Table 1
Overview of spatial reconstruction methods used in this work.
| ID | Theoretical order | Practical order | Number of ghost cells | Description |
|---|---|---|---|---|
| LIN | 2 | 2.0 | 2 | Piecewise linear, no limiter |
| LIN+VL | 2 | 2.0 | 2 | Piecewise linear, van Leer limiter |
| PAR | 3 | 3.0 | 2 | Piecewise parabolic, no limiter |
| PPM84 | 4 | 2.3, 1.6 | 3 | PPM method of Colella & Woodward (1984) |
| PPM08 | 6 | 6.0 | 4 | PPM method of Colella & Sekora (2008) |
| PSH | 7 | 7.0 | 4 | Hybrid piecewise sextic with no limiter for dynamic variables and PPM08 for passive scalars |
Notes. ID: identifier; Theoretical order: formal order of accuracy for smooth and monotonic solutions in 1D; Practical order: asymptotic order obtained in the 1D experiments reported in Appendix B (smooth but nonmonotonic solutions). In the case of PPM84, the higher order of accuracy corresponds to linear advection and the lower one to the propagation of a sound wave using the LHLLC flux function, see Appendix B for details.
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