An implicit algorithm for simulating the dynamics of small dust grains with smoothed particle hydrodynamics
arxiv(2024)
摘要
We present an implicit method for solving the diffusion equation for the
evolution of the dust fraction in the terminal velocity approximation using
dust-as-mixture smoothed particle hydrodynamics (SPH). The numerical scheme
involves casting the dust diffusion equation into implicit form, rearranging
into its resolvent cubic equation and solving analytically. This method is
relevant for small grains that are tightly coupled to the gas, such as
sub-micron dust grains in the interstellar medium or millimetre-sized dust
grains in protoplanetary discs. The method avoids problems with the variable
used to evolve the dust fraction becoming negative when evolved explicitly and
is fast and accurate, avoiding the need for dust stopping time limiters and
significantly reducing computational expense. Whilst this method is an
improvement over using the explicit terminal velocity approximation method, as
with any dust-as-mixture method it still fails to give accurate solutions in
the limit of large (weakly coupled) grains.
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