Recently, Chen (Physica A, 362, 2006, p.158) and Rohde (Int’l J Num. Meth. Fluids, 51, 2006, 439) proposed volumetric grid refinement methods. It includes two special steps: coalesce and explode.
I want to test the higher order schemes discussed in Chen’s paper. However, I’m not quite clear about the statements (in the first paragraph, page 162). The questions are,
- why the simple spacial central interpolation is not suitable ? (equation 3)
- why the new scheme can work. It seems only the coarse grid contributions are considered (only the gradient on interface-parallel direction is non-zero).
- How to implement the modified exploding procedure for population 0 (equation 6 in Chen’s paper)?
Thank you for your attention. And are there any body have experience on it?