Table 6.
Summary of the features of the approach presented in this work within the context of the works on which it is based.
| Method | Gradient accuracy | Tensile instability suppression | Conservative (a) | Lagrangian compatibility (b) | Reference |
|---|---|---|---|---|---|
| IAD | Very high | Small and moderate density jumps | No | No | García-Senz et al. (2012) |
| IAD0 | High | Small and moderate density jumps | Yes | Yes | Cabezón et al. (2012) |
| IAD0 + GVE (Explicit) | Very high | Large density jumps | Yes | No | Cabezón et al. (2017) |
| IAD0 + GVE (Implicit) + σ | Very high | Large density jumps | Yes | Mostly yes | This work |
Notes. The first column shows the method, where IAD stands for the integral approach to derivatives, which is at the core of our proposed ISPH; GVE stands for generalized volume elements, and σ is the methodology presented in this work that is used to obtain a crossed version of the momentum and energy equations only where it is needed to suppress the tensile instability. The second and third columns give a qualitative idea of the associated accuracy when evaluating gradients and when then tensile instability is suppressed. The fourth and fifth columns state if the method is fully conservative and Lagrangian compatible. The last column shows the associated reference. We note that the first row corresponds to the ncISPH scheme mentioned at the end of Sect. 2, whereas the other three are conservative ISPH schemes.
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