

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,
[pdf],
developed a recipe for constructing a localpreconditioning matrix in 2003 [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 firstorder hyperbolic system 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 extremely efficient unsteady highorder schemes with Alireza Mazaheri in 2014 [
pdf],
developed a thirdorder NS solver that is faster than widelyused secondorder NS solver
[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)




Hyperbolic Stories::
[
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 (First SushiBurger Talk)
[
pdf ] "Hyperbolize It"  Conference on Future Directions in CFD Research, August 2012 (Second SushiBurger Talk)
[
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


Papers of Interest :
 ThirdOrder Accuracy without Curved Elements
 Doesn't matter what you believe: this is a fact.
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
]
 A NewGeneration NavierStokes Solver
 So impossibly efficient and accurate hyperbolic viscous solvers.
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
]
 Another ThirdOrder Unsteady Hyperbolic Schemes for Diffusion
 Another example for unsteady schemes by hyperbolic method.
H. Nishikawa, P. L. Roe, T. A. Eymann, "Active Flux for Diffusion", AIAA20142092, 2014.
[ bib 
pdf 
slides ]
 HighOrder Unsteady Hyperbolic Schemes for AdvectionDiffusion
 It only takes highorder source term. So simple and economical.
A. Mazaheri and H. Nishikawa, "Very efficient highorder hyperbolic schemes for timedependent advectiondiffusion problems: Third, fourth, and sixthorder", Computers and Fluids, 102, pp.131147 2014.
[ bib 
pdf 
journal 
slides ]
 TimeAccurate Hyperbolic Schemes for AdvectionDiffusion
 Hyperbolic method is applicable to unsteady problems, of course.
A. Mazaheri and H. Nishikawa, "FirstOrder Hyperbolic System Method for
TimeDependent AdvectionDiffusion Problems", NASATM2014218175, March 2014.
[ bib  pdf ]
 Upwind Them All: Advection, Diffusion, and Source
 A truly unified construction of advectiondiffusion schemes.
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 ]
 Robust FirstOrder and Super ThirdOrder Diffusion Schemes
 See how advection schemes become diffusion schemes overnight.
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 ]
 Unification of Conservation Law and Source Term

Discretize source terms just like a conservation law. Yes, you can!
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!
 A Farewell to Traditional NavierStokes Codes
 Intrinsically efficient and accurate hyperbolic viscous solvers.
H. Nishikawa, "NewGeneration Hyperbolic NavierStokes Schemes:
O(1/h) SpeedUp and Accurate Viscous/Heat Fluxes", AIAA Paper 20113043,
20th AIAA Computational Fluid Dynamics Conference, Hawaii, 2011.
[ bib 
pdf 
slides 
poster 
story ]
 Robust and Accurate Viscous Discretization
 Extended recipe: Viscous discretization by upwind schemes.
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 ]
 Everybody's Recipe for Making Good Diffusion Schemes

A universal recipe for all methods. So simple, so good.
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 ]
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

Are you ready to say goodbye to 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

Remarkably simple and robust 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
 Amazingly fast
explicit diffusion scheme (6min>3sec).
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 ]



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 Books:
" I do like CFD, VOL. 1, Second Edition ".
Visit CFDbooks.com for free PDF and CFD codes.
Other Interests: Creative activities.
Details can be found somewhere else.

