Mimetic and stable numerical methods for nonlinear shallow water equations

The goal of this project is to develop high order accurate and stable numerical methods for efficient numerical simulations of nonlinear shallow water equations in two space dimensions using the Dual-Pair (DP) summation-by-parts (SBP) framework.

We will aim to design the method such that it preserves constraints imposed by the PDE.

Examples include:

  1. Energy conservation
  2. Vorticity conservation
  3. Stability

The preservation of these constraints is important for several numerical and practical reasons.

Further comments: Programming in Python/MATLAB will be required. No previous knowledge of SBP methods is required.