We introduce OpenPME, the Open Particle-Mesh Environment, a problem solving environment that provides a Domain Specific Language (DSL) for numerical simulations in scientific computing. It is built atop a domain metamodel that is general enough to cover the main types of numerical simulations: simulations using particles, meshes, and hybrid combinations of particles and meshes. Using model-to-model transformations, OpenPME generates code against the state-of-the-art C++ parallel computing library OpenFPM. This effectively lowers the programming barrier and enables users to implement scalable simulation codes for high-performance computing (HPC) systems using high-level abstractions. Plenty of recent research has shown that higher-level abstractions and problem solving environments are well suited to alleviate low-level implementation overhead. We demonstrate this for OpenPME and its compiler on three different test cases—particle-based, mesh-based, and hybrid particle-mesh—showing up to 7-fold reduction in the number of lines of code compared to a direct OpenFPM implementation in C++.