An Efficient HPC Framework for Parallel Long-Time and Large-Scale Simulation of a Class of Anomalous Single-Phase Models

Anomalous sub-diffusion models are currently considered to be efficient for characterization of complex single -- (and hence multi -- ) phase fluid flow in reservoir simulations. For simulation of such models in three space dimensions, typically, millions of degree of freedoms (DoF) are required to resolve multiscale features in reservoirs. Further, the key quantity of interest is on long-time behavior of reservoirs. Consequently, standard time-stepping serial algorithms are not practical. In this article, we develop a high performance computing (HPC) framework to efficiently simulate a class of anomalous sub-diffusion models. The framework is based on hybrid parallel-in-time and parallel-in-space multiple message passing interface (MPI) communicators and efficient load balancing techniques, in conjunction with efficient discretization of the continuous local and non-local operators in the sub-diffusion models.