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A new approach to solving Poisson system for free surface nonhydrostatic flow simulations
Author(s) -
Chegini Fatemeh,
Namin Masoud Montazeri
Publication year - 2011
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2698
Subject(s) - cartesian coordinate system , projection (relational algebra) , flow (mathematics) , constant (computer programming) , grid , matrix (chemical analysis) , finite volume method , plane (geometry) , poisson's equation , variable (mathematics) , projection method , regular grid , surface (topology) , series (stratigraphy) , mathematics , mechanics , mathematical analysis , geometry , computer science , algorithm , physics , geology , materials science , paleontology , composite material , programming language , grating
SUMMARY A nonhydrostatic finite volume model is presented to simulate free surface flow in a two‐dimensional vertical plane. The algorithm is based on a projection method including the solution of the pressure Poisson equation (PPE). The model is developed in a Cartesian grid in which the size of all the cells in the computational domain, excluding those of the top layer, is constant in time. To simulate the variable water surface, the heights of the top layer cells are variable and proportional to the local water elevation. Taking the layout of the grid system into consideration, a new method is proposed to solve the PPE derived in Cartesian coordinates. In this method, the system of pressure equations is divided into two subsystems, namely a subsystem for the upper layer cells and another for the remaining cells. The coefficient matrix of the former is variable with respect to time, whereas that of the latter remains constant. Therefore, the coefficient matrix of the latter subsystem can be inversed once and saved throughout the simulation. The application of this procedure reduces the computational cost compared with other PPE solvers in certain conditions. The model is applied to simulate a series of numerical tests including strong vertical accelerations and is verified against analytical and experimental results, demonstrating satisfactory performance. Copyright © 2011 John Wiley & Sons, Ltd.