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 varia...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2006-01, Vol.195 (7), p.742-762
Main Authors: Martineau, Richard C., Berry, Ray A.
Format: Article
Language:English
Subjects:
BOUNDARY CONDITIONS
Characteristic boundary conditions
COMPATIBILITY
Compatibility equations
Compressible flow
Computational techniques
Exact sciences and technology
EXTRAPOLATION
Fundamental areas of phenomenology (including applications)
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
Linear unstructured finite elements
Mathematical methods in physics
Physics
SYMMETRY
Two-step Taylor–Galerkin
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Summary: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.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2005.02.017