-surface and pressurized flows through different sets of equations [12,13]. Rigid Water Column Approach treats each phase separately on the basis of a specific set of equations in focusing on the air behaviour [14]. Nevertheless, such algorithms are very complicated and casespecific. Finally, the so-called shock-capturing approach is a family of method which computes pressurized and free-surface flows by using a single set of equations [8][9][10][11] . In this paper, such an approach is used, based on the model of the Preissmann slot [15]. In particular, this paper focuses on steady state flows which are of great interest for engineers. Design guidelines for many hydraulic structures specify indeed that specific critical steady states have to be addressed. Practitioners should then rely on robust and efficient 1D solvers suitable for each flow pattern (free-surface, pressurized and mixed) in o...

Semi-Explicit Modelling of Watersheds with Urban Drainage Systems

“…The rainfall runoff model computes lateral inflows to the rivers, which are next routed through the river network by means of the hydraulic model Wolf 1D. A suitable shock capturing scheme is used to solve the conservative form of the 1D Saint-Venant equations, enabling the simulation of flow regime changes and hydraulic jumps (Kerger et al, 2011).…”

“…Upwind evaluation of the fluxes is performed, according to the sign of the flow velocity (Erpicum et al, 2010b). The stability of the scheme has been demonstrated using a linear stability analysis (e.g., Kerger et al, 2011). Efficiency, simplicity and low computational cost are the main advantages of this scheme.…”

Advanced Topics in Sediment Transport Modelling: Non-alluvial Beds and Hyperconcentrated Flows

“…WOLF includes a set of complementary and interconnected modules for simulating a wide range of free surface flows, involving process-oriented rainfall-runoff modelling, 1D, 2DH, 2DV and 3D hydrodynamics, sediment or pollutant transport, air entrainment, as well as an optimisation tool based on Genetic Algorithms. Validity and efficiency of the model has already been proved for numerous applications (Dewals et al 2008b;Erpicum et al 2009;Kerger et al 2010a), including inundation mapping (Ernst et al 2010;Erpicum et al 2010a;Khuat Duy et al 2010), dam break and dam breaching simulations Erpicum et al 2010b;Roger et al 2009) as well as morphodynamic modelling (Dewals et al 2002a;Dewals et al 2002b;Dewals et al 2002c;Dewals et al 2004;Dewals et al 2008a;Dewals et al 2010b). …”

1D unified mathematical model for environmental flow applied to steady aerated mixed flows

“…Moreover the coefficients have been tuned to emphasize the dissipation and the stability properties of the scheme. For steady flows, an improved formulation of the flux vector splitting enables to speed up the computation [36].…”