An introduction to boundary conditions
The aim of this chapter is to introduce the unfamiliar reader to the topic of boundary conditions: we just want to give some insight into this question and do not pretend to give an exhaustive study. We recall first the main features of the initial boundary value problem (I.B.V.P.) before we present the numerical treatment of the question.
KeywordsBoundary Data Riemann Problem Positive Eigenvalue Incoming Wave Absorb Boundary Condition
Unable to display preview. Download preview PDF.
- Gustafsson, B., H.-O. Kreiss, and A. Sundström. Stability theory of difference approximations for mixed initial boundary value problems, II, Math. Comp., 26 (1972), 649–686.Google Scholar
- Thompson, K.W. Time dependent boundary conditions for hyperbolic systems, II, J. Comp. Phys. 89 (1990), 439–461.Google Scholar
- Le Floch, Ph. Entropy weak solutions to nonlinear hyperbolic systems in nonconservation form, in Nonlinear Hyperbolic Equations - Theory, Computation Methods, and Applications (Proceedings of the Second International Conference on Nonlinear Hyperbolic Problems, Aachen 1988), J. Ballmann and R. Jeltsch (Eds.), Notes on Numerical Fluid Mechanics 24, Vieweg, Braunschweig (1989), 362–373, and Comm. Part. Diff. Equations 13 (6) (1988), 669–127.Google Scholar
- Gisclon, M. Étude des conditions aux limites pour des système strictement hyperboliques, via l’approximation parabolique, Thesis Université Claude Bernard - Lyon I (France) (1994).Google Scholar
- Karni, S. Far field boundaries and their numerical treatment: an unconventional approach, Numerical methods for fluid dynamics III, Proceedings of the conference on Numerical methods for fluid dynamics (held in Oxford, March 1988 ), K.W. Morton and M.J. Baines (Eds.); IMA Conference Series 17, Clarendon Press, Oxford, 1988, 307–512.Google Scholar
- Sod, G.A. Numerical Methods in fluid dynamics: Initial and boundary value problems, Cambridge University Press, Cambridge 1987.Google Scholar
- Stoufflet, B. Implicit finite element methods for the Euler equations, in Numerical methods for the Euler equations of fluid dynamics, Proceedings of the IN-RIA workshop, Rocquencourt, France (1983), F. Angrand et al. (Eds.), SIAM Philadelphia (1985), 409–434.Google Scholar