The article considers a three-point central-difference scheme for the transfer equation, with different kinds of special boundary conditions that reduce wave reflection from artificial boundaries. For the corresponding problems, we prove stability in grid energy norms analogous to the ordinary L 2-norm or the differential (Sobolev) norm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
C. W. Rowley and T. Colonius, “Discretely nonreflecting boundary conditions for linear hyperbolic systems,” J. Comp. Phys., 157, No. 2, 500–538 (2000).
L. V. Dorodnitsyn, “Artificial boundary conditions in simulation of subsonic gas flows,” Zh. Vychisl. Matem. i Mat. Fiz., 45, No. 7, 1251–1278 (2005).
A. A. Samarskii, The Theory of Difference Schemes [in Russian], Nauka, Moscow (1989).
A.V. Gulin, N. I. Ionkin, and V. A. Morozova, Stability of Nonlocal Difference Schemes [in Russian], Izd. LKI, Moscow (2008).
L. D. Dorodnitsyn, “Analytical and numerical investigation of the spectra of three-point difference operators,” Prikl. Mat. Informat., Maks Press, Moscow, No. 27, 25–45 (2007).
A. A. Samarskii and A.V. Gulin, Stability of Difference Schemes [in Russian], Nauka, Moscow (1973).
C. Hirsch, Numerical Computation of Internal and External Flows, Vol. 2: Computational Method for Inviscid and Viscous Flows, Wiley, New York (1990).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Prikladnaya Matematika i Informatika, No. 49, 2015, pp. 97–102.
Rights and permissions
About this article
Cite this article
Dorodnitsyn, L.V. Stability of Finite-Difference Problems with Nonreflecting Boundary Conditions. Comput Math Model 27, 270–274 (2016). https://doi.org/10.1007/s10598-016-9320-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10598-016-9320-7