

Hiroaki Nishikawa:
Algorithm developer for Computational Fluid Dynamics (CFD).
Developed a nodegeneration algorithm for onedimensional curves in 1998 [pdf],
developed a method for simultaneously solving for both solution and grid to earn PhD in 2001 (Advisor: P. L. Roe),
[pdf],
developed a recipe for constructing a localpreconditioning matrix in 2003 with Phil Roe, Yoshifumi Suzuki, and
Bram van Leer [pdf ],
developed an optimal multigrid algorithm by hyperbolic/elliptic splitting with Bram van Leer in 2003 [pdf],
pointed out the importance of compatible discretization for the NavierStokes equations with Phil Roe in 2004 [pdf],
developed a multigrid thirdorder scheme in 2007
pdf,
developed a robust rotatedhybrid Riemann solver with Keiichi Kitamura in 2007 [pdf],
started to develop the hyperbolic method in 2007 [pdf],
proposed a recipe for constructing diffusion scheme in (perhaps) the longest AIAA paper in 2010 [pdf]
and extended the recipe to the NavierStokes equations in 2011 [pdf],
developed a formula that enables to write a source term in the divergence form in 2012
[pdf],
worked with Boris Diskin and Jim Thomas on the development of agglomerated multigrid for 3D unstructuredgrid solver [pdf],
developed a thirdorder NS solver that is faster than widelyused secondorder NS solver
[pdf],
developed a 3D hyperbolic NS solver with Yoshitaka Nakashima and Norihiko Watanabe
[ pdf ],
developed a hyperbolic method for an MHD model with Hubert Baty
[ pdf ],
developed a 3D hyperbolic NS solver in NASA's FUN3D with Yi Liu
[ pdf ],
developed hyperbolic reconstructedDG methods with Hong Luo, Jialin Lou, Xiaodong Liu, Lingquan Li
[ pdf ].

▶
Why do I want to post my preprints, notes, and codes in public? (Blog Article)
▶ NIA CFD Seminar (Presentation files, seminar videos available)
▶
FirstOrder Hyperbolic System Method (History, Development, and FAQ)



Mendeley
ORCID
Google Scholar
ResearchGate


Hyperbolic Stories::
[
pdf ] "Toward a Future NavierStokes Code: Exploiting Additional Degrees of Freedom" Seminar at NIA, June 2007
[
pdf ] "FirstOrder Hyperbolic System Method"  NIA CFD Seminar, October 2011
[
pdf ] "Robust and Accurate Viscous Discretization by Hyperbolic Recipe"  NIA CFD Seminar, November 2011
[
pdf ] "FirstOrder Hyperbolic System Method"  NIA Sandwitch Seminar, March 2012
[
pdf ] "Hyperbolize It"  Conference on Future Directions in CFD Research, August 2012
[
pdf ] "Radical or Traditional"  One page slide from JAXA CFD seminar in 2013
[
pdf ] "Past or Future?: A NeverEnding Story of CFD Algorithm Development"  JamesonRoeVanLeer Symposium in 2013
[
pdf ] "List of Papers for Hyperbolic Method (07222014)"  CRADLE Next Generation CFD Seminar in 2014
[
pdf ] "Discretization that ends well (3rdorder EB scheme)."  NIA CFD Seminar in 2015


Complete List of Papers::
Published/presented papers can be downloaded in the list of
papers.


CFD Notes::
Some unpublished CFD notes are available
at CFDnotes.com.


CFD Book::
" I do like CFD, VOL. 1, Second Edition ".
Visit CFDbooks.com for free PDF and CFD codes.


Papers of Interest :
 ThirdOrder EdgeBased Method
ThirdOrder Accuracy with Zero/NegativeVolume Elements
H. Nishikawa, "Uses of Zero and Negative Volume Elements for NodeCentered EdgeBased Discretization",
AIAA Paper 20174295, 23rd AIAA Computational Fluid Dynamics Conference, 5  9 June 2017, Denver, Colorado.
[ bib 
pdf 
slides
]
ThirdOrder Accuracy without Second Derivatives
H. Nishikawa and Y. Liu, " AccuracyPreserving Source Term Quadrature for ThirdOrder EdgeBased Discretization", Journal of Computational Physics, Volume 344, September 2017, Pages 595622.
[ bib 
pdf  journal 
slides 
seminar video
]
ThirdOrder Accuracy without Curved Elements
H. Nishikawa, " Accuracypreserving boundary flux quadrature for finitevolume discretization on unstructured grids", Journal of Computational Physics, Volume 281, January 2015, Pages 518555, 2015.
[ bib 
pdf  journal 
slides 
seminar video
]
 3D Hyperbolic NavierStokes (HNS) solvers
Y. Liu and H. Nishikawa, "
ThirdOrder EdgeBased Hyperbolic NavierStokes Scheme for ThreeDimensional Viscous Flows",
AIAA Paper 20173443, 23rd AIAA Computational Fluid Dynamics Conference, 5  9 June 2017, Denver, Colorado.
[ bib 
pdf 
slides
]
Y. Liu and H. Nishikawa, "ThirdOrder Inviscid and SecondOrder Hyperbolic NavierStokes Solvers for ThreeDimensional
Unsteady Inviscid and Viscous Flows",
AIAA Paper 20170738, 55th AIAA Aerospace Sciences Meeting, 9  13 January 2017, Grapevine, Texas.
[ bib 
pdf 
slides
]
H. Nishikawa and Y. Liu, "Hyperbolic AdvectionDiffusion Schemes for HighReynoldsNumber BoundaryLayer Problems",
Journal of Computational Physics, Volume 352, January 2018, Pages 2351, 2018.
[ bib 
pdf  journal
]  See also AIAA20170081 [ pdf 
slides ]
Y. Liu and H. Nishikawa, "ThirdOrder Inviscid and SecondOrder Hyperbolic NavierStokes Solvers
for ThreeDimensional Inviscid and Viscous Flows",
AIAA Paper 20163969, 46th AIAA Fluid Dynamics Conference, 1317 June 2016, Washington, D.C.
[ bib 
pdf 
slides
]
Y. Nakashima, N. Watanabe, H. Nishikawa, "Hyperbolic NavierStokes Solver for ThreeDimensional Flows",
AIAA Paper 20161101, 54th AIAA Aerospace Sciences Meeting, 48 January, San Diego, California, 2016.
[ bib 
pdf
]
 HNS20: A Versatile Hyperbolic NavierStokes System
H. Nishikawa, "Alternative Formulations for First, Second, and ThirdOrder Hyperbolic NavierStokes Schemes", AIAA Paper 20152451,
22nd AIAA Computational Fluid Dynamics Conference, Dallas, 2015.
[ bib 
pdf 
slides 
seminar video
]
HNS14: A Limited Hyperbolic NavierStokes System
H. Nishikawa, "First, Second, and Third Order FiniteVolume
Schemes for NavierStokes Equations", AIAA Paper 20142091,
7th AIAA Theoretical Fluid Mechanics Conference, Atlanta, 2014.
[ bib 
pdf 
seminar video
]
 Upwind Them All: Advection, Diffusion, and Source
H. Nishikawa, "First, Second, and Third Order FiniteVolume Schemes for AdvectionDiffusion", Journal of Computational Physics,
Volume 273, September 2014, Pages 287309, 2014.
[ bib 
pdf 
journal 
slides 
seminar video 
newspaper ]
H. Nishikawa, "First, Second, and Third Order FiniteVolume Schemes for Diffusion", Journal of Computational Physics,
Volume 256, Issue 1, January 2014, Pages 791805, 2014.
[ bib 
pdf 
journal  slides
 seminar video 
a derivation of Lr (pdf) ]
H. Nishikawa, "Divergence Formulation of Source Term", Journal of Computational Physics,
Volume 231, Issue 19, 1 August 2012, Pages 63936400, 2012.
[ bib  pdf 
journal 
slides

seminar video
]
Ranked in Top 25 Hottest Articles at ScienceDirect.
 Everybody's Recipe for Making Good Diffusion/Viscous Schemes
Effects of Damping Coefficient for Implicit Solver
H. Nishikawa and Y. Nakashima and N. Watanabe,
"Effects of HighFrequency Damping on Iterative Convergence of Implicit Viscous Solver",
Journal of Computational Physics, Volume 348, November 2017, Pages 6681
[ bib 
pdf 
journal
]
Recipe extended to NavierStokes
H. Nishikawa, "Two Ways to Extend Diffusion Schemes to
NavierStokes Schemes: Gradient Formula or Upwind Flux", AIAA Paper 20113044,
20th AIAA Computational Fluid Dynamics Conference, Hawaii, 2011.
[ bib 
pdf 
slides ]
Recipe: Long Version
H. Nishikawa, "Beyond Interface Gradient: A General Principle for Constructing Diffusion Schemes",
AIAA Paper 20105093, 40th AIAA Fluid Dynamics Conference and Exhibit,
Chicago, 2010.
[ bib 
pdf 
slides
note ]
Recipe: Short Version
H. Nishikawa, "Robust and Accurate Viscous Discretization via Upwind Scheme  I:
Basic Principle", Computers and Fluids, 49, pp.6286 2011.
[ bib 
pdf 
journal 
note ]
 Unification of Advection and Diffusion
H. Nishikawa, "A FirstOrder System Approach for Diffusion Equation. II:
Unification of Advection and Diffusion",
Journal of Computational Physics, 227, pp. 39894016, 2010.
[ bib 
pdf 
journal 
poster ]
Ranked in Top 25 Hottest Articles at ScienceDirect.
 Robust Euler Flux
H. Nishikawa and K. Kitamura,
"Very Simple, CarbuncleFree, BoundaryLayerResolving, RotatedHybrid Riemann Solvers",
Journal of Computational Physics, 227, pp. 25602581, 2008.
[ bib 
pdf 
journal 
2D subroutine
3D subroutine ]
 Hyperbolic Diffusion Schemes
H. Nishikawa, "A FirstOrder System Approach for Diffusion Equation. I: SecondOrder Residual Distribution Schemes",
Journal of Computational Physics, 227, pp. 315352, 2007.
[ bib 
pdf 
journal 
code 
poster ]




