A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy
نویسندگان
چکیده
Stable and accurate interface conditions are derived for the linear advection-diffusion equation. The conditions are functionally independent of the spatial order of accuracy and rely only on the form of the discrete operator. We focus on high-order finite-difference operators that satisfy the summation-by-parts (SBP) property. We prove that stability is a natural consequence of the SBP operators used in conjunction with the new boundary conditions. In addition, we show that the interface treatments are conservative. New finite-difference operators of spatial accuracy up to sixth order are constructed: these operators satisfy the SBP property. Finite-difference operators are shown to admit design accuracy (p-order global accuracy) when (p− 1)-order stencil closures are used near the boundaries if the physical boundary conditions are implemented to at least p-order accuracy. Stability and accuracy are demonstrated on the nonlinear Burgers’ equation for an twelve-subdomain problem with randomly distributed interfaces.
منابع مشابه
Corrigendum to "A stable and conservative interface treatment of arbitrary spatial accuracy" [J. Comput. Phys. 148 (1999) 341-365]
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