27 citations · 137 across the 14 of their papers we have counts for
14 papers
On Robust Alpha-Damping Viscous Scheme
Hiroaki Nishikawa
In this paper, we investigate the convergence of an implicit defect-correction solver for a viscous discretization based on the alpha-damping scheme for unstructured grids. We show…
An Efficient Quadratic Interpolation Scheme for a Third-Order Cell-Centered Finite-Volume Method on Tetrahedral Grids
Hiroaki Nishikawa, Jeffery A. White
In this paper, we propose an efficient quadratic interpolation formula utilizing solution gradients computed and stored at nodes and demonstrate its application to a third-order ce…
On Pitfalls in Accuracy Verification Using Time-Dependent Problems
Hiroaki Nishikawa
In this short note, we discuss the circumstances that can lead to a failure to observe the design order of discretization error convergence in accuracy verification when solving a…
Arithmetic Averages of Viscosity Coefficient are Sufficient for Second-Order Finite-Volume Viscous Discretization on Unstructured Grids
Hiroaki Nishikawa, Boris Diskin
In this short note, we discuss the use of arithmetic averages for the evaluation of viscous coefficients such as temperature and velocity components at a face as required in a cell…
Implicit gradients based conservative numerical scheme for compressible flows
Amareshwara Sainadh Chamarthi, Natan Hoffmann, Hiroaki Nishikawa +1
This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries for a cell-centered conservative numerical scheme. Explicit gradients used in deriving…
Resolving Confusion Over Third Order Accuracy of U-MUSCL
Emmett Padway, Hiroaki Nishikawa
In this paper, we discuss the U-MUSCL reconstruction scheme -- an unstructured-grid extension of Van Leer's kappa-scheme -- proposed by Burg for the edge-based discretization [AIAA…
Improved Wall-Normal Derivative Formulae for Anisotropic Adaptive Simplex-Element Grids
Hiroaki Nishikawa
In this paper, we explore methods for computing wall-normal derivatives used for calculating wall skin friction and heat transfer over a solid wall in unstructured simplex-element…
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…
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…