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.

17 pages, 2 figures, content matches published version