  Energy distributions of high frequency linear wave fields are often modelled
in terms of flow or transport equations with ray dynamics given by a
Hamiltonian vector field in phase space. Applications arise in underwater and
room acoustics, vibro-acoustics, seismology, electromagnetics, and quantum
mechanics. Related flow problems based on general conservation laws are used,
for example, in weather forecasting or molecular dynamics simulations.
Solutions to these flow equations are often large scale, complex and
high-dimensional, leading to formidable challenges for numerical approximation
methods. This paper presents an efficient and widely applicable method, called
discrete flow mapping, for solving such problems on triangulated surfaces. An
application in structural dynamics - determining the vibro-acoustic response of
a cast aluminium car body component - is presented.
