A 2D unstructured finite volume method (FVM) shallow water solver written in C++. Fluxes can be evaluated with the Lax–Friedrichs or the Roe method. Implicit and explicit time stepping is available. Expicit time stepping can be performed with the Euler, the Runge-Kutta 2nd-order, and the Runge-Kutta 4th-order methods. The jacobian used for the implicit time stepping is numerically evaluated and the linear system of equations is solved with the BiCGSTAB method. The Eigen C++ template library for linear algebra is used along with OpenMP.

Grid

Water height

Effect of the flux method; Gray surface is Lax-Friedrichs, red is Roe

Effect of the integration method; Gray surface is Euler, red is Runge-Kutta 2nd order, blue is Runge-Kutta 4th order

The code solves the following partial differential equations

where

The code requires the Eigen C++ template libary. Download the libary and extract its contents to a folder named Eigen inside the includes folder (includes/Eigen). Once extracted use make to compile the code. The sw_solver binary will be created in the bin folder.

To run the code navigate to the folder of the case e.g. dam_coarse_lf and run ../bin/sw_solver dam. The program will solve the dam break problem using the Lax-Friedrichs method for 1000 time steps with a time step of 0.003. The full list of options is:

• dt - timestep
• N_timesteps - number of timesteps
• riemann_solver - Riemman solver; 1 - Lax-Friedrichs, 2 - Roe
• output_frequency - Results output frequency; 0 - no output, i where i > 0 - every ith iteration
• integrator - Integration method; 0 - Euler, 1 - Runge-Kutta 2nd-order, 2 - Runge-Kutta 4th order
• implicit - Solve the equation explicitly or implicitly; 0 - Explicit, 1 - Implicit

Note: If the implicit option is set to 1 the integrator option is not used.