Journal
AIMS MATHEMATICS
Volume 8, Issue 4, Pages 9265-9289Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/math.2023465
Keywords
shallow water equations; source terms; a two-step explicit predictor-corrector approach; Fourier stability analysis; linear stability condition; convergence rate
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This paper presents a two-step explicit predictor-corrector approach, known as the two-step MacCormack formulation, for solving the one-dimensional nonlinear shallow water equations with source terms. The proposed numerical scheme uses the fractional steps procedure to handle the friction slope and upwind the convection term for controlling numerical oscillations and stability. The scheme incorporates forward and backward difference formulations in the predictor and corrector steps, respectively. The linear stability and convergence rate of the proposed method are analyzed and validated through numerical examples.
This paper deals with a two-step explicit predictor-corrector approach so-called the two-step MacCormack formulation, for solving the one-dimensional nonlinear shallow water equations with source terms. The proposed two-step numerical scheme uses the fractional steps procedure to treat the friction slope and to upwind the convection term in order to control the numerical oscillations and stability. The developed scheme uses both forward and backward difference formulations in the predictor and corrector steps, respectively. The linear stability of the constructed technique is deeply analyzed using the Von Neumann stability approach whereas the convergence rate of the proposed method is numerically obtained in the L2-norm. A wide set of numerical examples confirm the theoretical results.
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