Discretization of the 2D Convection-Diffusion Equation Using Discrete Exterior Calculus

While the Discrete Exterior Calculus (DEC) discretization of the diffusive term of the Trans- port Equation is well understood, the DEC discretization of the convective term, as well as its stabilization, is an ongoing area of research. In this paper, we propose a local discretization for this term based on DEC and geometric arguments, assuming the particle velocity field is prescribed at the vertices of the primal mesh. Since this formulation is similar to that of the Finite Element Method with linear interpolation functions (FEML), this numerical scheme can be stabilized us- ing known stabilization techniques, such as Artificial Diffusion. Using this stabilizaton technique, numerical tests are carried out on simple problems with domains discretized with coarse and fine simplicial meshes to show numerical convergence for stationary and transient problems.