A class of second-derivatives in the Smoothed Particle Hydrodynamics with 2nd-order accuracy and its application to incompressible flow simulations

Asai, Mitsuteru; FUJIOKA, Shujiro; SAEKI, Yusuke; Morikawa, Daniel S.; Tsuji, Kumpei

doi:10.1016/j.cma.2023.116203

Computer Methods in Applied Mechanics and Engineering

2023

DOI: 10.1016/j.cma.2023.116203

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A class of second-derivatives in the Smoothed Particle Hydrodynamics with 2nd-order accuracy and its application to incompressible flow simulations

Mitsuteru Asai

Shujiro FUJIOKA

Yusuke SAEKI

et al.

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Cited by 9 publications

References 83 publications

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A reliable SPH(2) formulation for Darcy–Forchheimer–Brinkman equation using a density-based particle shifting in the ALE description

Tsuji,

Fujioka,

Morikawa

et al. 2024

Comp. Part. Mech.

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This paper proposes a numerical framework to perform highly accurate simulations of seepage flow through porous media with the incompressible smoothed particle hydrodynamics (ISPH). Our approach follows the arbitrary Lagrangian–Eulerian description, which can introduce an arbitrary advection velocity for particle shifting techniques (PSTs) independently of the physical fluid velocity. The Darcy–Forchheimer–Brinkman equation is applied to deal with free surface flow and seepage flow simultaneously instead of the Navier–Stokes equation. There are three main improvements to solving this problem using ISPH. The first is replacing the SPH(2) with a highly accurate derivative operator. The second is modifying a volume-conserving particle shifting for seepage flow problems to maintain the apparent fluid density consistent with the spatially distributed porosity. Finally, we propose a newly geometric porosity estimation method automatically estimating numerical porosity referenced in the proposed PST from the soil particle distributions. Through simple convergence tests, we verify the convergence of truncation errors and the applicability limits of SPH(2) to simulate seepage flow problems. We also performed numerical simulations of hydrostatic pressure problems and dam-break experiments involving porous layers to demonstrate the proposed method’s excellent computational stability and volume conservation performance.

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A reliable SPH(2) formulation for Darcy–Forchheimer–Brinkman equation using a density-based particle shifting in the ALE description

Tsuji,

Fujioka,

Morikawa

et al. 2024

Comp. Part. Mech.

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Dispersion analysis of SPH for parabolic equations: High-order kernels against tensile instability

Stoyanovskaya,

Burmistrova,

Arendarenko

et al. 2025

Journal of Computational and Applied Mathematics

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Lagrangian Voronoï meshes and particle dynamics with shocks

Després

2024

Computer Methods in Applied Mechanics and Engineering

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A class of second-derivatives in the Smoothed Particle Hydrodynamics with 2nd-order accuracy and its application to incompressible flow simulations

Cited by 9 publications

References 83 publications

A reliable SPH(2) formulation for Darcy–Forchheimer–Brinkman equation using a density-based particle shifting in the ALE description

A reliable SPH(2) formulation for Darcy–Forchheimer–Brinkman equation using a density-based particle shifting in the ALE description

Dispersion analysis of SPH for parabolic equations: High-order kernels against tensile instability

Lagrangian Voronoï meshes and particle dynamics with shocks

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