Analytical implementation of Roe solver for two-layer shallow water equations with accurate treatment for loss of hyperbolicity (CROSBI ID 255725)
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Podaci o odgovornosti
Krvavica, Nino ; Tuhtan, Miran ; Jelenić, Gordan
engleski
Analytical implementation of Roe solver for two-layer shallow water equations with accurate treatment for loss of hyperbolicity
A new implementation of the Roe scheme for solving two-layer shallow-water equations is presented in this paper. The proposed A-Roe scheme is based on the analytical solution to the characteristic quartic of the flux matrix, which is an efficient alternative to a numerical eigensolver. Additionally, an accurate method for maintaining the hyperbolic character of the governing system is proposed. The efficiency of the quartic closed-form solver is examined and compared to numerical eigensolvers. Furthermore, the accuracy and computational speed of the A-Roe scheme is compared to the Roe, Lax-Friedrichs, GFORCE, PVM, and IFCP schemes. Finally, numerical tests are presented to evaluate the efficiency of the iterative treatment for the hyperbolicity loss. The proposed A-Roe scheme is as accurate as the Roe scheme, but much faster, with computational speeds closer to the GFORCE and IFCP scheme.
shallow-water equation ; quartic ; finite-volume method ; Roe solver ; two-layer flow ; hyperbolicity loss
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Podaci o izdanju
122 (C)
2018.
187-205
objavljeno
0309-1708
1872-9657
10.1016/j.advwatres.2018.10.017