Characteristic boundary conditions for the two-step Taylor–Galerkin FEM

A general framework for implementing numerical boundary conditions, based upon the rigorous application of characteristic theory, has been developed for the two-step Taylor–Galerkin FEM scheme. The method consists of solving the compatibility equations for the temporal change in characteristic variables using the first step of the two-step Taylor–Galerkin FEM. This application of characteristic boundary conditions is consistent with the spatial and temporal discretization of the two-step Taylor–Galerkin FEM. It is ideal for domains discretized with linear unstructured finite elements as time and space extrapolation from interior elements is not required. Boundary conditions are constructed from the characteristic solution for solid wall and symmetry boundaries, flow exits, and flow inlets. Two simulations are shown highlighting the performance of these boundary conditions.