Algorithm Development for
Computational Fluid Dynamics


Simple ideas for difficult problems
Hiroaki Nishikawa:
Algorithm developer for Computational Fluid Dynamics (CFD).

Developed a node-generation algorithm for one-dimensional 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 local-preconditioning 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 Navier-Stokes equations with Phil Roe in 2004 [pdf], developed a multigrid third-order scheme in 2007 pdf, developed a robust rotated-hybrid 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 Navier-Stokes 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 unstructured-grid solver [pdf], developed a third-order NS solver that is faster than widely-used second-order 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 reconstructed-DG 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)
First-Order Hyperbolic System Method (History, Development, and FAQ)

View Hiroaki Nishikawa's LinkedIn profile ResearcherID    Follow HiroNishikawa on Twitter Google Scholar    Hiroaki Nishikawa ar ResearchGate ResearchGate



    Hyperbolic Stories::  

[ pdf ]   "Toward a Future Navier-Stokes Code: Exploiting Additional Degrees of Freedom"- Seminar at NIA, June 2007
[ pdf ]   "First-Order Hyperbolic System Method" - NIA CFD Seminar, October 2011
[ pdf ]   "Robust and Accurate Viscous Discretization by Hyperbolic Recipe" - NIA CFD Seminar, November 2011
[ pdf ]   "First-Order 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 Never-Ending Story of CFD Algorithm Development" - Jameson-Roe-Van-Leer Symposium in 2013
[ pdf ]   "List of Papers for Hyperbolic Method (07-22-2014)" - CRADLE Next Generation CFD Seminar in 2014
[ pdf ]   "Discretization that ends well (3rd-order 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 :  
  1. Third-Order Edge-Based Method

    Third-Order Accuracy with Zero/Negative-Volume Elements
    H. Nishikawa, "Uses of Zero and Negative Volume Elements for Node-Centered Edge-Based Discretization", AIAA Paper 2017-4295, 23rd AIAA Computational Fluid Dynamics Conference, 5 - 9 June 2017, Denver, Colorado.
    [ bib | pdf | slides ]

    Third-Order Accuracy without Second Derivatives
    H. Nishikawa and Y. Liu, " Accuracy-Preserving Source Term Quadrature for Third-Order Edge-Based Discretization", Journal of Computational Physics, Volume 344, September 2017, Pages 595-622.
    [ bib | pdf | journal | slides | seminar video ]

    Third-Order Accuracy without Curved Elements
    H. Nishikawa, " Accuracy-preserving boundary flux quadrature for finite-volume discretization on unstructured grids", Journal of Computational Physics, Volume 281, January 2015, Pages 518-555, 2015.
    [ bib | pdf | journal | slides | seminar video ]
  2. 3D Hyperbolic Navier-Stokes (HNS) solvers





    Y. Liu and H. Nishikawa, " Third-Order Edge-Based Hyperbolic Navier-Stokes Scheme for Three-Dimensional Viscous Flows", AIAA Paper 2017-3443, 23rd AIAA Computational Fluid Dynamics Conference, 5 - 9 June 2017, Denver, Colorado.
    [ bib | pdf | slides ]

    Y. Liu and H. Nishikawa, "Third-Order Inviscid and Second-Order Hyperbolic Navier-Stokes Solvers for Three-Dimensional Unsteady Inviscid and Viscous Flows", AIAA Paper 2017-0738, 55th AIAA Aerospace Sciences Meeting, 9 - 13 January 2017, Grapevine, Texas.
    [ bib | pdf | slides ]

    H. Nishikawa and Y. Liu, "Hyperbolic Navier-Stokes Method for High-Reynolds-Number Boundary-Layer Flows", AIAA Paper 2017-0081, 55th AIAA Aerospace Sciences Meeting, 9 - 13 January 2017, Grapevine, Texas.
    [ bib | pdf | slides ]

    Y. Liu and H. Nishikawa, "Third-Order Inviscid and Second-Order Hyperbolic Navier-Stokes Solvers for Three-Dimensional Inviscid and Viscous Flows", AIAA Paper 2016-3969, 46th AIAA Fluid Dynamics Conference, 13-17 June 2016, Washington, D.C.
    [ bib | pdf | slides ]

    Y. Nakashima, N. Watanabe, H. Nishikawa, "Hyperbolic Navier-Stokes Solver for Three-Dimensional Flows", AIAA Paper 2016-1101, 54th AIAA Aerospace Sciences Meeting, 4-8 January, San Diego, California, 2016.
    [ bib | pdf ]
  3. HNS20: A Versatile Hyperbolic Navier-Stokes System

    H. Nishikawa, "Alternative Formulations for First-, Second-, and Third-Order Hyperbolic Navier-Stokes Schemes", AIAA Paper 2015-2451, 22nd AIAA Computational Fluid Dynamics Conference, Dallas, 2015.
    [ bib | pdf | slides | seminar video ]

    HNS14: A Limited Hyperbolic Navier-Stokes System
    H. Nishikawa, "First, Second, and Third Order Finite-Volume Schemes for Navier-Stokes Equations", AIAA Paper 2014-2091, 7th AIAA Theoretical Fluid Mechanics Conference, Atlanta, 2014.
    [ bib | pdf | seminar video ]
  4. Upwind Them All: Advection, Diffusion, and Source

    H. Nishikawa, "First, Second, and Third Order Finite-Volume Schemes for Advection-Diffusion", Journal of Computational Physics, Volume 273, September 2014, Pages 287-309, 2014.
    [ bib | pdf | journal | slides | seminar video | newspaper ]

    H. Nishikawa, "First, Second, and Third Order Finite-Volume Schemes for Diffusion", Journal of Computational Physics, Volume 256, Issue 1, January 2014, Pages 791-805, 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 6393-6400, 2012.
    [ bib | pdf | journal | slides | seminar video ]
    Ranked in Top 25 Hottest Articles at ScienceDirect.
  5. Everybody's Recipe for Making Good Diffusion/Viscous Schemes

    Recipe extended to Navier-Stokes
    H. Nishikawa, "Two Ways to Extend Diffusion Schemes to Navier-Stokes Schemes: Gradient Formula or Upwind Flux", AIAA Paper 2011-3044, 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 2010-5093, 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.62-86 2011.
    [ bib | pdf | journal | note ]
  6. Unification of Advection and Diffusion

    H. Nishikawa, "A First-Order System Approach for Diffusion Equation. II: Unification of Advection and Diffusion", Journal of Computational Physics, 227, pp. 3989-4016, 2010.
    [ bib | pdf | journal | poster ]
    Ranked in Top 25 Hottest Articles at ScienceDirect.
  7. Robust Euler Flux

    H. Nishikawa and K. Kitamura, "Very Simple, Carbuncle-Free, Boundary-Layer-Resolving, Rotated-Hybrid Riemann Solvers", Journal of Computational Physics, 227, pp. 2560-2581, 2008.
    [ bib | pdf | journal | 2D subroutine| 3D subroutine ]
  8. Hyperbolic Diffusion Schemes

    H. Nishikawa, "A First-Order System Approach for Diffusion Equation. I: Second-Order Residual Distribution Schemes", Journal of Computational Physics, 227, pp. 315-352, 2007.
    [ bib | pdf | journal | code | poster ]

    Background: Osaka[Sakai]-Kanagawa-Tokyo, Japan (1971-1994; BS), Michigan (1994 - 2007; MS, MSE, PhD), Virginia (2007 - Present), Aerospace Engineering, Applied Mathematics, Scientific Computing.

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