The exact Riemann solver for the shallow water equations with a discontinuous bottom

2021 ◽  
pp. 110801
Author(s):  
Andrey I. Aleksyuk ◽  
Maxim A. Malakhov ◽  
Vitaly V. Belikov
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Riemann Solver ◽  
Exact Riemann Solver

scholarly journals A Two-Layer Hydrostatic-Reconstruction Method for High-Resolution Solving of the Two-Layer Shallow-Water Equations over Uneven Bed Topography

2019 ◽  
Vol 2019 ◽  
pp. 1-14
Author(s):  
Jiang Lin ◽  
Bing Mao ◽  
Xinhua Lu
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
Ad Hoc ◽  
Finite Volume Methods ◽  
Reconstruction Method ◽  
Riemann Solver ◽  
Robust Solutions ◽  
Bed Topography ◽  
Benchmark Tests ◽  
Nonlinear Shallow Water Equations

In this study, attention is focused on numerically solving the two-dimensional, two-layer nonlinear shallow-water equations (2LSWEs) over uneven bed topography. A two-layer hydrostatic-reconstruction method (2LHRM) is proposed for face value reconstructions. A numerical model is then developed based on the 2LHRM in the framework of finite-volume methods using the slope-limited centered (SLIC) approximate Riemann solver for flux evaluations. The validations against various benchmark tests show that the 2LHRM by working with the SLIC scheme predicts robust solutions around large gradients and is able to simulate lake-at-rest solutions without using any ad-hoc techniques.

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