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26 2.5 The momentum equation modified by the corrected density . Appendix B Appendix: Adaptive Harmonic Kernel As it has been mentioned one of the most important challenges of the SPH technique is to adequately capture the physical discontinuities that appear in some situations, for example in those were shocks or thermal discontinuities are present.
The spatial distribution of particles and radial density profile after this third stage are shown in the rightmost panels of Fig A.1.
Such jump is difficult to achieve in more than 1D because of the limited resolution of simulations.
In these cases the nature of the kernel becomes relevant to reduce the errors associated to interpolations which can especially affect the calculation of gradients.
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After several hundreds models the system achieves the adequate configuration to be used as an initial model.
In a third step we let the system evolve without any constraint.