Fluid dynamics of heavy ion collisions with mode expansion

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 pseudospectral 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 fluid dynamics with mode expansion (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.