Research Interests

• Computational Science.
• Algorithm development for computational fluid dynamics.

Education

• Ph.D., Aerospace Engineering and Scientific Computing, University of Michigan, Ann Arbor, Michigan (2001)
• M.S., Applied Mathematics, University of Michigan, Ann Arbor, Michigan (1999)
• M.S.E., Aerospace Engineering, University of Michigan, Ann Arbor, Michigan (1996)
• B.S., Aeronautics and Astronautics, Tokai University, Tokyo, Japan (1994)

Current Research

Extremely Fast Practical 3D CFD Solver:  This research aims to develop an agglomeration multigrid method that accelerates convergence of Reynolds-Averaged Navier-Stokes solvers for fully unstructured practical large-scale 3D geometries. Essential components to achieve the goal have been developed, including: a fast and robust agglomeration scheme, consistent and accurate coarse grid discretization, and efficient parallel implementation. Robustness of the developed method is being further improved.

First-Order Hyperbolic System Method: This research aims to accelerate CFD computations and achieve higher-order accuracy simultaneously, and also dramatically improve the accuracy in the derivatives such as the viscous stresses and heat fluxes on irregular (fully adapted) viscous grids. The core idea is to solve higher-order partial differential equations (PDEs) as a first-order hyperbolic system, which is applicable to various PDEs and discretization methods.

Publications

H. Nishikawa, First, Second, and Third Order Finite-Volume Schemes for Navier-Stokes Equations, AIAA Paper 2014-2091, 7th AIAA Theoretical Fluid Mechanics Conference, June 2014. pdf

H. Nishikawa, P. L. Roe, and T. A. Eymann, Active Flux for Diffusion, AIAA Paper 2014-2092, 7th AIAA Theoretical Fluid Mechanics Conference, June 2014. pdf

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. pdf

H. Nishikawa, First, Second, and Third Order Finite-Volume Schemes for Advection Diffusion, Journal of Computational Physics, Volume 273, Issue 15, September 2014, Pages 287-309, 2014. pdf

A. Mazaheri and H. Nishikawa, First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems, NASA-TM-2014-218175, March 2014. pdf

H. Nishikawa and B. Diskin, Evaluation of Multigrid Solutions for Turbulent Flows, AIAA Paper 2014-0082, AIAA SciTech, June 2014. pdf

H. Nishikawa, Divergence Formulation of Source Term, Journal of Computational Physics, Volume 231, Issue 19, 1 August 2012, Pages 6393-6400, 2012. pdf

H. Nishikawa, Two Ways to Extend Diffusion Schemes to Navier-Stokes Schemes: Gradient Formula or Upwind Flux, AIAA Paper 2011-3044, 20th Computational Fluid Dynamics Conference, June 2011.  pdf

H. Nishikawa, A First-Order System Approach for Diffusion Equation. II: Unification of Advection and Diffusion, Journal of Computational Physics, 229, pp. 3989-4016, 2010. pdf

H. Nishikawa, Adaptive-Quadrature Fluctuation-Splitting Schemes for the Euler Equations, International Journal for Numerical Methods in Fluids, 57, pp. 1-12, 2008. pdf

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.  pdf

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. pdf

H. Nishikawa, Multigrid Third-Order Least-Squares Solution of Cauchy-Riemann Equations on Unstructured Triangular Grids, International Journal for Numerical Methods in Fluids, 53: 443-454, 2007. pdf

H. Nishikawa and B. van Leer, Optimal Multigrid Convergence by Elliptic/Hyperbolic Splitting, Journal of Computational Physics, 190, pp. 52-63, 2003. pdf

P. L. Roe and H. Nishikawa, Adaptive Grid Generation by Minimising Residuals, International Journal for Numerical Methods in Fluids, 40: 121-136, 2002. pdf