This thesis spans several research areas, where the main topics being parallel programming based on message-passing, general-purpose computation on graphics processing units (GPGPU), numerical simulations, and domain decomposition. The graphics processing unit (GPU) on modern graphics adapters is an inexpensive source of wast parallel computing power. To harvest this power, general purpose graphics programming is used. The main agenda of the thesis is to make a case for GPU clusters. Numerical simulations of hyperbolic conservation laws using explicit temporal difference methods (finite-difference methods (FDM), finite-volume methods (FVM) and modern high-resolution methods) are used as test-cases. The GPU cluster is proven to be usable, efficient and sufficiently accurate on the chosen test-cases. A white paper where the GPU cluster is used to perform PLU-factorizations of matrices is also included as an appendix.