TY - JOUR
T1 - Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems
T2 - Methodology and application to high-order compact schemes
AU - Carpenter, Mark H.
AU - Gottlieb, David
AU - Abarbanel, Saul
PY - 1994/4
Y1 - 1994/4
N2 - We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Padé-like) high-order finite-difference schemes for hyperbolic systems. First a proper summation-by-parts formula is found for the approximate derivative, A “simultaneous approximation term” is then introduced to treat the boundary conditions. This procedure leads to timestable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.
AB - We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Padé-like) high-order finite-difference schemes for hyperbolic systems. First a proper summation-by-parts formula is found for the approximate derivative, A “simultaneous approximation term” is then introduced to treat the boundary conditions. This procedure leads to timestable schemes even in the system case. An explicit construction of the fourth-order compact case is given. Numerical studies are presented to verify the efficacy of the approach.
UR - http://www.scopus.com/inward/record.url?scp=0001473098&partnerID=8YFLogxK
U2 - 10.1006/jcph.1994.1057
DO - 10.1006/jcph.1994.1057
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AN - SCOPUS:0001473098
SN - 0021-9991
VL - 111
SP - 220
EP - 236
JO - Journal of Computational Physics
JF - Journal of Computational Physics
IS - 2
ER -