Algorithm Development for
Computational Fluid Dynamics


Simple ideas for difficult problems
Hiroaki Nishikawa
Research Interests:   Algorithm development for Computational Fluid Dynamics (CFD) --- Viscous discretizations, Riemann solvers, discretization methods for unstructured grids: residual-distribution, finite-volume, discontinuous Galerkin, spectral-volume, multigrid methods, grid adaptation, etc.
Why do I want to post my preprints, notes, and codes in public? (Blog Article)
NIA CFD Seminar (Presentation files, seminar videos available)


    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. Wedding of Finite-Volume and Residual Distribution
    --- "Aha!":   A new idea for guaranteeng discrete conservation.

    H. Nishikawa, Multidimensional Upwind Finite-Volume Schemes by Residual-Distribution Schemes, coming someday.
  2. 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 | online | slides ]
  3. 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 ]
  4. 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 | slides | seminar video | newspaper ]
  5. 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 | online | slides | seminar video ]
  6. 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 | online | slides | seminar video ]
    Ranked in Top 25 Hottest Articles at ScienceDirect!
  7. 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 ]
  8. 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 ]
  9. 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 | online | note ]
  10. 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 | online | poster ]
    Ranked in Top 25 Hottest Articles at ScienceDirect!
  11. 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 | online | 2D subroutine| 3D subroutine ]
  12. 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 | online | 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.

View Hiroaki Nishikawa's LinkedIn profileView Hiroaki Nishikawa's profile    Follow HiroNishikawa on Twitter Hiroaki Nishikawa on twitter