27 citations · 137 across the 14 of their papers we have counts for
6 papers · 1 filter
Economically High-Order Unstructured-Grid Methods: Clarification and Efficient FSR Schemes
Hiroaki Nishikawa
In this paper, we clarify reconstruction-based discretization schemes for unstructured grids and discuss their economically high-order versions, which can achieve high-order accura…
Grid Quality Measures for Iterative Convergence
Hiroaki Nishikawa
In this paper, we discuss two grid-quality measures, F- and G-measures, in relation to iterative convergence of an implicit unstructured-grid Navier-Stokes solver. The F-measure is…
On False Accuracy Verification of UMUSCL Scheme
Hiroaki Nishikawa
In this paper, we reveal a mechanism behind a false accuracy verification encountered with unstructured-grid schemes based on solution reconstruction such as UMUSCL. Third- (or hig…
On Estimating Machine-Zero Residual
Hiroaki Nishikawa
In this paper, we propose two techniques to estimate the magnitude of a machine-zero residual for a given problem, which is the smallest possible residual that can be achieved when…
The QUICK Scheme is a Third-Order Finite-Volume Scheme with Point-Valued Numerical Solutions
Hiroaki Nishikawa
In this paper, we resolve the ever-present confusion over the QUICK scheme: it is a second-order scheme or a third-order scheme. The QUICK scheme, as proposed in the original refer…
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…