  The fluid dynamics of a relativistic fireball with longitudinal and
transverse expansion is described using a background-fluctuation splitting.
Symmetry representations of azimuthal rotations and longitudinal boosts are
used for a classification of initial state configurations and their fluid
dynamic propagation in terms of a mode expansion. We develop an accurate and
efficient numerical scheme based on the pseudo-spectral method to solve the
resulting hyperbolic partial differential equations. Comparison to the
analytically known Gubser solution underlines the high accuracy of this
technique. We also present first applications of FluiduM to central heavy ion
collisions at the LHC energies featuring a realistic thermodynamic equations of
state as well as shear and bulk viscous dissipation.
