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_ The paper presents a high-order consistent incompressible smoothed particle hydrodynamics (ISPH) fluid model for accurate simulation of ocean engineering problems. The high-order consistent discretization schemes on differential operators are derived through consideration of Taylor-series expansion up to second-order differential terms. The derived consistent discretization schemes are applied to the calculations of a Laplacian term of pressure in the Poisson pressure equation (PPE) and pressure gradient term in the momentum equation. To enhance and ensure the accuracy, stability, and conservation property of the model, the enhanced schemes developed by our research teamโnamely, the higher-order source term, error-compensating source term, and dynamic stabilizer schemesโare also incorporated. The proposed high-order consistent ISPH fluid model is validated through reproduction of a set of numerical examples. Introduction Lagrangian meshfree computational methods, or the so-called particle methods such as smoothed particle hydrodynamics (SPH; Gingold and Monaghan, 1977) or incompressible SPH (ISPH; Shao and Lo, 2003), have recently been attracting a lot of interest in various engineering fields. Thanks to their Lagrangian meshfree description of motion, the particle methods possess great advantagesโ for example, being free from calculation of an advection term and stable/natural tracking of complex moving boundaries. In the field of ocean engineering, one can easily find a number of existing applications of particle methods toward violent free-surface fluid flow and its interaction with rigid/deformable structures, as comprehensively reviewed in Luo et al. (2021) and Gotoh et al. (2021).
Abstract The moving particle semi-implicit (MPS) method is a Lagrangian meshless method to simulate incompressible fluid flows. Since its development, the MPS method has almost always been applied with a simple explicit Euler scheme, and the effect of higher-order time-integration schemes on the accuracy of this method has not yet been examined in detail. In this paper, the effect of higher-order time-integration schemes is investigated by considering a set of appropriate ocean engineering-related benchmark tests. It will be shown that the accuracy of the MPS method is not noticeably sensitive to the applied time-integration scheme. Hence, for further enhancement of the MPS method, especially for the simulation of the violent fluid flows often encountered in ocean engineering, the main focus should be given to the accuracy, consistency and convergence properties of differential operator models and an applied projection scheme. Introduction The moving particle semi-implicit (MPS) method was originally developed by Koshizuka and Oka (1996) as a Lagrangian meshless method for the simulation of viscous incompressible fluid flows. In general, particle methods, including the MPS method, have a distinct advantage in reproducing the complicated violent flows with free surface often encountered in offshore and ocean engineering, due to their Lagrangian tracking scheme without the advection term. However, particle methods, including the MPS method, have an inevitable shortcoming regarding unphysical pressure fluctuations that usually leads to computational inaccuracy. A set of enhanced schemes for suppressing pressure fluctuations was developed until now (Khayyer and Gotoh, 2008, 2009, 2010, 2011; Tsuruta et al., 2013; Wendland, 1995), so this method can be reliably applied to ocean engineering applications. By applying the enhanced schemes to particle-based simulations, various challenging engineering problems such as breaking waves (Khayyer and Gotoh, 2008) or wave impact (Khayyer and Gotoh, 2009) have been widely studied. However, up to now and to our best knowledge, the effect of a time-integration scheme on the accuracy of the MPS method has not been studied rigorously and comprehensively. On the other hand, a number of studies have applied different time-integration schemes in the smoothed particle hydrodynamics (SPH) framework (Molteni and Colagrossi, 2009; Blanc and Pastor, 2012). This is because SPH has a simple explicit algorithm, whereas the MPS method is founded on a semi-implicit solution process; thus, application of different time-integration schemes would not be straightforward in comparison to explicit SPH. Jeong et al. (2013) applied the Runge-Kutta scheme to the MPS method and obtained slightly improved results. However, their study did not mainly target the effect of time-integration schemes, and other higher-order time-integration schemes that may be superior to the Runge-Kutta scheme in terms of applicability or calculation time were not examined.
This paper presents a novel compressible-incompressible multiphase projection-based particle method for the prediction of water slamming pressures. The particle method considered is an extended version of an enhanced multiphase moving particle semi-implicit (MPS) method. The proposed method solves an integrated form of Poisson pressure equations (PPEs) for the liquid and gas phases. To further enhance accuracy, a modified version of the previously developed ECS scheme is devised for the gas phase through calculations of minimum and maximum theoretical base values for activation of the ECS scheme, thus imposing an allowable range of density variations for the compressible phase. Verifications are conducted by means of 2D liquid impact and impacts of rigid plates on flat water surfaces. Introduction The high-speed impacts between water and structures, often referred to as โslamming,โ are of crucial importance in the design of coastal/offshore structures. Several theoretical studies have been devoted to the prediction of slam loads (e.g., von Kรกrmรกn, 1929; Wagner, 1932). However, in most classical theoretical studies, the air phase and its cushioning effect have been ignored. Several experimental works, on the other hand, highlighted the importance of the air phase during the impact. In particular, a pioneering experimental study by Chuang (1966) demonstrated considerably reduced impact pressures compared with the Wagner theoretical solution. Hence, numerical predictions of slam loads should be conducted by robust multiphase numerical methods that can appropriately model the dynamics of air and its cushioning (compressibility) effect. A number of interesting numerical works have been devoted to the simulation of wave slamming with consideration of air entrapment and its cushioning effect. In particular, Ma et al. (2014) developed an advanced finite volume method (FVM)-based compressible multiphase method for violent aerated wave impact problems. Lind et al. (2015) proposed a compressible-incompressible smoothed particle hydrodynamics (SPH)-based method for wave slamming by solving the air phase via an explicit weakly compressible SPH (WCSPH) method and calculating the fluid phase via a semi-implicit incompressible SPH (ISPH). This paper presents a novel compressible-incompressible multiphase projection-based particle method for the prediction of wave slamming loads. The considered particle method is an extended version of an enhanced multiphase moving particle semi-implicit (MPS) method (Khayyer and Gotoh, 2013). The proposed method solves an integrated form of Poisson pressure equations (PPEs) for the liquid phase and the gas phase. To further enhance accuracy, a modified version of the previously developed ECS scheme (Khayyer and Gotoh, 2013) is devised through calculations of minimum and maximum theoretical base values for activation of the ECS scheme, thus imposing allowable ranges of density variations for the phases. Verifications are conducted by considering a set of liquid impact and slamming problems, including a 2D liquid impact (Braeunig et al., 2009) and impacts of rigid plates on flat water surfaces corresponding to the experiments by Lin and Shieh (1997) and Verhagen (1967).
- Asia > Japan (0.28)
- North America > United States (0.28)
Wave Impact Pressure Calculations By Improved SPH Methods
Khayyer, Abbas (Department of Urban and Environmental Engineering, Kyoto University Katsura Campus Nishikyo-ku, Kyoto, Japan) | Gotoh, Hitoshi (Department of Urban and Environmental Engineering, Kyoto University Katsura Campus Nishikyo-ku, Kyoto, Japan)
This paper presents improved Incompressible SPH (ISPH) methods for the prediction of wave impact pressure, more specifically, impact pressure due to sloshing waves. The first improvement is the employment of a corrective function for enhancing angular momentum conservation. The second improvement applies a higher-order source term that is derived from a higher-order differentiation for a less fluctuating and more accurate pressure calculation. The third improvement proposes a new criterion for a more accurate assessment of free-surface particles in a particle-based calculation. The enhanced performance of improved ISPH methods in predicting wave impact pressure has been shown by simulating 4 cases of sloshing waves induced by sway excitations (Kishev et al., 2006) and rotational ones (Delorme et al., 2009). INTRODUCTION With the trend towards the LNG industry's massive expansion and development, the sloshing of LNG in partially filled tanks has attracted many researchers in the marine and offshore community. In this context, one of the major concerns is the prediction of sloshing-induced impact pressure which can cause critical damage to the LNG carriers. During the past 3 decades, a great number of experimental (e.g. Berg, 1987; Akyildiz and Unal, 2005; Bunnik and Huijsmans, 2009) and theoretical (e.g. Abramson, 1966; Popov et al., 1992; Ibrahim, 2005) studies have been devoted to sloshing flows and sloshing-induced impact loads. In parallel to the experimental and theoretical investigations, extensive numerical simulations of sloshing flows have been carried out, based on solving the continuity and Navier-Stokes equations (e.g. Aus Der Wiesche, 2003), or the potential flow equations (e.g. Firouz-Abadi et al., 2008). Nevertheless, because a violent sloshing flow characterized by free-surf ace breaking and fluid fragmentations can no longer be assumed to be irrotational, potential flow-based methods do not seem to be applicable in such a case. On the other hand, grid-based Navier-Stokes solvers require an appropriate mathematical treatment of the free surface for simulation of a violent sloshing flow.
- Facilities Design, Construction and Operation > Natural Gas Conversion and Storage > Liquified natural gas (LNG) (0.95)
- Reservoir Description and Dynamics > Reservoir Simulation (0.89)
- Reservoir Description and Dynamics > Formation Evaluation & Management (0.68)
- Reservoir Description and Dynamics > Reservoir Fluid Dynamics (0.68)
The particle method, which is a solver of the Navier-Stokes equation without using a computational grid, has excellent robustness in analyzing a violent water-surface change accompanied with a fragmentation and coalescence of water. Thus the particle method is an optimum tool for the analysis of the process of wave breaking and runup. Here are outlined the calculation fundamentals of the particle method. The state-of-the-art of the particle method is briefly introduced, including highly precise particle methods, by improving momentum conservation in discretization of governing equations and the new methods for control of pressure fluctuation. Finally, we show as prospective studies on the particle method a few of the significant issues for promoting the substantial contribution of the particle method to a numerical wave flume, which is the computer-aided resistive design tool of coastal structures against wave action. INTRODUCTION In order to describe nonlinear wave transformation, the Boussinesq (1872) theory and its extension (e.g. Nwogu, 1993) are popular and reliable. However, these models are unable to describe wave breaking directly, because they are derived under the assumption of potential flow, namely irrotational flow, while neglecting viscosity. In extended models of the Boussinesq theory, wave breaking was described empirically as an energy damping effect using ad hoc energy dissipating schemes (e.g. Svendsen, 1984). Computations based on analytical governing equations of wave motion, such as the Boussinesq equation, must be replaced by numerical solutions of the Navier-Stokes equation in order to analyze a wave breaking and runup process without ad hoc sub-models of energy dissipation. In the wave breaking phenomena, there exists one more difficulty: the existence of multiple connected flow domain, or topological change of the free surface, due to the plunging jet striking the toe of the wave.