Smoothed Particle Hydrodynamics Algorithm Research Articles

Simulation of Gravity Wave Propagation in Free Surface Flows by an Incompressible SPH Algorithm

This paper presents an incomp ressible smoothed particle hydrodynamics (SPH) model to simulate wave propagation in a free surface flow. The Navier-Stokes equations are solved in a Lagrangian framework using a three-step fractional method. In the first step, a temporary velocity field is provided according to the relevant body forces. This velocity field is renewed in the second step to include the viscosity effects. A Poisson equation is employed in the third step as an alternative for the equation of state in order to evaluate pressure. This Poisson equation considers a trad e-off between density and pressure which is utilized in the third step to impose the incompressibility effect. The computations are compared with the experimental as well as numerical data and a good agreement is observed. In order to validate proposed algorithm, a dam-break problem is solved as a benchmark solution and the computational results are compared with the previous numerical ones.

A stabilized Runge–Kutta, Taylor smoothed particle hydrodynamics algorithm for large deformation problems in dynamics

SUMMARYNumerical simulation of large deformation and failure problems present a series of difficulties when solved using mesh based methods. Meshless methods present an interesting alternative that has been explored in the past years by researchers. Here we propose a Runge–Kutta Taylor SPH model based on formulating the dynamic problem as a set of first‐order PDEs. Two sets of nodes are used for time steps n and n + 1 ∕ 2, resulting on avoiding the classical tensile instability of some other SPH formulations. To improve the accuracy and stability of the algorithm, the Taylor expansion in time of the advective terms is combined with a Runge–Kutta integration of the sources. Finally, as boundaries change during the process, a free surface detection algorithm is introduced. Copyright © 2012 John Wiley & Sons, Ltd.

A combined strip theory and Smoothed Particle Hydrodynamics approach for estimating slamming loads on a ship in head seas

Smoothed Particle Hydrodynamics (SPH) is a mesh-free Lagrangian numerical method suited to modelling fluids with a freely deforming surface. A two-dimensional SPH algorithm has been developed and applied to the problem of ship keel and bow-flare slamming. Freely decelerating drop tests of a model flared hull section were used as a basis for an initial validation of the SPH model. Relative vertical velocity profiles measured during tow tank experiments were then imposed on two-dimensional SPH models and reasonable agreement between the experimental and numerical slamming pressures was found. Finally, relative vertical velocity profiles calculated using SEAWAY software were implemented in the SPH algorithm, so as to simulate slamming on a typical V-form hull model.

Smoothed Particle Hydrodynamics and Its Diverse Applications

This review focuses on the applications of smoothed particle hydrodynamics (SPH) to incompressible or nearly incompressible flow. In the past 17 years, the range of applications has increased as researchers have realized the ability of SPH algorithms to handle complex physical problems. These include the disruption of free surfaces when a wave hits a rocky beach, multifluid problems that may involve the motion of rigid and elastic bodies, non-Newtonian fluids, virtual surgery, and chemical precipitation from fluids moving through fractured media. SPH provides a fascinating tool that has some of the properties of molecular dynamics while retaining the attributes of the macroscopic equations of continuum mechanics.

A smoothed-particle hydrodynamics model for ice-sheet and ice-shelf dynamics

AbstractMathematical modeling of ice sheets is complicated by the nonlinearity of the governing equations and boundary conditions. Standard grid-based methods require complex front-tracking techniques and have a limited capability to handle large material deformations and abrupt changes in bottom topography. Consequently, numerical methods are usually restricted to shallow ice-sheet and ice-shelf approximations. We propose a new smoothed-particle hydrodynamics (SPH) model for coupled ice-sheet and ice-shelf dynamics. SPH, a fully Lagrangian particle method, is highly scalable and its Lagrangian nature and meshless discretization are well suited to the simulation of free surface flows, large material deformation and material fragmentation. In this paper, we use the SPH model to study ice-sheet/ice-shelf behavior, and the dynamics of the grounding line. The steady-state position of the grounding line obtained from SPH simulations is in good agreement with laboratory observations for a wide range of simulated bedrock slopes and density ratios, similar to those of ice and sea water. The numerical accuracy of the SPH algorithm is verified by simulating the plane-shear flow of two immiscible fluids and the propagation of a highly viscous blob of fluid along a horizontal surface. In the experiment, the ice was represented with a viscous Newtonian fluid. For consistency, in the described SPH model the ice is also modeled as a viscous Newtonian fluid. Typically, ice sheets are modeled as a non-Newtonian fluid, accounting for the changes in the mechanical properties of the ice. Implementation of a non-Newtonian rheology in the SPH model is the subject of our ongoing research.

Dusty gas with smoothed particle hydrodynamics - II. Implicit timestepping and astrophysical drag regimes

In a companion paper (Laibe & Price 2011b), we have presented an algorithm for simulating two-fluid gas and dust mixtures in Smoothed Particle Hydrodynamics (SPH). In this paper, we develop an implicit timestepping method that preserves the exact conservation of the both linear and angular momentum in the underlying SPH algorithm, but unlike previous schemes, allows the iterations to converge to arbitrary accuracy and is suited to the treatment of non- linear drag regimes. The algorithm presented in Paper I is also extended to deal with realistic astrophysical drag regimes, including both linear and non-linear Epstein and Stokes drag. The scheme is benchmarked against the test suite presented in Paper I, including i) the analytic solutions of the dustybox problem and ii) solutions of the dustywave, dustyshock, dustysedov and dustydisc obtained with explicit timestepping. We find that the implicit method is 1- 10 times faster than the explicit temporal integration when the ratio r between the the timestep and the drag stopping time is 1 < r < 1000.

Protective design of a warship broadside liquid cabin

Based on the traditional Smoothed Particle Hydrodynamics (SPH) algorithm, the linked-list search algorithm combined with the variable smoothing length and square support domain was put forward to improve the calculation efficiency and guarantee the calculation accuracy. The physical process of high velocity fragment impact on a broadside liquid cabin was programmed for simulation. The numerical results agreed well with those of the general software ANSYS AUTODYN, which verifies the effectiveness and feasibility of the numerical method. From the perspective of the outer plate thickness of the liquid cabin, the width of the liquid cabin, and incident angle of the fragment, the influence of these parameters on protective mechanisms was analyzed to provide a basis for protective design of a broadside liquid cabin. Results show that the influence of outer plate thickness is not obvious; therefore, the conventional design can be adopted in the design of the outer plate. The width of the liquid cabin has a great influence on the residual velocity of the fragment and the width of the liquid cabin should be designed to be as wide as possible under the premise of meeting other requirements. There is a certain incident angle in which the velocity attenuation of the fragment is most obvious, and the high-pressure zone near the inner plate is asymmetric. The inner plate of liquid cabin should be strengthened according to the hull form, principal dimensions, and vulnerable points.

RpSPH: a novel smoothed particle hydrodynamics algorithm

We suggest a novel discretisation of the momentum equation for Smoothed Particle Hydrodynamics (SPH) and show that it significantly improves the accuracy of the obtained solutions. Our new formulation which we refer to as relative pressure SPH, rpSPH, evaluates the pressure force in respect to the local pressure. It respects Newtons first law of motion and applies forces to particles only when there is a net force acting upon them. This is in contrast to standard SPH which explicitly uses Newtons third law of motion continuously applying equal but opposite forces between particles. rpSPH does not show the unphysical particle noise, the clumping or banding instability, unphysical surface tension, and unphysical scattering of different mass particles found for standard SPH. At the same time it uses fewer computational operations. and only changes a single line in existing SPH codes. We demonstrate its performance on isobaric uniform density distributions, uniform density shearing flows, the Kelvin-Helmholtz and Rayleigh-Taylor instabilities, the Sod shock tube, the Sedov-Taylor blast wave and a cosmological integration of the Santa Barbara galaxy cluster formation test. rpSPH is an improvement these cases. The improvements come at the cost of giving up exact momentum conservation of the scheme. Consequently one can also obtain unphysical solutions particularly at low resolutions.

EvoL: the new Padova Tree-SPH parallel code for cosmological simulations

<i>Context. <i/>We present the new release of the Padova <i>N<i/>-body code for cosmological simulations of galaxy formation and evolution, EvoL. The basic Tree + SPH code is presented and analysed, together with an overview of the software architectures.<i>Aims. <i/>EvoL is a flexible parallel Fortran95 code, specifically designed for simulations of cosmological structure formations on cluster, galactic and sub-galactic scales.<i>Methods. <i/>EvoL is a fully Lagrangian self-adaptive code, based on the classical oct-tree by Barnes & Hut (1986, Nature, 324, 446) and on the smoothed particle hydrodynamics algorithm (SPH, Lucy 1977, AJ, 82, 1013). It includes special features like adaptive softening lengths with correcting extra-terms, and modern formulations of SPH and artificial viscosity. It is designed to be run in parallel on multiple CPUs to optimise the performance and save computational time.<i>Results. <i/>We describe the code in detail, and present the results of a number of standard hydrodynamical tests.

Structure, kinematics and chemical enrichment patterns after major gas-rich disc-disc mergers

We used an N-body smoothed particle hydrodynamics algorithm, with a detailed treatment of star formation, supernovae feedback, and chemical enrichment, to perform eight simulations of mergers between gas-rich disc galaxies. We vary the mass ratio of the progenitors, their rotation axes, and their orbital parameters and analyze the kinematic, structural, and chemical properties of the remnants. Six of these simulations result in the formation of a merger remnant with a disc morphology as a result of the large gas-fraction of the remnants. We show that stars formed during the merger (a sudden starburst occur in our simulation and last for 0.2-0.3 Gyr) and those formed after the merger have different kinematical and chemical properties. The first ones are located in thick disc or the halo. They are partially supported by velocity dispersion and have high [alpha/Fe] ratios even at metallicities as high as [Fe/H]=-0.5. The former ones -- the young component -- are located in a thin disc rotationally supported and have lower [alpha/Fe] ratios. The difference in the rotational support of both components results in the rotation of the thick disc lagging that of the thin disc by as much as a factor of two, as recently observed.We find that, while the kinematic and structural properties of the merger remnant depends strongly upon the orbital parameters of the mergers, there is a remarkable uniformity in the chemical properties of the mergers. This suggests that general conclusions about the chemical signature of gas-rich mergers can be drawn.

Developing a component-based framework for subsurface simulation using the Common Component Architecture

This paper will provide a brief overview of two frameworks being developed for subsurface simulations. The first is based on the Smoothed Particle Hydrodynamics algorithm and is designed to model flow and transport at the pore scale. The second is based on the Subsurface Transport Over Multiple Phases subsurface continuum code (STOMP) and is designed to simulate flow at the Darcy scale. Both frameworks have been built using the Common Component Architecture toolkit. These frameworks will eventually be combined into a single framework for performing hybrid multiscale simulations that seamlessly integrate both the particle and continuum simulations together.

Numerical simulation of water mitigation effects on shock wave with SPH method

The water mitigation effect on the propagation of shock wave was investigated numerically. The traditional smoothed particle hydrodynamics (SPH) method was modified based on Riemann solution. The comparison of numerical results with the analytical solution indicated that the modified SPH method has more advantages than the traditional SPH method. Using the modified SPH algorithm, a series of one-dimensional planar wave propagation problems were investigated, focusing on the influence of the air-gap between the high-pressure air and water and the thickness of water. The numerical results showed that water mitigation effect is significant. Up to 60% shock wave pressure reduction could be achieved with the existence of water, and the shape of shock wave was also changed greatly. It is seemly that the small air-gap between the high-pressure air and water has more influence on water mitigation effect.

Comparisons of weakly compressible and truly incompressible algorithms for the SPH mesh free particle method

In the smoothed particle hydrodynamics (SPH) discretisation method for the Navier–Stokes equations the most widespread method to solve for pressure and mass conservation is the weakly compressible assumption (WCSPH). This includes hydraulics applications and leads to some drawbacks such as severe artificial pressure fluctuations and a limitation to very small time steps related to the WCSPH Mach number and explicit method. This paper presents comparisons of a semi-implicit and truly incompressible SPH (ISPH) algorithm with the classical WCSPH method, showing how some of the problems encountered in WCSPH have been resolved by using ISPH to simulate incompressible flows. Mathematical models are presented before describing SPH formalism. Several standard boundary conditions are introduced and special attention is given to tracking the surface particles. The lid-driven cavity flow ( Re = 400 and 1000) is performed as a benchmarking test. A bluff body test case (a square cylinder in a closed channel, Re d = 20 and 100 based on the cylinder diameter) shows that pressure fields extracted from WCSPH are very unreliable whereas ISPH predict pressures and forces in closer agreement with classical finite volume CFD methods. Dam-breaking cases, with dry or wet beds downstream, are then presented to highlight free-surface flow and rapid dynamics effects. The WCSPH and ISPH results are generally verified with reference data from experiment and/or another numerical method. All the comparisons show improvement with ISPH and good agreement in general.

A fully explicit three‐step SPH algorithm for simulation of non‐Newtonian fluid flow

PurposeThis paper sets out to present a fully explicit smoothed particle hydrodynamics (SPH) method to solve non‐Newtonian fluid flow problems.Design/methodology/approachThe governing equations are momentum equations along with the continuity equation which are described in a Lagrangian framework. A new treatment similar to that used in Eulerian formulations is applied to viscous terms, which facilitates the implementation of various inelastic non‐Newtonian models. This approach utilizes the exact forms of the shear strain rate tensor and its second principal invariant to calculate the shear stress tensor. Three constitutive laws including power‐law, Bingham‐plastic and Herschel‐Bulkley models are studied in this work. The imposition of the incompressibility is fulfilled using a penalty‐like formulation which creates a trade‐off between the pressure and density variations. Solid walls are simulated by the boundary particles whose positions are fixed but contribute to the field variables in the same way as the fluid particles in flow field.FindingsThe performance of the proposed algorithm is assessed by solving three test cases including a non‐Newtonian dam‐break problem, flow in an annular viscometer using the aforementioned models and a mud fluid flow on a sloping bed under an overlying water. The results obtained by the proposed SPH algorithm are in close agreement with the available experimental and/or numerical data.Research limitations/implicationsIn this work, only inelastic non‐Newtonian models are studied. This paper deals with 2D problems, although extension of the proposed scheme to 3D is straightforward.Practical implicationsThis study shows that various types of flow problems involving fluid‐solid and fluid‐fluid interfaces can be solved using the proposed SPH method.Originality/valueUsing the proposed numerical treatment of viscous terms, a unified and consistent approach was devised to study various non‐Newtonian flow models.

EFFECT OF CHEMICAL FREEZE OUT ON IDENTIFIED PARTICLE SPECTRA AT 200 AGeV Au-Au COLLISIONS AT RHIC USING SPheRIO

We investigate the effect of chemical freeze-out on identified particle spectra at 200 A GeV Au - Au Collisions at RHIC, by utilizing a full three-dimensional hydrodynamical calculation. The hydrodynamical code SPheRIO we employed is based on the smoothed particle hydrodynamic algorithm. In order to describe the spectra of strange hadrons, the code has been further improved by explicitly incorporating the strangeness conservation and a chemical freeze-out mechanism. In our model, strange hadrons such as Λ, Ξ, Ω and φ undergo the chemical freeze-out immediately after the hadronization, and their multiplicities are fixed thereafter. At a lower temperature the thermal freeze-out takes place for all the particles. It is shown that the present model provides a reasonably good description for the spectra of identified particles, in particular, considerable improvement is observed for those of strange hadrons.

Toy Stars in two dimensions

Toy Stars are gas masses where the compressibility is treated without approximations but gravity is replaced by a force which, for any pair of masses, is along their line of centres and proportional to their separation. They provide an invaluable resource for testing the suitability of numerical codes for astrophysical gas dynamics. In this paper we derive the equations for both small amplitude oscillations and non linear solutions for rotating and pulsating Toy Stars in two dimensions, and show that the solutions can be reduced to a small number of ordinary differential equations. We compare the accurate solutions of these equations with Smoothed Particle Hydrodynamics (SPH) simulations. The two dimensional Toy Star solutions are found to provide an excellent benchmark for SPH algorithms, highlighting many of the strengths and also some weaknesses of the method.

Smoothed Particle Hydrodynamics in cosmology: a comparative study of implementations

We analyse the performance of 12 different implementations of Smoothed Particle Hydrodynamics (SPH) using seven tests designed to isolate key hydrodynamic elements of cosmological simulations which are known to cause the SPH algorithm problems. In order, we consider a shock tube, spherical adiabatic collapse, cooling flow model, drag, a cosmological simulation, rotating cloud-collapse and angular momentum transport. In the implementations special attention is given to the way in which force symmetry is enforced in the equations of motion. We study in detail how the hydrodynamics are affected by different implementations of the artificial viscosity including those with a shear-correction modification. We present an improved first-order smoothing-length update algorithm that is designed to remove instabilities that are present in simple forward prediction algorithms. Gravity is calculated using the adaptive particle–particle, particle–mesh algorithm. For all tests we find that the artificial viscosity is the single most important factor distinguishing the results from the various implementations. The shock tube and adiabatic collapse problems show that the artificial viscosity used in the hydra code prior to version 4.0 performs relatively poorly for simulations involving strong shocks when compared to a more standard artificial viscosity. The shear-correction term is shown to reduce the shock-capturing ability of the algorithm and to lead to a spurious increase in angular momentum in the rotating cloud-collapse problem. For the disc stability test, the shear-corrected and previous hydra artificial viscosities are shown to reduce outward angular momentum transport. The cosmological simulations produce comparatively similar results, with the fraction of gas in the hot and cold phases varying by less than 10 per cent amongst the versions. Similarly, the drag test shows little systematic variation amongst versions. The cooling flow tests show that implementations using the force symmetrization of Thomas & Couchman are more prone to accelerate the overcooling instability of SPH, although the problem is generic to SPH. The second most important factor in code performance is the way force symmetry is achieved in the equation of motion. Most results favour a kernel symmetrization approach. The exact method by which SPH pressure forces are included in the equation of motion appears to have comparatively little effect on the results. Combining the equation of motion presented by Thomas & Couchman with a modification of the Monaghan & Gingold artificial viscosity leads to an SPH scheme that is both fast and reliable.

Smoothed Particle Hydrodynamics in cosmology: a comparative study of implementations

We analyse the performance of 12 different implementations of Smoothed Particle Hydrodynamics (SPH) using seven tests designed to isolate key hydrodynamic elements of cosmological simulations which are known to cause the SPH algorithm problems. In order, we consider a shock tube, spherical adiabatic collapse, cooling flow model, drag, a cosmological simulation, rotating cloud-collapse and angular momentum transport. In the implementations special attention is given to the way in which force symmetry is enforced in the equations of motion. We study in detail how the hydrodynamics are affected by different implementations of the artificial viscosity including those with a shear-correction modification. We present an improved first-order smoothing-length update algorithm that is designed to remove instabilities that are present in simple forward prediction algorithms. Gravity is calculated using the adaptive particle–particle, particle–mesh algorithm. For all tests we find that the artificial viscosity is the single most important factor distinguishing the results from the various implementations. The shock tube and adiabatic collapse problems show that the artificial viscosity used in the hydra code prior to version 4.0 performs relatively poorly for simulations involving strong shocks when compared to a more standard artificial viscosity. The shear-correction term is shown to reduce the shock-capturing ability of the algorithm and to lead to a spurious increase in angular momentum in the rotating cloud-collapse problem. For the disc stability test, the shear-corrected and previous hydra artificial viscosities are shown to reduce outward angular momentum transport. The cosmological simulations produce comparatively similar results, with the fraction of gas in the hot and cold phases varying by less than 10 per cent amongst the versions. Similarly, the drag test shows little systematic variation amongst versions. The cooling flow tests show that implementations using the force symmetrization of Thomas & Couchman are more prone to accelerate the overcooling instability of SPH, although the problem is generic to SPH. The second most important factor in code performance is the way force symmetry is achieved in the equation of motion. Most results favour a kernel symmetrization approach. The exact method by which SPH pressure forces are included in the equation of motion appears to have comparatively little effect on the results. Combining the equation of motion presented by Thomas & Couchman with a modification of the Monaghan & Gingold artificial viscosity leads to an SPH scheme that is both fast and reliable.

Cosmological Smoothed Particle Hydrodynamic Simulations with Four Million Particles: Statistical Properties of X‐Ray Clusters in a Low‐Density Universe

We present results from a series of cosmological smoothed particle hydrodynamics (SPH) simulations coupled with the particle-particle-particle-mesh solver for the gravitational force. The simulations are designed to predict the statistical properties of X-ray clusters of galaxies as well as to study the formation of galaxies. We have seven simulation runs with different assumptions about the thermal state of the intracluster gas. Following the recent work by Pearce and coworkers, we modify our SPH algorithm so as to phenomenologically incorporate galaxy formation by decoupling the cooled gas particles from the hot gas particles. All the simulations employ 1283 particles both for dark matter and for gas components and thus constitute the largest systematic catalogs of clusters simulated in the SPH method performed so far. These enable us to compare the analytical predictions about statistical properties of X-ray clusters against our direct simulation results in an unbiased manner. We find that the luminosities of the simulated clusters are quite sensitive to the thermal history and also to the numerical resolution of the simulations and thus are not reliable. On the other hand, the mass-temperature relation for the simulated clusters is fairly insensitive to the assumptions of the thermal state of the intracluster gas, is robust against the numerical resolution, and in fact agrees well with the analytic prediction. Therefore, prediction of the X-ray temperature functions of clusters on the basis of the Press-Schechter mass function and the virial equilibrium is fairly reliable.

A treatment of zero-energy modes in the smoothed particle hydrodynamics method

This paper describes the development and testing of an approach for treatment of zero-energy modes in the Smoothed Particle Hydrodynamics (SPH) method. The zero-energy modes are a consequence of the fact that field variables and their derivatives are calculated at the same points, so that an alternating field variable has a zero gradient at the particles. An alternative discretisation method that uses two types of particles, “velocity particles” where the velocity is known and “stress particles” where the stress is known, is proposed as a solution to this problem. This approach prevents the zero-energy modes from occurring, and also is a probable solution to the tensile instability problem. 1D and 2D algorithms are presented and test results shown, demonstrating that it does solve the zero-energy mode problem. This approach also offered a method to satisfy the stress-free boundary condition with out the need to explicitly enforce it, as is required in conventional normalised SPH. This was achieved by placing only the velocity points (points where the velocity is known) at material boundaries. The proposed type of discretisation and boundary treatment significantly improves performance and simplifies penalty based contact algorithm for SPH.