اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدParticle-particle Particle-tree Code for Planetary System Formation with Individual Cut-off Method: GPLUM
181
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
In a standard theory of the formation of the planets in our Solar System, terrestrial planets and cores of gas giants are formed through accretion of kilometer-sized objects (planetesimals) in a protoplanetary disk. Gravitational $N$-body simulations of a disk system made up of numerous planetesimals are the most direct way to study the accretion process. However, the use of $N$-body simulations has been limited to idealized models (e.g. perfect accretion) and/or narrow spatial ranges in the radial direction, due to the limited number of simulation runs and particles available. We have developed new $N$-body simulation code equipped with a particle-particle particle-tree (${rm P^3T}$) scheme for studying the planetary system formation process: GPLUM. For each particle, GPLUM uses the fourth-order Hermite scheme to calculate gravitational interactions with particles within cut-off radii and the Barnes-Hut tree scheme for particles outside the cut-off radii. In existing implementations, ${rm P^3T}$ schemes use the same cut-off radius for all particles, making a simulation become slower when the mass range of the planetesimal population becomes wider. We have solved this problem by allowing each particle to have an appropriate cut-off radius depending on its mass, its distance from the central star, and the local velocity dispersion of planetesimals. In addition to achieving a significant speed-up, we have also improved the scalability of the code to reach a good strong-scaling performance up to 1024 cores in the case of $N=10^6$. GPLUM is freely available from https://github.com/YotaIshigaki/GPLUM with MIT license.
قيم البحث
اقرأ أيضاً
We describe the implementation and performance of the ${rm P^3T}$ (Particle-Particle Particle-Tree) scheme for simulating dense stellar systems. In ${rm P^3T}$, the force experienced by a particle is split into short-range and long-range contribution
s. Short-range forces are evaluated by direct summation and integrated with the fourth order Hermite predictor-corrector method with the block timesteps. For long-range forces, we use a combination of the Barnes-Hut tree code and the leapfrog integrator. The tree part of our simulation environment is accelerated using graphical processing units (GPU), whereas the direct summation is carried out on the host CPU. Our code gives excellent performance and accuracy for star cluster simulations with a large number of particles even when the core size of the star cluster is small.
This work presents a new multiphase SPH model that includes the shifting algorithm and a variable smoothing length formalism to simulate multi-phase flows with accuracy and proper interphase management. The implementation was performed in the DualSPH
ysics code and validated for different canonical experiments, such as the single-phase and multiphase Poiseuille and Couette test cases. The method is accurate even for the multiphase case for which two phases are simulated. The shifting algorithm and the variable smoothing length formalism has been applied in the multiphase SPH model to improve the numerical results at the interphase even when it is highly deformed and non-linear effects become important. The obtained accuracy in the validation tests and the good interphase definition in the instability cases indicate an important improvement in the numerical results compared with single-phase and multiphase models where the shifting algorithm and the variable smoothing length formalism are not applied.
The Athena MHD code has been extended to integrates the motion of particles coupled with the gas via aerodynamic drag, in order to study the dynamics of gas and solids in protoplanetary disks and the formation of planetesimals. Our particle-gas hybri
d scheme is based on a second order predictor-corrector method. Careful treatment of the momentum feedback on the gas guarantees exact conservation. The hybrid scheme is stable and convergent in most regimes relevant to protoplanetary disks. We describe a semi-implicit integrator generalized from the leap-frog approach. In the absence of drag force, it preserves the geometric properties of a particle orbit. We also present a fully-implicit integrator that is unconditionally stable for all regimes of particle-gas coupling. Using our hybrid code, we study the numerical convergence of the non-linear saturated state of the streaming instability. We find that gas flow properties are well converged with modest grid resolution (128 cells per pressure length eta r for dimensionless stopping time tau_s=0.1), and equal number of particles and grid cells. On the other hand, particle clumping properties converge only at higher resolutions, and finer resolution leads to stronger clumping before convergence is reached. Finally, we find that measurement of particle transport properties resulted from the streaming instability may be subject to error of about 20%.
We describe Pegasus, a new hybrid-kinetic particle-in-cell code tailored for the study of astrophysical plasma dynamics. The code incorporates an energy-conserving particle integrator into a stable, second-order--accurate, three-stage predictor-predi
ctor-corrector integration algorithm. The constrained transport method is used to enforce the divergence-free constraint on the magnetic field. A delta-f scheme is included to facilitate a reduced-noise study of systems in which only small departures from an initial distribution function are anticipated. The effects of rotation and shear are implemented through the shearing-sheet formalism with orbital advection. These algorithms are embedded within an architecture similar to that used in the popular astrophysical magnetohydrodynamics code Athena, one that is modular, well-documented, easy to use, and efficiently parallelized for use on thousands of processors. We present a series of tests in one, two, and three spatial dimensions that demonstrate the fidelity and versatility of the code.
For multi-time wave functions, which naturally arise as the relativistic particle-position representation of the quantum state vector, the analog of the Schrodinger equation consists of several equations, one for each time variable. This leads to the
question of how to prove the consistency of such a system of PDEs. The question becomes more difficult for theories with particle creation, as then different sectors of the wave function have different numbers of time variables. Petrat and Tumulka (2014) gave an example of such a model and a non-rigorous argument for its consistency. We give here a rigorous version of the argument after introducing an ultraviolet cut-off into the creation and annihilation terms of the multi-time evolution equations. These equations form an infinite system of coupled PDEs; they are based on the Dirac equation but are not fully relativistic (in part because of the cut-off). We prove the existence and uniqueness of a smooth solution to this system for every initial wave function from a certain class that corresponds to a dense subspace in the appropriate Hilbert space.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
