2018
DOI: 10.1016/j.amc.2017.12.041
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On a third order CWENO boundary treatment with application to networks of hyperbolic conservation laws

Abstract: High order numerical methods for networks of hyperbolic conservation laws have recently gained increasing popularity. Here, the crucial part is to treat the boundaries of the single (one-dimensional) computational domains in such a way that the desired convergence rate is achieved in the smooth case but also stability criterions are fulfilled, in particular in the presence of discontinuities. Most of the recently proposed methods rely on a WENO extrapolation technique introduced by Tan and Shu in [J. Comput. P… Show more

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Cited by 11 publications
(29 citation statements)
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“…Within the following numerical examples, we consider two different discretization schemes. The first is a third-order CWENO scheme (CWENO3) with suitable boundary treatment [20,23], which relies on a local Lax-Friedrichs flux function for the inner discretization points of each pipe and handles coupling points by explicitly solving equation (27). The second scheme is an implicit box scheme (IBOX) [21], suitable for sub-sonic flows.…”
Section: Numerical Resultsmentioning
confidence: 99%
“…Within the following numerical examples, we consider two different discretization schemes. The first is a third-order CWENO scheme (CWENO3) with suitable boundary treatment [20,23], which relies on a local Lax-Friedrichs flux function for the inner discretization points of each pipe and handles coupling points by explicitly solving equation (27). The second scheme is an implicit box scheme (IBOX) [21], suitable for sub-sonic flows.…”
Section: Numerical Resultsmentioning
confidence: 99%
“…For example, close to the top‐left boundary of the domain, one may use only trueu0,,trueu8,trueu11,trueu12 to determine an optimal polynomial of degree 3, the standard polynomial of degree 2 in the south‐west direction, and three first‐degree polynomials in the other directions. In order to obtain reconstructions that do not require ghost cells, one may investigate the adaption to the 2D case of a technique that avoids altogether the use of ghost cells …”
Section: Central Weighted Essentially Nonoscillatory Reconstruction (mentioning
confidence: 99%
“…In order to obtain reconstructions that do not require ghost cells, one may investigate the adaption to the 2D case of a technique that avoids altogether the use of ghost cells. 30…”
Section: Boundary Treatmentmentioning
confidence: 99%
“…A different approach, entirely based on extrapolation is studied in [2,3]. In [29] a different strategy was considered. There, in a one-dimensional finite volume context, ghost values are entirely avoided and the point value reconstruction at the boundary is performed with a type reconstruction that makes use only of interior cell averages.…”
Section: Introductionmentioning
confidence: 99%