TY - JOUR
T1 - Runge-Kutta Characteristic Methods for First-Order Linear Hyperbolic Equations
AU - Wang, Hong
AU - Al-Lawatia, Mohamed
AU - Telyakovskiy, Aleksey S.
PY - 1997/11
Y1 - 1997/11
N2 - We develop two Runge-Kutta characteristic methods for the solution of the initial-boundary value problems for first-order linear hyperbolic equations. One of the methods is based on a backtracking of the characteristics, while the other is based on forward tracking. The derived schemes naturally incorporate inflow boundary conditions into their formulations and do not need any artificial outflow boundary condition. They are fully mass conservative and can be viewed as higher-order time integration schemes improved over the ELLAM (Eulerian-Lagrangian localized adjoint method) method developed previously. Moreover, they have regularly structured, well-conditioned, symmetric, and positive-definite coefficient matrices. Extensive numerical results are presented to compare the performance of these methods with many well studied and widely used methods, including the Petrov-Galerkin methods, the streamline diffusion methods, the continuous and discontinuous Galerkin methods, the MUSCL, and the ENO schemes. The numerical experiments also verify the optimal-order convergence rates of the Runge-Kutta methods developed in this article.
AB - We develop two Runge-Kutta characteristic methods for the solution of the initial-boundary value problems for first-order linear hyperbolic equations. One of the methods is based on a backtracking of the characteristics, while the other is based on forward tracking. The derived schemes naturally incorporate inflow boundary conditions into their formulations and do not need any artificial outflow boundary condition. They are fully mass conservative and can be viewed as higher-order time integration schemes improved over the ELLAM (Eulerian-Lagrangian localized adjoint method) method developed previously. Moreover, they have regularly structured, well-conditioned, symmetric, and positive-definite coefficient matrices. Extensive numerical results are presented to compare the performance of these methods with many well studied and widely used methods, including the Petrov-Galerkin methods, the streamline diffusion methods, the continuous and discontinuous Galerkin methods, the MUSCL, and the ENO schemes. The numerical experiments also verify the optimal-order convergence rates of the Runge-Kutta methods developed in this article.
KW - Characteristic methods
KW - Eulerian-Lagrangian methods
KW - Numerical solution of first-order hyperbolic equations
KW - Rung-Kutta methods
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U2 - 10.1002/(SICI)1098-2426(199711)13:6<617::AID-NUM3>3.0.CO;2-U
DO - 10.1002/(SICI)1098-2426(199711)13:6<617::AID-NUM3>3.0.CO;2-U
M3 - Article
AN - SCOPUS:0001417548
SN - 0749-159X
VL - 13
SP - 617
EP - 661
JO - Numerical Methods for Partial Differential Equations
JF - Numerical Methods for Partial Differential Equations
IS - 6
ER -