Flood modelling with HydraTE: 2+1-dimensional smoothed-particle hydrodynamics

We present HydraTE, our own implementation of the smoothed-particle hydrodynamics technique for shallow water that uses the adaptive size of the smoothing kernel as a proxy for the local water depth. We derive the equations of motion for this approach from the Lagrangian before demonstrating that we can model the depth of water in a trough, implement vertical walls, recover the correct acceleration and terminal velocity for water flowing down a slope and obtain a stable hydraulic jump with the correct jump condition. We demonstrate that HydraTE performs well on two of the UK Environment Agency flood modelling benchmark tests. Benchmark EA3 involves flow down an incline into a double dip depression and studies the amount of water that reaches the second dip. Our results are in agreement with those of the other codes that have attempted this test. Benchmark EA6 is a dam break into a horizontal channel containing a building. HydraTE again produces results that are in good agreement with the other methods and the experimetal validation data except where the vertical velocity structure of the flow is expected to be multi-valued, such as the hydralic jump where the precise location is not recovered even though the preand postjump water heights are. We conclude that HydraTE is suitable for a wide range of flood modelling problems as it preforms at least as well as the best available commercial alternatives for the problems we have tested.