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physics.comp-ph2020★ 17 cited
A Truncation Error Analysis of Third-Order MUSCL Scheme for Nonlinear Conservation Laws
Hiroaki Nishikawa
This paper is a rebuttal to the claim found in the literature that the MUSCL scheme cannot be third-order accurate for nonlinear conservation laws. We provide a rigorous proof for…
physics.comp-ph2019★ 18 cited
First order hyperbolic approach for Anisotropic Diffusion equation
Amareshwara Sainadh Chamarthi, Hiroaki Nishikawa, Kimiya Komurasaki
In this paper, we present a high order finite difference solver for anisotropic diffusion problems based on the first-order hyperbolic system method. In particular, we demonstrate…