  The Atacama Large Millimeter/submillimeter Array (ALMA) offers new diagnostic
possibilities that complement other commonly used diagnostics for the study of
our Sun. In particular, ALMA's ability to serve as an essentially linear
thermometer of the chromospheric gas at unprecedented spatial resolution at
millimetre wavelengths and future polarisation measurements have great
diagnostic potential. Solar ALMA observations are therefore expected to
contribute significantly to answering long-standing questions about the
structure, dynamics and energy balance of the outer layers of the solar
atmosphere. In this regard, current and future ALMA data are also important for
constraining and further developing numerical models of the solar atmosphere,
which in turn are often vital for the interpretation of observations. The
latter is particularly important given the Sun's highly intermittent and
dynamic nature that involves a plethora of processes occurring over extended
ranges in spatial and temporal scales. Realistic forward modelling of the Sun
therefore requires time-dependent three-dimensional radiation
magnetohydrodynamics that account for non-equilibrium effects and, typically as
a separate step, detailed radiative transfer calculations, resulting in
synthetic observables that can be compared to observations. Such artificial
observations sometimes also account for instrumental and seeing effects, which,
in addition to aiding the interpretation of observations, provide instructive
tools for designing and optimising ALMA's solar observing modes. In the other
direction, ALMA data in combination with other simultaneous observations
enables the reconstruction of the solar atmospheric structure via data
inversion techniques. This article highlights central aspects of the impact of
ALMA for numerical modelling for the Sun, their potential and challenges,
together with selected examples.
