A Sequel of Inverse Lax–Wendroff High Order Wall Boundary Treatment for Conservation Laws

Borges, Rafael Brandão de Rezende; Silva, Nicholas Dicati Pereira da; Gomes, Francisco Augusto Aparecido; Shu, Chi‐Wang; Tan, Sirui

doi:10.1007/s11831-020-09454-w

Cited by 6 publications

(2 citation statements)

References 26 publications

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“…where Q d,h is the d-th order accurate approximation of the differential operator Q given in (26) applied for points x i on the grid Ω h . The discrete operator B d,h is a d-th order accurate approx-imation of the boundary operator B given in (28) applied on the boundary BΩ h , and the LCBC method is used to obtain ghost values on the extended domain.…”

Section: Fully Discrete Schemesmentioning

confidence: 99%

“…CBCs have been used by LeVeque and Li with their immersed interface method to develop accurate approximations at embedded interfaces [24][25][26]. Shu and collaborators have used CBCs in their inverse-Lax-Wendroff approach for hyperbolic equations and conservation laws [27][28][29][30] as well as for parabolic and advection-diffusion equations [31][32][33].…”

Section: Introductionmentioning

confidence: 99%

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Local Compatibility Boundary Conditions for High-Order Accurate Finite-Difference Approximations of PDEs

Al¹,

Banks²,

Henshaw³

et al. 2021

Preprint

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We describe a new approach to derive numerical approximations of boundary conditions for highorder accurate finite-difference approximations. The approach, called the Local Compatibility Boundary Condition (LCBC) method, uses boundary conditions and compatibility boundary conditions derived from the governing equations, as well as interior and boundary grid values, to construct a local polynomial, whose degree matches the order of accuracy of the interior scheme, centered at each boundary point. The local polynomial is then used to derive a discrete formula for each ghost point in terms of the data. This approach leads to centered approximations that are generally more accurate and stable than one-sided approximations. Moreover, the stencil approximations are local since they do not couple to neighboring ghost-point values which can occur with traditional compatibility conditions. The local polynomial is derived using continuous operators and derivatives which enables the automatic construction of stencil approximations at different orders of accuracy. The LCBC method is developed here for problems governed by second-order partial differential equations, and it is verified for a wide range of sample problems, both time-dependent and time-independent, in two space dimensions and for schemes up to sixth-order accuracy.

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Section: Fully Discrete Schemesmentioning

confidence: 99%