This paper addresses the accuracy of the weakly-compressible SPH method. Interpolation defects due to the presence of anisotropic particle structures inherent to the Lagrangian character of the ...Smoothed Particle Hydrodynamics (SPH) method are highlighted. To avoid the appearance of these structures which are detrimental to the quality of the simulations, a specific transport velocity is introduced and its inclusion within an Arbitrary Lagrangian Eulerian (ALE) formalism is described. Unlike most of existing particle disordering/shifting methods, this formalism avoids the formation of these anisotropic structures while a full consistency with the original Euler or Navier–Stokes equations is maintained. The gain in accuracy, convergence and numerical diffusion of this formalism is shown and discussed through its application to various challenging test cases.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
The present work is dedicated to the improvement of the δ-SPH scheme. This is an enhanced weakly-compressible SPH model widely used in recent years thanks to its benefits to the standard SPH scheme, ...to its low CPU costs and to its ease of implementation. Nonetheless, the δ-SPH still presents some drawbacks as other SPH models. For example, in some critical conditions it does not prevent the tensile instability and the consequent numerical fragmentation. Furthermore, even if the use of a diffusive term in the SPH continuity equation is able to reduce numerical high frequencies on the pressure field, the velocity gradients are generally noisy because of the irregularities of the particle spatial configurations, which, in specific flow conditions, can induce also extra numerical-dissipation. For these reasons a particle shifting technique is used to improve the model and a special treatment has been developed for particles that are close to the free-surface region. The introduction of the particle-shifting procedure is generalized in the context of multi-resolutions for which a novel algorithm is formulated to handle the particle re-positioning in the different resolution levels. The proposed algorithms can be straightforwardly implemented in an SPH model without requiring cumbersome code modifications. The δ+-SPH is validated on seven different benchmarks giving a wide panorama on the improvements of this new SPH model.
•The present work is dedicated to the improvement of the δ-SPH scheme.•A particle shifting technique is introduced in the context of weakly-compressible models.•A special treatment for particles that are close to the free-surface region is developed.•The particle-shifting procedure is generalized for multi-resolutions approaches.•The δ+-SPH is validated on seven different benchmarks.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
A weakly compressible SPH scheme has been used to describe the evolution of viscous flows around blunt bodies at Reynolds numbers ranging from 10 to 2400. The simulation of such a wide range, rarely ...addressed to in the SPH literature, has been possible thanks to the use of a proper ghost-fluid technique and to an accurate enforcement of the boundary conditions along the solid boundaries. In this context, a new numerical technique based on previous works by Takeda et al. (1994) 48, Marrone et al. (2011) 28 and De Leffe et al. (2011) 16 has been proposed, along with a new method for the evaluation of the global loads on bodies. Particular care has been taken to study the influence of the weakly-compressibility assumption and of different ghost-fluid techniques on the numerical results. An in-depth validation of the model has been performed by comparing the numerical outcome with experimental data from the literature and other numerical references. The influence of the domain size has been discussed in order to avoid wall side effects and, at the same time, to limit the computational costs. The convergence of the numerical solutions has been checked on both global and local quantities by choosing appropriate Reynolds-cell number.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK
A weakly compressible SPH solver is presented for applications involving nonlinear interaction between water waves and floating bodies. A complete algorithm able to compute fully coupled viscous ...Fluid–Solid interactions is described. No slip boundary condition on the solid surface is enforced through a ghost–fluid technique and the global loads are evaluated through the momentum exchange between fluid and ghost particles. A dedicated algorithm is developed to manage the intersection between the free surface and the solid profile. An explicit synchronous algorithm is proposed for the full coupling between fluid and rigid bodies. Stability, convergence and conservation properties are tested on several freely floating test cases and a final validation of the full algorithm is performed for the interaction between a 2-D box and a wave packet.
► An SPH solver for simulating nonlinear water waves interaction with floating bodies is presented. ► A complete algorithm to compute fullycoupled viscous FluidSolid interactions is reported. ► No slip boundary condition on the solid surface are enforced through a ghost-fluid technique. ► An algorithm to manage the intersection between the free surface and the solid profile is described. ► The full model is validated for the interaction between a 2D box and a wave packet.
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•SPH system is recast in the ALE framework and expressed through primitive variables.•Differently from the literature, standard SPH operators are adopted.•ALE-SPH schemes are shown to be unstable ...unless suitable diffusive terms are added.•We bridge the gap between ALE weak formulation and standard Lagrangian approach.•Comparisons against simplified SPH models are shown on standard numerical benchmarks.
The behaviour of a weakly-compressible SPH scheme obtained by rewriting the Navier-Stokes equations in an arbitrary Lagrangian-Eulerian (ALE) format is studied. Differently from previous works on ALE, which generally adopt conservative variables (i.e. mass and momentum) and rely on the use of Riemann solvers inside the spatial operators, the proposed model is expressed in terms of primitive variables (i.e. density and velocity) and is written by using the standard differential formulations of the weakly-compressible SPH schemes. Similarly to ALE-SPH models, the arbitrary velocity field is obtained by modifying the pure Lagrangian velocity of the material point through a velocity δu→ given by a Particle Shifting Technique (PST). We show that the above-mentioned ALE-SPH equations are, however, unstable when they are integrated in time. The instability appears in the form of large volume variations in those fluid regions characterised by high velocity strain rates. Nonetheless, the scheme can be stabilised if appropriate diffusion terms are included in both the equations of density and mass. This latter scheme, hereinafter called δ-ALE-SPH scheme, is validated against reference benchmark test-cases: the viscous flow around an inclined elliptical cylinder, the lid-driven cavity and a dam-break flow impacting a vertical wall.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
In the present work a consistent inclusion of a particle shifting technique (PST) in the weakly compressible Smoothed Particle Hydrodynamic (SPH) models is discussed. Recently, it has been shown that ...the use of PST can largely improve both the accuracy and the robustness of SPH models. In particular, the δ+-SPH model is a weakly-compressible SPH model where a PST is adopted along with a diffusive term in the continuity equation that helps removing the high-frequency noise on the pressure field. This specific SPH model is able to overcome the main drawbacks that afflict the standard weakly-compressible SPH model. In this work we demonstrate that a consistent introduction of the PST inside the SPH model leads to a new set of equations where some additional terms containing the particle shifting velocity δu have to be taken into account. The effects of these δu-terms become crucial for problems in confined or periodic domains, as well as for long-time simulations of free-surface flows. The proposed scheme is tested against challenging benchmark cases, highlighting when the δu-terms play an important role or not. Further improvements of the PST algorithms for the numerical treatment of the scheme close to the free surface and along the solid boundaries are also discussed.
•Derivation of a consistent particle shifting technique (PST) within the SPH model is presented.•SPH discretization of the additional terms due to PST in the momentum equation is discussed.•Validation of the proposed model on four different benchmark test-cases is conducted.•Unphysical drift of the solution is shown when PST is not included in a consistent way.•Application of the model to a long-time 3D simulation of a violent sloshing flow is presented.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UL, UM, UPCLJ, UPUK, ZRSKP
The present paper proposes a novel algorithm to detect the free-surface in particle simulations, both in two and three dimensions. Since the proposed algorithms are based on SPH interpolations their ...implementation does not require complex geometrical procedures. Thus the free-surface detection can be easily embedded in SPH solvers, without a significant increase of the CPU time. Throughout this procedure accurate normal vectors to the free-surface are made available. Then it is possible to define a level-set function algorithm which is presented in detail. The latter allows in-depth analyses of three-dimensional free-surface simulations by using standard visualization tools, including internal features of the flow. The algorithms proposed for detecting free-surface particles and defining the level-set function are validated on simple and complex two- and three-dimensional flow simulations. The usefulness of the proposed procedures to post-process and analyze complex flows are illustrated on realistic examples.
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10.
Energy balance in the δ-SPH scheme Antuono, M.; Marrone, S.; Colagrossi, A. ...
Computer methods in applied mechanics and engineering,
06/2015, Volume:
289
Journal Article
Peer reviewed
An in-depth analysis of the energy balance in the δ-SPH model has been carried on. In comparison to the standard SPH scheme, the mechanical energy equation of the δ-SPH variant is characterized by a ...further term that is generally dissipative and is related to the diffusive operator inside the continuity equation. The behaviour and the structure of such a term have been studied in detail and a number of specifically conceived test cases have been considered, highlighting that the dissipative term is generally small and it mainly acts when spurious high-frequency acoustic components are excited. In spite of such a dissipation mechanism, the δ-SPH appears more accurate than the standard SPH scheme even in simulating inviscid fluids.
•The theoretical analysis of the energy balance in the δ-SPH model has been carried on.•Inviscid free-surface problems have been used to study the model dissipation.•δ-SPH numerical dissipation mainly acts on spurious high-frequency acoustic components.•Higher accuracy of the solutions with respect to the standard SPH model is observed.•δ-SPH prevents numerical accumulation from mechanical energy to compressible energy.
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