Testing the concept of integral approach to derivatives within the smoothed particle hydrodynamics technique in astrophysical scenarios

摘要: Context. The smoothed particle hydrodynamics (SPH) technique is a well-known numerical method that has been applied to simulating the evolution of wide variety systems. Modern astrophysical applications rely on Lagrangian formulation fluid Euler equations, which fully conservative. A different scheme, based matrix approach SPH equations currently being used in computational dynamics. An original an integral derivatives, called IAD0, recently proposed and conservative well-suited processes. Aims. behavior IAD0 scheme analyzed connection with several scenarios, compared same simulations carried out standard technique. Methods. hydrodynamic validated using tests cover important topics astrophysics, such as supernova remnants, stability self-gravitating bodies, coalescence compact objects. Results. analysis hydrodynamical above-mentioned scenarios suggests built derivatives improves results technique. In particular, there better development instabilities, good description structures equilibrium reasonable process two white dwarfs. We also observed conservations energy both linear angular momenta were generally than those SPH. addition new less susceptible pairing instability. Conclusions. present formalism tensor we checked three-dimensional interest. This more accurate because re-normalization imposed interpolations, prone undergoing instability. these test cases may improve simulation many problems only moderate overload.