A truly incompressible smoothed particle hydrodynamics based on artificial compressibility method

Rouzbahani, Fardin; Hejranfar, Kazem

doi:10.1016/j.cpc.2016.09.008

Cited by 15 publications

(11 citation statements)

References 38 publications

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“…More than 200 papers were retrieved by database searches for 2015-2020 using the terms artificial compressibility, pseudo compressibility, and dual time stepping. These studies include analysis of the relationships between AC and fractional step methods [86,87], studies of turbulent flow [88][89][90], development of discontinuous Galerkin methods [91][92][93], parallel solution of large-scale problems [94][95][96], multi-fluid simulations [97], further advances to entropically-damped AC methods [98][99][100], implementation high-order numerical schemes [101][102][103], use of characteristic methods [104][105][106], application for non-hydrostatic effects [107,108], magneto-hydrodynamic simulations [109][110][111], solution with lattice Boltzmann methods [112], and solution by smoothed particle hydrodynamics [113,114]. Note the above are examples and should not be considered an exhaustive list of recent work.…”

Section: Recent Development Of the Artificial Compressibility Methodsmentioning

confidence: 99%

An Artificial Compressibility Method for 1D Simulation of Open-Channel and Pressurized-Pipe Flow

Hodges

2020

Water

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Piping systems (e.g., storm sewers) that transition between free-surface flow and surcharged flow are challenging to model in one-dimensional (1D) networks as the continuity equation changes from hyperbolic to elliptic as the water surface reaches the pipe ceiling. Previous network models are known to have poor mass conservation or unpredictable convergence behavior at such transitions. To address this problem, a new algorithm is developed for simulating unsteady 1D flow in closed conduits with both free-surface and surcharged flow. The shallow-water (hydrostatic) approximation is used as the governing equations. The artificial compressibility (AC) method is implemented as a dual-time-stepping discretization for a finite-volume solver with timescale interpolation used for face reconstruction. A new formulation for the AC celerity parameter is proposed such that the AC celerity matches the equivalent gravity wave speed for the local hydraulic head—which has some similarities to the classic Preissmann Slot used to approximate pressurized flow in conduits. The new approach allows the AC celerity to be set locally by the flow (i.e., non-uniform in space) and removes it as a free parameter of the AC solution method. The derivation of the AC method provides for only a minor change in the form of the solution equations when a computational element switches from free-surface to surcharged. The new solver is tested for both unsteady free-surface (supercritical, subcritical) and surcharged flow transitions in a circular pipe and is implemented in an open-source Python code available under the name “PipeAC.” The results are compared to laboratory experiments that include rapid flow changes due to opening/closing of gates. Results show that the new algorithm is satisfactory for 1D representation of unsteady transition behavior with two caveats: (i) sufficient grid resolution must be applied, and (ii) the shallow-water equation approximations (hydrostatic, single-fluid) limit the accuracy of the solution with regards to the celerity of the turbulent unsteady bore that propagates upstream. This research might benefit any piping network model that must smoothly handle unsteady transitions from free surface to surcharged flow.

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Section: Recent Development Of the Artificial Compressibility Methodsmentioning

confidence: 99%

An Artificial Compressibility Method for 1D Simulation of Open-Channel and Pressurized-Pipe Flow

Hodges

2020

Water

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“…In the penalty method, the errors in the divergence of velocity are transferred to the boundaries [24]. An alternative related technique is the artificial compressibility technique (ACT) [25][26][27][28][29], in which the deviations from incompressibility determine ∂p/∂t rather than p itself. Also, the ACT diffuses errors in velocity divergence.…”

Section: Introductionmentioning

confidence: 99%

A combined method for simulating MHD convection in square cavities through localized heating by method of line and penalty-artificial compressibility

Mousa

Ali

2021

Journal of Taibah University for Science

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A new combined technique is developed for studying free convection of magnetohydrodynamic unsteady incompressible flow in a square cavity that partially heated from lower wall and regular cooling from lateral walls. Convection has been studied for several lengths of heat source, Hartman and the Rayleigh numbers. The local and average Nusselt numbers are calculated and presented graphically along the heat source portion. The proposed technique is a combination of the method of lines (MOL) and a developed penalty-artificial compressibility technique (PACT). Unsteady penalty compressibility governing equations are used instead of solving steady-state balances. The penalty and artificial compressibility factors are estimated using a deduced stability restriction. The validation of the MOL-PACT is verified by comparing the current data with other numerical and experimental ones existing in the literature. The proposed technique provides a new choice through the investigation of MHD mass and heat transfer.

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“…Two types of Iterative WCSPH (IWCSPH) methods have recently been proposed. 5,25 The artificial compressible incompressible SPH (ACISPH) methods are WCSPH methods based on the artificial compressible method introduced by Chorin (1967). 5,26 In the ACISPH methods, the continuity equation is reformulated by using the relation between the pressure and the density, P = 2 where is the artificial compressibility.…”

Section: Introductionmentioning

confidence: 99%

“…In the WCSPH methods, an iterative scheme is introduced in the time step calculation to avoid the non‐physical oscillations of pressure field. Two types of Iterative WCSPH (IWCSPH) methods have recently been proposed 5,25 . The artificial compressible incompressible SPH (ACISPH) methods are WCSPH methods based on the artificial compressible method introduced by Chorin (1967) 5,26 .…”

Section: Introductionmentioning

confidence: 99%

Optimized incompressible smoothed particle hydrodynamics methods and validations

Ortega¹,

Beaudoin²,

Huberson³

2020

Numerical Methods in Fluids

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The solution of the Poisson's equation used by the incompressible smoothed particle hydrodynamics (ISPH) methods for estimating the pressure field is expensive in CPU time. The CPU time, consumed by the inversion of the operator ∇(1∕ ∇) and the estimation of the right hand side of the Poisson's equation, increases with the number N of particles used in a purely Lagrangian framework. In this work, this default of ISPH methods is overcome by solving the Poisson's equation on a Cartesian grid. This SPH-mesh coupling is equivalent to the particle in cell method. In a first step, in order to analyze its efficiency, the optimized version of two ISPH methods (divergence free and density invariant) is compared with the standard weakly compressible SPH method through two benchmarks of incompressible bidimensional flows characterized by the Reynolds number Re, Lamb-Oseen vortex (10 ≤ Re ≤ 100) and lid-driven cavity flow (100 ≤ Re ≤ 1000). In a second step, the numerical results obtained by the three SPH methods are compared to laboratory experimental data of a dam break flow in order to show the performance of the SPH-mesh coupling in a practical and complex flow problem. As in the configuration of the experimental setup, the numerical results are obtained for a Reynolds number Re = 3.8 10 6 .

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A truly incompressible smoothed particle hydrodynamics based on artificial compressibility method

Cited by 15 publications

References 38 publications

An Artificial Compressibility Method for 1D Simulation of Open-Channel and Pressurized-Pipe Flow

An Artificial Compressibility Method for 1D Simulation of Open-Channel and Pressurized-Pipe Flow

A combined method for simulating MHD convection in square cavities through localized heating by method of line and penalty-artificial compressibility

Optimized incompressible smoothed particle hydrodynamics methods and validations

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