|Article title||DEVELOPMENT OF REGULARIZED MATHEMATICAL MODEL FOR SIMULATION HYDRODYNAMICS AND SURGE PHENOMENA IN SHALLOW WATER BASINS AND ITS PARALLEL IMPLEMENTATION FOR SHRED MEMORY COMPUTER SYSTEMS|
|Authors||A.V. Shishenya, A.I. Sukhinov|
|Section||SECTION III. THE USE OF SUPERCOMPUTER TECHNOLOGIES|
|Month, Year||12, 2014 @en|
|Abstract||In the paper we develop mathematical models for free-surface hydrodynamics simulation based on both classical Navies-Stokes equations and it’s hyperbolized analogous. We also pose adjusted boundary conditions for both models and perform discretization with finite volume method accounting fullness of the grid cells that allows us to improve precision of the obtaining results. It allows to improve the accuracy of the results, as well as to take into account the motion of the free surface and the change in the coastline due to surge phenomena. Adjusted boundary conditions are especially important for shallow water basins due to close location of horizontal boundaries, which introduce approximation errors into velocity and pressure fields inside the computational domain. The application of the created mathematical models for predicting adverse and dangerous phenomena in water media requires it’s effective parallel implementation. It could be reached by using explicit stencils when solving PDEs numerically. It is well-known that using explicit stencil imposes hard stability conditions on temporal step that’s why we suggest to use regularizer, that allows to ease this restriction. We also derived asymptotic condition of efficiency of the hyperbolized model compared to the classical one. Parallel implementation of the regularized model is performed for shared memory supercomputer system; efficiency and speed-up of the parallel program were measured.|
|Keywords||Hydrodynamics; free surface; shallow water basin; hyperbolized system of hydrodynamics; parallel algorithms for shared memory supercomputer systems.|
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