Flow diagnostics tools yield quantitative information about the flow behaviour of a model, based on controlled numerical flow experiments. We consider a family of flow diagnostic measures that are constructed based on a single pressure solution and can be used to quickly establish flow patterns and well-allocation factors. This offers a means to rank, compare, and validate reservoir models, upscaling procedures, and production scenarios that is significantly less computationally expensive than full-featured multiphase flow simulations. All flow diagnostic measures considered herein are defined from time-of-flight and tracer partitions. From these basic quantities, one can compute many interesting diagnostics such as: tracer partitions, drainage and swept regions, well-pair connections, well allocation factors, flow-and-storage-capacity (F-Phi) diagrams, sweep efficiency, and Lorenz heterogeneity coefficients. Time-of-flight and tracers are often associated with streamlines, but can equally well be computed from a standard Eulerian discretization. Herein, we discuss two improved discretizations, a multidimensional upwind method and a higher-order discontinuous Galerkin method, that both are applicable to a large family of general, polyhedral grids. We validate the methods, compare their accuracy, and investigates how the improved accuracy impacts flow-diagnostic measures and to what extent this is important for their use in various workflows.