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)

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    Papers/Notes/Codes: Papers, notes, presentation files, and codes are available at Hiroaki Nishikawa ar ResearchGate ResearchGate
    CFD Book: " I do like CFD, VOL. 1, Second Edition ". Visit for free PDF and CFD codes.

    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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