WSEAS Transactions on Fluid Mechanics
Print ISSN: 1790-5087, E-ISSN: 2224-347X
Volume 18, 2023
Linear and Nonlinear Splitting Schemes Conserving Total Energy and Mass in the Shallow Water Model
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Abstract: Two linear and one nonlinear implicit unconditionally stable finite-difference schemes of the second-order approximation in all variables are given for a shallow-water model including the rotation and topography of the earth. The schemes are based on splitting the model equation into two one-dimensional subsystems. Each of the subsystems conserves the mass and total energy in both differential and discrete (in time and space) forms. One of the linear schemes contains a smoothing procedure not violating the conservation laws and suppressing spurious oscillations caused by the application of central-difference approximations of spatial derivatives. The unique solvability of the linear schemes and convergence of iterations used to find their solutions are proved.
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Keywords: Shallow-water model, splitting method, linear and nonlinear numerical schemes, conservative laws, unique solvability of the linear schemes, convergence of the iterative process
Pages: 193-200
DOI: 10.37394/232013.2023.18.18