About Chen & Filippova 's Grid refinement method

Hello guys,

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,

  1. why the simple spacial central interpolation is not suitable ? (equation 3)
  2. 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).
  3. 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?