High-order Tensor-Train Finite Volume Method for Shallow Water Equations

• Published in: arXiv.org
• Main Authors: Danis, Mustafa Engin, Truong, Duc P, DeSantis, Derek, Petersen, Mark, Rasmussen, Kim O, Alexandrov, Boian S
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 07.08.2024
• Subjects: Acceleration; Algorithms; Essentially non-oscillatory schemes; Finite volume method; Fluxes; Interpolation; Mathematical analysis; Reconstruction; Shallow water equations; Solvers; Taylor series; Tensors; Thickness; Upwind schemes (mathematics)

In this paper, we introduce a high-order tensor-train (TT) finite volume method for the Shallow Water Equations (SWEs). We present the implementation of the \(3^{rd}\) order Upwind and the \(5^{th}\) order Upwind and WENO reconstruction schemes in the TT format. It is shown in detail that the linear...