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In this paper a new scalable hydrodynamic code GPUPEGAS (GPUaccelerated PErformance Gas Astrophysic Simulation) for simulation of interacting galaxies is proposed. The code is based on combination of Godunov method as well as on the original implementation of FlIC method, specially adapted for GPU-implementation. Fast Fourier Transform is used for Poisson equation solution in GPUPEGAS. Software implementation of the above methods was tested on classical gas dynamics problems, new Aksenov's test and classical gravitational gas dynamics problems. Collisionless hydrodynamic approach was used for modelling of stars and dark matter. The scalability of GPUPEGAS computational accelerators is shown.

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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.

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