Title: Evaluation and modification of time splitting method applied to the fully dynamic numerical solution of water wave propagation

Authors: Ali Shirkavand; Peyman Badiei

Addresses: School of Civil Engineering University College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran ' School of Civil Engineering University College of Engineering, University of Tehran, P.O. Box 11365-4563, Tehran, Iran

Abstract: Time splitting method has gained popularity in the numerical solution of two and three dimensional advection diffusion problems. This paper critically evaluates the suitability of applying this method to water wave propagation. The model which is used for this purpose solves Navier-Stokes equations with dynamic pressure. Finite volume method is applied to a boundary fitted staggered grid with equal number of layers in the vertical direction. Assuming non-hydrostatic pressure distribution in the upper layer, this model is able to simulate the short wave propagation using only a few vertical layers (3-5 layers). Comparison of the results of this model with experimental and analytical data indicates that amplitude and phase errors are present which seems to be caused by applying time splitting algorithm. A method already proposed to overcome the poor results of this algorithm for the advection of scalar quantities is modified and extended to vector quantities applicable to the present study. The results of this modified method exhibit a significant improvement in the model and indicate the weakness of time splitting method in the solution of non-hydrostatic nonlinear wave propagation problems.

Keywords: time splitting method; projection method; advection equation; non-hydrostatic pressure; free surface flow; boundary fitted grids; water wave propagation; Navier-Stokes equations; modelling; dynamic pressure; finite volume method; FVM; simulation.

DOI: 10.1504/PCFD.2015.070437

Progress in Computational Fluid Dynamics, An International Journal, 2015 Vol.15 No.4, pp.228 - 235

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 06 Jul 2015 *

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