Discontinuous Galerkin for 1D Nonlinear Advection-Diffusion
Course: Computational Fluid Dynamics (MAE 766)
Instructor: Dr. Hong Luo
Overview
This project develops a one-dimensional discontinuous Galerkin solver for the heat equation and a nonlinear advection-diffusion equation.
Work completed
The DG(P1) method uses Taylor nodal basis functions, Direct Discontinuous Galerkin diffusive fluxes, and upwind advection fluxes. Exact-solution comparisons and convergence studies verify the implementation, while the nonlinear case demonstrates the evolution of a sine wave into a shock.