K-mouflage at high $k$: extending the reach of $\mathtt{\text{Hi-COLA}}$

The $\mathtt{\text{Hi-COLA}}$ code is an efficient dark matter simulation suite that flexibly handles the Horndeski family of modified gravity models. In this work we extend the scope of $\mathtt{\text{Hi-COLA}}$ to accommodate Horndeski theories with K-mouflage screening, allowing for the computation of matter power spectra in the non-linear regime in these models. We explore the boost of the dark matter power spectrum relative to GR-$\mathrm{\Lambda }$CDM in K-mouflage gravity, and also discuss how large-scale structure computations change between the Einstein and Jordan frames. A dissection of the relative contributions of the modified background, linear growth, fifth force, and the conformal factor (a new inclusion to $\mathtt{\text{Hi-COLA}}$) to the boost factor is presented. The ability of $\mathtt{\text{Hi-COLA}}$ to run with general Horndeski models and multiple screening mechanisms makes it an ideal tool for testing gravity with upcoming galaxy survey data.