This thesis explores the multi-GPU implementation of a patch-based hyperbolic finite volume solver in ExaHyPE 2, a versatile numerical simulation framework for solving hyperbolic partial differential equations. We investigate two approaches to offload patches to the GPU: one utilizing OpenMP and the other employing a hybrid approach involving MPI with OpenMP. These approaches are analyzed and compared to determine their respective benefits and limitations. We then apply one of these methods to benchmark the finite volume Rusanov solver and extend our analysis to simulate the 3D Euler equations using a patch-based enclave solver. All implementations are rigorously benchmarked and tested. Our goal is to provide a comprehensive understanding of the potential of multi-GPU acceleration within the ExaHyPE 2 framework, enabling scientists and engineers to perform simulations more efficiently on large scale machines and gain deeper insights into complex phenomena.