Hyperbolic diffusion in flux reconstruction: Optimisation through kernel fusion within tensor-product elements

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