首页|Boundary treatment of linear multistep methods for hyperbolic conservation laws
Boundary treatment of linear multistep methods for hyperbolic conservation laws
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NSTL
Elsevier
When using high-order schemes to solve hyperbolic conservation laws in bounded do-mains, it is necessary to properly treat boundary conditions so that the overall accuracy and stability are maintained. In [1, 2] a finite difference boundary treatment method is proposed for Runge-Kutta methods of hyperbolic conservation laws. The method combines an inverse Lax-Wendroff procedure and a WENO type extrapolation to achieve desired ac-curacy and stability. In this paper, we further develop the boundary treatment method for high-order linear multistep methods (LMMs) of hyperbolic conservation laws. We test the method through both 1D and 2D benchmark numerical examples for two third-order LMMs, one with a constant time step and the other with a variable time step. Numeri-cal examples show expected high order accuracy and excellent stability. In addition, the approach in [3] may be adopted to deal with an exceptional case where eigenvalues of the flux Jacobian matrix change signs at the boundary. These results demonstrate that the combined boundary treatment method works very well for LMMs of hyperbolic conserva-tion laws. (c) 2022 Elsevier Inc. All rights reserved.
NSTL
Elsevier
