  Novel methods are presented in this initial study for the fusion of GPU
kernels in the artificial compressibility method (ACM), using tensor product
elements with constant Jacobians and flux reconstruction. This is made possible
through the hyperbolisation of the diffusion terms, which eliminates the
expensive algorithmic steps needed to form the viscous stresses. Two fusion
approaches are presented, which offer differing levels of parallelism. This is
found to be necessary for the change in workload as the order of accuracy of
the elements is increased. Several further optimisations of these approaches
are demonstrated, including a generation time memory manager which maximises
resource usage. The fused kernels are able to achieve 3-4 times speedup, which
compares favourably with a theoretical maximum speedup of 4. In three
dimensional test cases, the generated fused kernels are found to reduce total
runtime by ${\sim}25\%$, and, when compared to the standard ACM formulation,
simulations demonstrate that a speedup of $2.3$ times can be achieved.
