  A large scientific community depends on the precise modelling of complex
processes in particle cascades in various types of matter. These models are
used most prevalently in cosmic-ray physics, astrophysical-neutrino physics,
and gamma-ray astronomy. In this white paper, we summarize the necessary steps
to ensure the evolution and future availability of optimal simulation tools.
The purpose of this document is not to act as a strict blueprint for
next-generation software, but to provide guidance for the vital aspects of its
design. The topics considered here are driven by physics and scientific
applications. Furthermore, the main consequences of implementation decisions on
performance are outlined. We highlight the computational performance as an
important aspect guiding the design since future scientific applications will
heavily depend on an efficient use of computational resources.
