  Tidal disruption events involve numerous physical processes (fluid dynamics,
magnetohydrodynamics, radiation transport, self-gravity, general relativistic
dynamics) in highly nonlinear ways, and, because TDEs are transients by
definition, frequently in non-equilibrium states. For these reasons, numerical
solution of the relevant equations can be an essential tool for studying these
events. In this chapter, we present a summary of the key problems of the field
for which simulations offer the greatest promise and identify the capabilities
required to make progress on them. We then discuss what has been---and what
cannot be---done with existing numerical methods. We close with an overview of
what methods now under development may do to expand our ability to understand
these events.
