Using the PPML approach for constructing a low-dissipation, operator-splitting scheme for numerical simulations of hydrodynamic flows

Protasov

2019

JIT

The complexity of astrophysical processes lies in simultaneous consideration of components with different nature. So, for example, in the problem of collision of galaxies the three-dimensional dynamics of interstellar gas and stellar component is considered. The modeling of these components could be based on completely different classes of numerical methods. One possible solution to this problem is the use of the Eulerian-Lagrangian approach, in which the physical quantities are concentrated in material points, which is typical for the SPH method, and the calculation of forces is made on an adaptive grid bound to the system of material points. This approach uniformly takes into account both the dynamics of the continuous medium and discrete particles, and also eliminates a number of disadvantages typical for the original method. The calculation of the gravitational interaction is carried out by solving the Poisson equation for the gravitational potential. Herewith, all the particles are projected onto the computational grid and the potential values in each cell are calculated using this grid. The solution of the Poisson equation for the gravitational potential is performed using Fast Fourier Transform. The new “Virtual Planetarium” code for astrophysical objects modeling based on SPH method, supplemented by Godunov method for calculating pressure and momentum flows between particles, and Fast Fourier Transform method to solve the Poisson equation for the gravitational potential, is described in the paper. Rationale for the transition to such numerical model is given in the paper. Kinetic and hydrodynamic approaches are described in detail. The modeling of collapse of an isothermal gas cloud is performed, the ability of the method to reproduce the development of instabilities in the form of the formation of two density sleeves is shown.

Section: дискуссияunclassified

Section: результаты моделированияunclassified

“Virtual Planetarium” Code for Astrophysical Objects Modeling: Mathematical Model, Methodology and First Results

Protasov

2019

JIT

“…Its time derivative can be described by the Cauchy-Kovalevskaya equation. By using this mathematical model it becomes possible to formulate a generalized parallelization calculation method [15], which is based on a combination of an operator-splitting method, Godunov method, and a piecewise-parabolic approximation on a regular grid cell. Fig.…”

Section: Modeling Of Magneto-hydrodynamics Turbulence Evolutionmentioning

confidence: 99%

“…A comparison of different codes for subsonic turbulence is presented in [13]. Classical methods for simulation of magnetohydrodynamic turbulence such as adaptive mesh refinement (AMR) and smoothed-particle hydrodynamics are still widely used, but in recent years an impressive range of new methods have been proposed (a good review of these methods can be found in [14][15][16]). …”

Section: Introductionmentioning

confidence: 99%

Multilevel Parallelization: Grid Methods for Solving Direct and Inverse Problems

Titarenko

Communications in Computer and Information Science

Chernykh³

et al. 2016

Abstract. In this paper we present grid methods which we have developed for solving direct and inverse problems, and their realization with different levels of optimization. We have focused on solving systems of hyperbolic equations using finite difference and finite volume numerical methods on multicore architectures. Several levels of parallelism have been applied: geometric decomposition of the calculative domain, workload distribution over threads within OpenMP directives, and vectorization. The run-time efficiency of these methods has been investigated. These developments have been tested using the astrophysics code AstroPhi on a hybrid cluster Polytechnic RSC PetaStream (consisting of Intel Xeon Phi accelerators) and a geophysics (seismic wave) code on an Intel Core i7-3930K multicore processor. We present the results of the calculations and study MPI run-time energy efficiency.

“…In practice, various numerical methods are often employed to compute the gravitational potential using the Poisson equation (e.g., Binney et al 1987;Press et al 1992;Bodenheimer et al 2007). The gravity force can then be calculated from the gradient of the potential using discretization schemes with various levels of complexity (e.g., Stone & Norman 1992;Kulikov & Vorobyov 2016;Wang & Yen 2020). The required computational resources are often substantial and may take up a large portion of the entire runtime of a three-dimensional numerical hydrodynamics code.…”

Section: Introductionmentioning

confidence: 99%

Computing the gravitational potential on nested meshes using the convolution method

Vorobyov

McKevitt

et al. 2023

A&A

Aims. Our aim is to derive a fast and accurate method for computing the gravitational potential of astrophysical objects with high contrasts in density, for which nested or adaptive meshes are required. Methods. We present an extension of the convolution method for computing the gravitational potential to the nested Cartesian grids. The method makes use of the convolution theorem to compute the gravitational potential using its integral form. Results. A comparison of our method with the iterative outside-in conjugate gradient and generalized minimal residual methods for solving the Poisson equation using nonspherically symmetric density configurations has shown a comparable performance in terms of the errors relative to the analytic solutions. However, the convolution method is characterized by several advantages and outperforms the considered iterative methods by factors 10-200 in terms of the runtime, especially when graphics processor units are utilized. The convolution method also shows an overall second-order convergence, except for the errors at the grid interfaces where the convergence is linear. Conclusions. High computational speed and ease in implementation can make the convolution method a preferred choice when using a large number of nested grids. The convolution method, however, becomes more computationally costly if the dipole moments of tightly spaced gravitating objects are to be considered at coarser grids.