A Finite Volume Formulation of Hydrodynamic Pressure in Dam-Reservoir Systems with non-uniform reservoir geometry

Abstract
In the present paper a new numerical simulation method based on finite volume is developed for calculating hydrodynamic pressure distribution in the reservoir of dams during earthquake excitation. An explicit finite volume scheme is applied for discretization of dynamic governs equation. In the proposed method the asymmetry effect of reservoir shape on hydrodynamic pressure distribution can be considered. In the simulation quadrilateral elements with center cell algorithm is used. Because of the negligible changing of hydrodynamic pressure in the cross direction with averaging, the average differential partial equation in central vertical plan of reservoir is solved. The absorption effects of bottom sediment and lateral wall are included in the analysis and an exact far end boundary condition is applied in the truncation boundary. Different approaches to the solution of the coupled field problems exist solution of the entire set of equations as one discretized system, referred to as the monolithic approach. This approach is often inefficient due to its attempt to capture with one discretization methodology the completely different spatial and temporal characteristics of fluid and the structure. The second approach often mentioned is the notion of strong coupling, referring to solvers which might use different discretizations for the fluid and the structure but which employ sub-iteration in each time step to enforce coupling between the fluid and the structure. In these methods, the governing equations for fluid and structure are discretized separately in each of the sub-domains and coupled using a synchronization procedure both in time and in space without sub-iteration. Weakly –coupled schemes have been extensively applied to a variety of different fluid-structure interaction problems of engineering interest in past ten years. wo vital issues when coupling two domains are: the method of data transformation between domains and what information must be transferred. The property of fluid adjacent of a structure such as density and viscosity are also key parameters in the efficiency of a numerical scheme.A dense fluid coupled with a structure cause a strong coupling and required some special technique to overcome corresponding difficulties. Key questions with this approach include properly enforcing boundary conditions at the solid-fluid interface, and accurately transmitting tractions between the solid and fluid. The biggest complaint about the explicit staggered partitioned solution procedure is the typical instability associated with the method,that is generally caused by the time lag between the integration of the fluid and structure equations. In the typical partitioned method, the fluid and the structure equations are integrated in time, and the interface conditions are enforced asynchronously. In the solution of coupled problems using partitioned methods, it is necessary to find a cost-minimization (optimization) compromise between a few passes solution with small time steps and a more iterated solution with larger time steps. This compromise may depend, among other things, in the degree of nonlinearity of the structural problem, which may require equilibrium iterations independently of the interaction effects. From the computational point of view, a one–pass solution with no iteration would be optimal, but stability consideration may prove this impractical.

Keywords

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Modares Civil Engineering journal
Volume 18, Issue 3
September and October 2018
Pages 181-194