Conservative numerical schemes with optimal dispersive wave relations: Part I. Derivation and analysis
An energy-conserving and an energy-and-enstrophy conserving numerical schemes are derived by approximating the Hamiltonian formulation of the inviscid shallow water flows based on the vorticity-divergence variables. These schemes also conserve the first-order moments such as mass and vorticity, as usual. The conservative properties of the schemes stem from the skew-symmetry and singularities of the Poisson brackets, which are carefully retained in the discrete approximations. Here, the schemes operate on unstructured orthogonal dual meshes, over bounded or unbounded domains, and they are also shown to possess the same optimal dispersive wave relations as those of the Z-grid scheme, which is a consequence of the use of the vorticity and divergence variables.
- Research Organization:
- Univ. of South Carolina, Columbia, SC (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC); USDOE Office of Science (SC), Biological and Environmental Research (BER). Earth and Environmental Systems Science Division
- Grant/Contract Number:
- SC0020270
- OSTI ID:
- 1959999
- Journal Information:
- Numerische Mathematik, Journal Name: Numerische Mathematik Journal Issue: 1 Vol. 149; ISSN 0029-599X
- Publisher:
- Springer Berlin HeidelbergCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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