A Finite Volume Method for the Two-dimensional Euler Equations with Solution Adaptation on Unstructured Meshes

A cell-vertex finite volume method is used to discretize the Euler equations on unstructured triangular meshes. A five-stage Runge-Kutta pseudo-time integration scheme is used to march the solution to steady state. Non-linear artificial viscosity is added to eliminate pressure-velocity decoupling and to capture shocks. The boundary conditions at inflow and outflow are based on the method of characteristics. Starting from a Delaunay mesh triangulation, an edge-based mesh adaptation library using mesh reorientation and stretching is used to equi-distribute the solution errors as the solution evolves in pseudo-time. To validate the method, and demonstrate the usefulness of the mesh adaptation library, numerical solutions are presented for some standard test cases.