**9. Particle-to-cell density and energy remapping algorithm**

For each cell containing particles, the quantities are remapped as follows:

$$\begin{aligned} \rho\_{\xi}^{\mathrm{n}+1} &= \sum\_{\mathrm{P}} \rho\_{\xi \mathrm{p}} \mathbf{V}\_{\xi \mathrm{p}} / \sum\_{\mathrm{P}} \mathbf{V}\_{\xi \mathrm{p}}, \\ \mathbf{e}\_{\xi}^{\mathrm{n}+1} &= \sum\_{\mathrm{P}} \mathbf{e}\_{\xi \mathrm{p}} \rho\_{\xi \mathrm{p}} \mathbf{V}\_{\xi \mathrm{p}} / \sum\_{\mathrm{P}} \rho\_{\xi \mathrm{p}} \mathbf{V}\_{\xi \mathrm{p}}, \end{aligned} \tag{19}$$

where summing is performed for the particles of material ξ in the cell.
