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Improved Riemann solvers for an accurate resolution of 1D and 2D shock profiles with application to hydraulic jumps

AuthorsNavas-Montilla, A.; Murillo, J.
KeywordsRiemann solver
Shallow water
Source terms
Shockwave anomalies
Issue Date1-Feb-2019
CitationJournal of Computational Physics 378: 445-476 (2019)
AbstractFrom the early stages of CFD, the computation of shocks using Finite Volume methods has been a very challenging task as they often prompt the generation of numerical anomalies. Such anomalies lead to an incorrect and unstable representation of the discrete shock profile that may eventually ruin the whole solution. The two most widespread anomalies are the slowly-moving shock anomaly and the carbuncle, which are deeply addressed in the literature in the framework of homogeneous problems, such as Euler equations. In this work, the presence of the aforementioned anomalies is studied in the framework of the 1D and 2D SWE and novel solvers that effectively reduce both anomalies, even in cases where source terms dominate the solution, are presented. Such solvers are based on the augmented Roe (ARoe) family of Riemann solvers, which account for the source term as an extra wave in the eigenstructure of the system. The novel method proposed here is based on the ARoe solver in combination with: (a) an improved flux extrapolation method based on a previous work, which circumvents the slowly-moving shock anomaly and (b) a contact wave smearing technique that avoids the carbuncle. The resulting method is able to eliminate the slowly-moving shock anomaly for 1D steady cases with source term. When dealing with 2D cases, the novel method proves to handle complex shock structures composed of hydraulic jumps over irregular bathymetries, avoiding the presence of the aforementioned anomalies.
Publisher version (URL)https://doi.org/10.1016/j.jcp.2018.11.023
Appears in Collections:(LIFTEC) Artículos
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