Adaptive Mesh Refinement for Dam-Break Models using the Shallow Water Equations

The 2D shallow water equations are a common tool for the simulation of free surface fluid dynamics in civil engineering. However, nonlinear structures equations' straightforward implementations lead to numerical problems, such as spurious oscillations and unphysical diffusion. Therefore, this research compared several strategies overcome these using various finite element formulations combinations stabilization methods mesh options. accuracy performance numerous approaches examined on models dam-break one two space dimensions. analytical solution checks numerical, derived shock wave heights velocities 1D classical benchmark. result showed that streamlined diffusion capturing deal with problems but still indicate similar locally vicinity steep fronts waves when used fixed meshes. As adaptive meshing is most promising method situations, concerned options detail. It important fine-tune model's needs, i.e. adapt maximum number refinements, indicator functions, starting mesh. use techniques leads accurate solutions usual parameter range 2D, requiring less computational resources than simulations Meanwhile, reduces model size dam break by almost order magnitude execution time factor 20.