In fluid dynamical simulations in astrophysics, large deformations are common and surface tracking is sometimes necessary. Smoothed Particle Hydrodynamics (SPH) method has been used in many of such simulations. Recently, however, it has been shown that SPH cannot handle contact discontinuities or free surfaces accurately. There are several reasons for this problem. The first one is that SPH requires that the density is continuous and differentiable. The second one is that SPH does not have the consistency, and thus the accuracy is zeroth order in space. In addition, we cannot express accurate boundary conditions with SPH. In this paper, we propose a novel, high-order scheme for particle-based hydrodynamics of compress- ible fluid. Our method is based on kernel-weighted high-order fitting polynomial for intensive variables. With this approach, we can construct a scheme which solves all of the three prob- lems described above. For shock capturing, we use a tensor form of von-Neumann-Richtmyer artificial viscosity. We have applied our method to many test problems and obtained excel- lent result. Our method is not conservative, since particles do not have mass or energy, but only their densities. However, because of the Lagrangian nature of our scheme, the violation of the conservation laws turned out to be small. We name this method Consistent Particle Hydrodynamics in Strong Form (CPHSF).
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