This project concerns numerical methods and developing novel, high-order accurate algorithms for physical models of shallow water flows. The need for computational resources comes from two perspectives.
The first involves validation and verification that the new methods maintain their accuracy in space and time for several academic test problems in one and two spatial dimensions. This validation process involves constructing and running methods at very high-order (e.g. up to 20th order in space) in order to reveal the convergence properties of the underlying numerics. In doing so, the computations on these academic test cases also verify important physical properties, like the conservation of total energy or the stability of the new methods, that reinforce the theoretical proofs stemming from the design of the numerical approximations.
After this verification and validation step, the second perspective comes into play. It involves the need to simulate relevant test cases that come from real-world applications. One example would be the wave run-up and flooding of a city. Such application driven problem setups are inherently large scale in space as we require many degrees of freedom to accurately model a portion of the Earth, e.g., the harbour of a coastal city and the nearby oceanic bathymetry. Temporal scales also tend to be large, for instance, accurately propagating a wave from the deep ocean to the coastline in order to estimate its time to make landfall. It is this two-fold combination of method validation and real-world applications that necessitate additional computational resources.