Non-Hydrostatic Pressure Shallow Flows: GPU Implementation Using Finite Volume and Finite Difference Scheme
For researchers simulating coastal and shallow water flows, this work provides a GPU-accelerated numerical method that handles wave breaking over complex bathymetries, though it is an incremental improvement over existing schemes.
The paper proposes an efficient second-order well-balanced hybrid finite volume/finite difference scheme for non-hydrostatic shallow flows, adapted for GPU architectures, and demonstrates its accuracy and efficiency on experimental test cases.
We consider the depth-integrated non-hydrostatic system derived by Yamazaki et al. An efficient formally second-order well-balanced hybrid finite volume finite difference numerical scheme is proposed. The scheme consists of a two-step algorithm based on a projection-correction type scheme initially introduced by Chorin-Temam [15]. First, the hyperbolic part of the system is discretized using a Polynomial Viscosity Matrix path-conservative finite volume method. Second, the dispersive terms are solved by means of compact finite differences. A new methodology is also presented to handle wave breaking over complex bathymetries. This adapts well to GPU-architectures and guidelines about its GPU implementation are introduced. The method has been applied to idealized and challenging experimental test cases, which shows the efficiency and accuracy of the method.