INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS Int. J. Numer. Meth. Fluids (2011) Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/fld.2698 A new approach to solving Poisson system for free surface nonhydrostatic flow simulations Fatemeh Chegini * ,† and Masoud Montazeri Namin School of Civil Engineering, University College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran SUMMARY A nonhydrostatic finite volume model is presented to simulate free surface flow in a two-dimensional ver- tical 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 compu- tational 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 lay- out 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 sub- system 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. Received 13 July 2011; Revised 15 September 2011; Accepted 18 September 2011 KEY WORDS: free surface flow; nonhydrostatic pressure; projection method; Poisson system solver; Cartesian coordinate; finite volume 1. INTRODUCTION The hydrostatic pressure approximation has been widely used to develop numerical free surface flow models. Such an approximation is valid for many applications in shallow water flows and reduces the computational effort considerably. However, with the rapid increase in computer power, hydrostatic models are now applied with higher resolution. The enhancement of spatial resolution requires, as a rule, that the physical content of the models be enriched [1]. One of these enrichments is to consider the nonhydrostatic pressure by solving the complete Navier–Stokes equations (NSE). Furthermore, the nonhydrostatic effect should be included to accurately simulate the dynamics of many oceanographic phenomena such as dispersive internal solitary waves [2], short period waves, abruptly changing bed topography [3], a weak or unstable stratification or turbulent fluctuation [4]. In recent years, the development of nonhydrostatic free surface flow models has been the topic of many research activities. These models solve the complete NSE to include the nonhydrostatic pressure. In general, two approaches, namely, the projection method first proposed by Chorin [5] and the implicit method, have been employed to solve these equations. In the latter method, all governing equations are solved coupled, resulting in accurate solutions without decoupling errors *Correspondence to: Fatemeh Chegini, School of Civil Engineering, University College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran. † E-mail: cheginif@ut.ac.ir Copyright © 2011 John Wiley & Sons, Ltd.