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Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations. (English) Zbl 0964.76071
Smooth particle hydrodynamics (SPH) is a robust and conceptually simple method which suffers from unsatisfactory performance due to lack of consistency. The kernel function can be corrected to enforce the consistency conditions and improve the accuracy. For simplicity, in this paper the SPH method with the corrected kernel is referred to as corrected smooth particle hydrodynamics. The numerical solutions can be further improved by introducing an integration correction which also enables the method to pass patch tests. It is also shown that the nodal integration of this corrected SPH method suffers from spurious singular modes. This spatial instability results from under integration of the weak form, and it is treated by a least-squares stabilization procedure. The effects of the stabilization and improvement in the accuracy are illustrated by simulation of metal forming problems.

MSC:
76M28 Particle methods and lattice-gas methods
76T99 Multiphase and multicomponent flows
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