A modified fluids-in-cell method for problems of gravitational gas dynamics

AstroPhi: A code for complex simulation of the dynamics of astrophysical objects using hybrid supercomputers

“…In the Lagrangian stage the flows are computed via the total cell deformation technique along each direction [55]. This technique is more suitable for computation with GPUs and Intel Xeon Phi accelerators than the previously used flow computation technique [48]. At each time step the energy balance is verified and corrected [50].…”

“…The complexity of the Lagrangian stage is dictated by the use of the operator approach for computation of flows through boundaries [41]. A flow chart of the AstroPhi code is shown in Fig.…”

“…During the second (Lagrangian) stage, advective transport is taken into account. Separation of the method into two stages allows elimination of Galilean non-invariance [48] and use of Godunov method in the Eulerian stage facilitates correct simulation of discontinuities. It should be mentioned that a first-order Godunov scheme is used.…”

“…Our research group has been developing the Lagrangian-Eulerian approach on the basis of the fluids in cells (FlIC) and Godunov methods for several years [3,22,[48][49][50][51]. The AstroPhi code proposed here is based on an equation solver for gas dynamics comprising two stages.…”

“…The main bottleneck of mesh-based methods is solving non-invariance with respect to rotation or Galilean non-invariance [38,39]. However, this bottleneck can be easily overcome using different approaches for numerical scheme design [40,41]. One of the main issues in both the Lagrangian and Eulerian approaches is the lack of scalability [42,43].…”