An explicit numerical algorithm for solving two-dimensional system of shallow-water equations is presented. The algorithm is based on the control volume method with recording mass and momentum fluxes through the faces of the volume with the use of an approximate solution of the Riemann problem. A numerical solution is compared with analytical solutions for a flow over a bottom step and with data of laboratory experiments in a flume with a sloped bed or a bed with an obstacle.
A design is proposed for a stepped spillway.A detailed design of the Boguchany HPP with a rated capacity of 3000 MW (nine generating sets each with a capacity of 330,000 kW and a reservoir at elevation 208 m was approved in 1979 by order of the Council of Ministers of the USSR in an agreement reached with the State Committee on Construction. In 1982, the first cubic meter of concrete was placed in the basic structures of the hydroproject. From 1993 through 2005, construction proceeded at extremely low rates on structures of the hydroproject. After the decision was made to resume construction on the BoHPP in 2006, the institute Gidroproekt (Moscow) was commissioned to render a partial adjustment to technical solutions of the 1979 design. Basic premises for partial revision of the technical solutions were:-a change in basic positions of the regulatory base for the design of water-development works;-a deficiency of carrying capacity of the spillway structures at the hydroproject in periods of permanent and temporary service; and, -the need to ensure operational reliability of the spillway structures, and the possibility of performing their running repairs.Agricultural and water-power analyses performed in compliance with requirements of the Construction Rules and Regulations indicated that the carrying capacity of the hydroproject in the periods of temporary and permanent service is lower than that required for passage of the spring flood and high water of the summer and fall. To retain the design values for the maximum water level in the upper pool, and ensure reliable passage of flows into the lower pool, it was necessary to increase the carrying capacity of the hydroproject by installing a second spillway (No. 2) in addition to the existing and partially constructed No. 1 spillway.In the design, the No. 2 spillway is to be placed in the segment containing the unfinished No. 20 -22 sections of the concrete dam alongside the partially constructed No. 1 spillway using the pit opened for resumed construction of generating sets No. 10 -12 of the powerhouse (a decision to cancel construction of these sets was made after the pit had been opened). Three alternate construction schemes of the No. 2, spillway, which are distinguished one from the other primarily by the method used to dissipate the energy of the discharge flow, are called for in the design. In two of the alternate schemes, it is specified that the energy of the flow be dissipated in a tow basin, and a scheme whereby the flow is discharged into the lower pool beyond the limits of the structures being erected is called for in the third.In hydrotechnical construction, problems associated with effective dissipation of excess flow energy, and erosion control of the surface of the water-passing structures determine their design for the most part. Preliminary analysis indicated that the installation of a stepped overflow face for the No. 2 spillway will ensure: -operation of the spillway in a cavitation-free regime by reducing the velocities of the flow, and its vi...
Summary
This paper describes a pressure correction method for single‐ and multilayer open flow models. The method does not require any complex procedures to solve the discretization of the Poisson equation and is distinguished by a high computational efficiency. The algorithm can easily be adapted to irregular meshes and parallelized. Parabolic interpolation of the pressure profile is used for the free surface. The discretization of the Poisson equation is written in a matrix form, allowing its usage also in the case of basic function expansion of the depth pressure profile. The paper presents the results of algorithm verification where experimental data sensitive to the numerical dissipation of the calculation model was used. Iteration convergence is high including problems with dry‐bed flooding. The complete described technique of pressure correction is implemented in OpenCL on the GPU. Computation time for a test problem solved using CPU and GPU is compared.
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