A Field-length based refinement criterion for adaptive mesh simulations of the interstellar medium

Adequate modelling of the multiphase interstellar medium requires optically thin radiative cooling, comprising an inherent thermal instability. The size of the occurring condensation and evaporation interfaces is determined by the so-called Field-length, which gives the dimension at which the instability is significantly damped by thermal conduction. Our aim is to study the relevance of conduction scale effects in the numerical modelling of a bistable medium and check the applicability of conventional and alternative adaptive mesh techniques. The low physical value of the thermal conduction within the ISM defines a multiscale problem, hence promoting the use of adaptive meshes. We here introduce a new refinement strategy that applies the Field condition by Koyama & Inutsuka as a refinement criterion. The described method is very similar to the Jeans criterion for gravitational instability by Truelove and efficiently allows to trace the unstable gas situated at the thermal interfaces. We present test computations that demonstrate the greater accuracy of the newly proposed refinement criterion in comparison to refinement based on the local density gradient. Apart from its usefulness as a refinement trigger, we do not find evidence in favour of the Field criterion as a prerequisite for numerical stability.