Improving the Smoothed Particle Hydrodynamics with an integral approach to calculate gradients (original) (raw)
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Improving smoothed particle hydrodynamics with an integral approach to calculating gradients
Astronomy & Astrophysics, 2012
Context. The smoothed particle hydrodynamics (SPH) technique is a well-known numerical method that has been applied to simulate the evolution of a wide variety of systems. Modern astrophysical applications of the method rely on the Lagrangian formulation of fluid Euler equations which is fully conservative. A different scheme, based on a matrix approach to the SPH equations is currently being used in computational fluid dynamics (CDF). These matrix formulations achieve better interpolations of the physical magnitudes but they are, in general, not fully conservative. The matrix approach to the Euler equations has never been used in astrophysics. Aims. We develop and test a fully conservative SPH scheme based on a tensor formulation that can be applied to simulate astrophysical systems.
The behavior of IAD_0 scheme, a fully conservative SPH scheme based on a tensor formulation, is analyzed in connection with several astrophysical scenarios, and compared to the same simulations carried out with the standard SPH technique. The proposed hydrodynamic scheme is validated using a variety of numerical tests that cover important topics in astrophysics, such as the evolution of supernova remnants, the stability of self-gravitating bodies and the coalescence of compact objects. The results suggest that the SPH scheme built with the integral approach to the derivatives premise improves the results of the standard SPH technique. In particular, it is observed a better development of hydrodynamic instabilities, an improved description of self-gravitant structures in equilibrium and a reasonable description of the process of coalescence of two white dwarfs. A good energy, and linear and angular momentum conservation, generally better than that of standard SPH, was also obtained. In addition the new scheme is less susceptible to suffer pairing instability.
Smoothed particle hydrodynamics: checking a tensor approach to calculating gradients
We describe and check a novel formulation of Smoothed Particle Hydrodynamics (SPH) based on an Integral Approach to the Derivatives, called IAD_0, that can be applied to simulate astrophysical systems. The method relies in a tensor approach to calculating gradients, which is more accurate than the standard procedure (STD), due to its better renormalization properties. The proposed scheme fully conserves momentum and energy in isentropic flows, and is less susceptible to the pairing instability. The resulting algorithm is verified using two tests: a two-dimensional simulation of the Kelvin-Helmholtz instability and the three-dimensional simulation of the merging of two polytropes. The analysis of these test cases suggests that the method is able to improve the results of the standard technique with only a moderate computational overload.
An improved SPH scheme for cosmological simulations
We present an implementation of smoothed particle hydrodynamics (SPH) with improved accuracy for simulations of galaxies and the large-scale structure. In particular, we combine, implement, modify and test a vast majority of SPH improvement techniques in the latest instalment of the GADGET code. We use the Wendland kernel functions, a particle wake-up time-step limiting mechanism and a time-dependent scheme for artificial viscosity, which includes a high-order gradient computation and shear flow limiter. Additionally, we include a novel prescription for time-dependent artificial conduction, which corrects for gravitationally induced pressure gradients and largely improves the SPH performance in capturing the development of gas-dynamical instabilities. We extensively test our new implementation in a wide range of hydrodynamical standard tests including weak and strong shocks as well as shear flows, turbulent spectra, gas mixing, hydrostatic equilibria and self-gravitating gas clouds....
Smoothed particle hydrodynamics calculations of stellar interactions
Journal of Computational and Applied Mathematics, 1999
Smoothed Particle Hydrodynamics is a multidimensional Lagrangian method of numerical hydrodynamics that has been used to tackle a wide variety of problems in astrophysics. Here we develop the basic equations of the SPH scheme, and we discuss some of its numerical properties and limitations. As an illustration of typical astrophysical applications, we discuss recent calculations of stellar interactions, including collisions between main sequence stars and the coalescence of compact binaries.
SPHYNX: an accurate density-based SPH method for astrophysical applications
Astronomy & Astrophysics
Aims. Hydrodynamical instabilities and shocks are ubiquitous in astrophysical scenarios. Therefore, an accurate numerical simulation of these phenomena is mandatory to correctly model and understand many astrophysical events, such as supernovas, stellar collisions, or planetary formation. In this work, we attempt to address many of the problems that a commonly used technique, smoothed particle hydrodynamics (SPH), has when dealing with subsonic hydrodynamical instabilities or shocks. To that aim we built a new SPH code named SPHYNX, that includes many of the recent advances in the SPH technique and some other new ones, which we present here. Methods. SPHYNX is of Newtonian type and grounded in the Euler-Lagrange formulation of the smoothed-particle hydrodynamics technique. Its distinctive features are: the use of an integral approach to estimating the gradients; the use of a flexible family of interpolators called sinc kernels, which suppress pairing instability; and the incorporation of a new type of volume element which provides a better partition of the unity. Unlike other modern formulations, which consider volume elements linked to pressure, our volume element choice relies on density. SPHYNX is, therefore, a density-based SPH code. Results. A novel computational hydrodynamic code oriented to Astrophysical applications is described, discussed, and validated in the following pages. The ensuing code conserves mass, linear and angular momentum, energy, entropy, and preserves kernel normalization even in strong shocks. In our proposal, the estimation of gradients is enhanced using an integral approach. Additionally, we introduce a new family of volume elements which reduce the so-called tensile instability. Both features help to suppress the damp which often prevents the growth of hydrodynamic instabilities in regular SPH codes. Conclusions. On the whole, SPHYNX has passed the verification tests described below. For identical particle setting and initial conditions the results were similar (or better in some particular cases) than those obtained with other SPH schemes such as GADGET-2, PSPH or with the recent density-independent formulation (DISPH) and conservative reproducing kernel (CRKSPH) techniques.
Particle Mesh Hydrodynamics for Astrophysics Simulations
2007
We present a particle method for the simulation of three dimensional compressible hydrodynamics based on a hybrid Particle-Mesh discretization of the governing equations. The method is rooted on the regularization of particle locations as in remeshed Smoothed Particle Hydrodynamics (rSPH). The rSPH method was recently introduced to remedy problems associated with the distortion of computational elements in SPH, by periodically re-initializing the particle positions and by using high order interpolation kernels.
Adaptive Smoothed Particle Hydrodynamics: Methodology. II
The Astrophysical Journal Supplement Series, 1998
are presented. The ASPH method replaces the isotropic smoothing algorithm of standard SPH, in which interpolation is performed with spherical kernels of radius given by a scalar smoothing length, with anisotropic smoothing involving ellipsoidal kernels and tensor smoothing lengths. In standard SPH the smoothing length for each particle represents the spatial resolution scale in the vicinity of that particle, and is typically allowed to vary in space and time so as to reflect the local value of the mean interparticle spacing. This isotropic approach is not optimal, however, in the presence of strongly anisotropic volume changes such as occur naturally in a wide range of astrophysical flows, including gravitational collapse, cosmological structure formation, cloud-cloud collisions, and radiative shocks. In such cases, the local mean interparticle spacing varies not only in time and space, but in direction as well. This problem is remedied in ASPH, where each axis of the ellipsoidal smoothing kernel for a given particle is adjusted so as to reflect the different mean interparticle spacings along different directions in the vicinity of that particle. By deforming and rotating these ellipsoidal kernels so as to follow the anisotropy of volume changes local to each particle, ASPH adapts its spatial resolution scale in time, space, and direction. This significantly improves the spatial resolving power of the method over that of standard SPH at fixed particle number per simulation. This paper presents an alternative formulation of the ASPH algorithm for evolving anisotropic smoothing kernels, in which the geometric approach of Paper I, based upon 1 Current Address: LLNL, L-16, Livermore, CA 94551 -2the Lagrangian deformation of ellipsoidal fluid elements surrounding each particle, is replaced by an approach involving a local transformation of coordinates to those in which the underlying anisotropic volume changes appear to be isotropic. Using this formulation the ASPH method is presented in 2D and 3D, including a number of details not previously included in Paper I, some of which represent either advances or different choices with respect to the ASPH method detailed in Paper I. Among the advances included here are an asynchronous time-integration scheme with different time steps for different particles and the generalization of the ASPH method to 3D. In the category of different choices, the shock-tracking algorithm described in Paper I for locally adapting the artificial viscosity to restrict viscous heating just to particles encountering shocks, is not included here. Instead, we adopt a different interpolation kernel for use with the artificial viscosity, which has the effect of spatially localizing effects of the artificial viscosity. This version of the ASPH method in 2D and 3D is then applied to a series of 1D, 2D, and 3D test problems, and the results are compared to those of standard SPH applied to the same problems. These include the problem of cosmological pancake collapse, the Riemann shock tube, cylindrical and spherical Sedov blast waves, the collision of two strong shocks, and problems involving shearing disks intended to test the angular momentum conservation properties of the method. These results further support the idea that ASPH has significantly better resolving power than standard SPH for a wide range of problems, including that of cosmological structure formation. Subject headings: cosmology: theory -galaxies: formation -hydrodynamicsintergalactic medium -large scale structure of the universe -methods: numerical
Accuracy Improvement of Smoothed Particle Hydrodynamics
The smoothed particle hydrodynamics (SPH) is a mesh-free particle method, which has been successfully applied to a wide range of astrophysical problems. So far, the SPH method has been extended to elastic dynamics and computational fluid dynamics. High order derivatives have to be approximated when elastic dynamics problems are modeled. However, the approximation errors in SPH could lead to computational failure in the case that the order of derivative is high. The present paper proposes a novel method to improve the accuracy of SPH method by the lemma proved by the authors. The proposed method shows the relationship between the selected functions and their SPH approximations. In addition, error comparisons are made between SPH methods with and without the improvement. Keywords: smoothed particle hydrodynamics; high order accuracy; second order derivative
Cosmological Simulations with Adaptive Smoothed Particle Hydrodynamics
Proceedings of the International Astronomical Union
We summarize the ideas that led to the Adaptive Smoothed Particle Hydrodynamics (ASPH) algorithm, with anisotropic smoothing and shock-tracking. We then identify a serious new problem for SPH simulations with shocks and radiative cooling -false cooling -and discuss a possible solution based on the shock-tracking ability of ASPH.