Authors:
Yuri N. Skiba
1
and
Denis M. Filatov
2
Affiliations:
1
National Autonomous University of Mexico (UNAM), Mexico
;
2
National Polytechnic Institute (IPN), Mexico
Keyword(s):
Simulation of Fluid Dynamics Problems, Shallow-water Flows, Conservative Finite Difference Schemes, Complex Computational Domain, Closed and Open Boundaries.
Related
Ontology
Subjects/Areas/Topics:
Complex Systems Modeling and Simulation
;
Computer Simulation Techniques
;
Dynamical Systems Models and Methods
;
Fluid Dynamics
;
Formal Methods
;
Mathematical Simulation
;
Simulation and Modeling
;
Simulation Tools and Platforms
Abstract:
A new numerical method for the simulation of shallow-water flows in a bay-like domain is suggested. The method is based on the splitting of the original nonlinear operator by physical processes and by coordinates. An essential advantage of our finite difference splitting-based method versus others in the field is that it leads to a model allowing accurate simulation of shallow-water flows in a domain of an arbitrary shape with both closed and open boundaries, which besides may contain onshore parts inside (interior isles in the bay); the model also takes into account irregular bottom topography. Specially constructed approximations of the temporal and spatial derivatives result in second-order unconditionally stable finite difference schemes that conserve the mass and the total energy of the discrete inviscid unforced shallow-water system. Moreover, the potential enstrophy results to be bounded, oscillating in time within a narrow range. Therefore, the numerical solution, aside from
being accurate from the mathematical point of view, appears to be physically adequate, inheriting a number of substantial properties of the original differential shallow-water system. Furthermore, the method can straightforwardly be implemented for distributed simulation of shallow-water flows on high-performance parallel computers. To test the method numerically, we start with the inviscid shallow-water model and verify the conservatism of the schemes in a simple computational domain. Then we introduce a domain with a more complex boundary consisting of closed and open segments, and consider more realistic viscous wind-driven shallow-water flows. Numerical experiments presented confirm the skills of the developed method.
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