Introduction
The objective of this document is to outline the design for an numerical solution to the Diffusion Wave and Shallow Water Equations for use within the RAS computational engine. Depending on the domain and computational hardware the explicit method can be more efficient than semi-implicit approaches. Its efficiency stems from avoiding a matrix solve step which in turn avoids the need for global communication of model state. This can make efficient parallelization more tractable, including parallel computations via a Graphics Processing Unit (GPU). This will allow for more efficient simulation of overland flow in problems with very large spatial extents. It may provide a faster or more stable alternative to the semi-implicit solver in other classes of problems as well.
Although an explicit solver will be limited by a time step restriction resulting from surface wave propagation, the speed-up associated with the doing calculations in parallel is expected to outpace this restriction for many problems using a large number of computational cells.
This document will not cover aspects of the explicit solver implementation through the CUDA API or hardware considerations related to GPUs.