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, [pdf], developed a recipe for constructing a local-preconditioning 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 Navier-Stokes equations with Phil Roe in 2004 [pdf], develped 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 first-order 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 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 extremely efficient unsteady high-order schemes with Alireza Mazaheri in 2014 [ pdf], developed a third-order NS solver that is faster than widely-used second-order 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)
First-Order Hyperbolic System Method (History, Development, and FAQ)


    Hyperbolic Stories::  

[ 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 (First Sushi-Burger Talk)
[ pdf ]   "Hyperbolize It" - Conference on Future Directions in CFD Research, August 2012 (Second Sushi-Burger Talk)
[ 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

    Papers of Interest :  
  1. Third-Order Accuracy without Curved Elements
    --- Doesn't matter what you believe: this is a fact.

    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. A New-Generation Navier-Stokes Solver
    --- So impossibly efficient and accurate hyperbolic viscous solvers.

    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 ]
  3. Another Third-Order 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", AIAA2014-2092, 2014.
    [ bib | pdf | slides ]
  4. High-Order Unsteady Hyperbolic Schemes for Advection-Diffusion
    --- It only takes high-order source term. So simple and economical.

    A. Mazaheri and H. Nishikawa, "Very efficient high-order hyperbolic schemes for time-dependent advection-diffusion problems: Third-, fourth-, and sixth-order", Computers and Fluids, 102, pp.131-147 2014.
    [ bib | pdf | journal | slides ]
  5. Time-Accurate Hyperbolic Schemes for Advection-Diffusion
    --- Hyperbolic method is applicable to unsteady problems, of course.

    A. Mazaheri and H. Nishikawa, "First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems", NASA-TM-2014-218175, March 2014.
    [ bib | pdf ]
  6. Upwind Them All: Advection, Diffusion, and Source
    --- A truly unified construction of advection-diffusion schemes.

    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 ]
  7. Robust First-Order and Super Third-Order Diffusion Schemes
    --- See how advection schemes become diffusion schemes overnight.

    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 ]
  8. 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 6393-6400, 2012.
    [ bib | pdf | journal | slides | seminar video ]
    Ranked in Top 25 Hottest Articles at ScienceDirect!
  9. A Farewell to Traditional Navier-Stokes Codes
    --- Intrinsically efficient and accurate hyperbolic viscous solvers.

    H. Nishikawa, "New-Generation Hyperbolic Navier-Stokes Schemes:
    O(1/h) Speed-Up and Accurate Viscous/Heat Fluxes",
    AIAA Paper 2011-3043, 20th AIAA Computational Fluid Dynamics Conference, Hawaii, 2011.
    [ bib | pdf | slides | poster | story ]
  10. Robust and Accurate Viscous Discretization
    --- Extended recipe: Viscous discretization by upwind schemes.

    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 ]
  11. 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 2010-5093, 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.62-86 2011.
    [ bib | pdf | journal | note ]
  12. Unification of Advection and Diffusion
    --- Are you ready to say goodbye to 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!
  13. Robust Euler Flux
    --- Remarkably simple and robust 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 ]
  14. Hyperbolic Diffusion Schemes
    --- Amazingly fast explicit diffusion scheme (6min->3sec).

    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 ]
   

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.
Kuromame Taro (Black Bean Taro)
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.

    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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