An exact Riemann solver and a Godunov scheme for simulating highly transient mixed flows

• Published in: Journal of computational and applied mathematics Vol. 235; no. 8; pp. 2030 - 2040
• Main Authors: Kerger, F., Archambeau, P., Erpicum, S., Dewals, B.J., Pirotton, M.
• Format: Journal Article Web Resource
• Language: English
• Published: Kidlington Elsevier B.V 15-02-2011; Elsevier; Elsevier Science
• Subjects: Assessments; Civil engineering; Computation; Computer simulation; Derivation; Engineering, computing & technology; Exact sciences and technology; Finite volume method; Global analysis, analysis on manifolds; Hydraulics; Ingénierie civile; Ingénierie, informatique & technologie; Mathematical analysis; Mathematical models; Mathematics; Methodology; Negative Preissmann slot; Numerical analysis; Numerical analysis. Scientific computation; Numerical methods in probability and statistics; Riemann solver; Saint-Venant equations; Sciences and techniques of general use; Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds; Transient flow; Water hammer; Transient flow; Finite volume method; Water hammer; Negative Preissmann slot; Hydraulics; Saint-Venant equations; Godunov scheme; Numerical method; Stochastic method; Experimental result; Numerical analysis; Applied mathematics; One dimensional model; Free surface flow; Mathematical model
• ISSN: 0377-0427; 1879-1778; 1879-1778
• DOI: 10.1016/j.cam.2010.09.026

The current research
aims at deriving a one-dimensional numerical model for describing highly transient mixed flows. In particular, this paper focuses on the development and assessment of a unified numerical scheme adapted to describe free-surface flow, pressurized flow and mixed flow (characterized by the simultaneous occurrence of free-surface and pressurized flows). The
methodology includes three steps. First, the authors derived a unified mathematical model based on the Preissmann slot model. Second, a first-order explicit finite volume Godunov-type scheme is used to solve the set of equations. Third, the numerical model is assessed by comparison with analytical, experimental and numerical results. The key
results of the paper are the development of an original negative Preissmann slot for simulating sub-atmospheric pressurized flow and the derivation of an exact Riemann solver for the Saint-Venant equations coupled with the Preissmann slot.