Hiroaki Nishikawa
Resident at: NASA Langley Research Center
Tel: 757-864-7244
Email: hiro@nianet.org
Personal Website: http://research.nianet.org/~hiro
Research Interests
· Algorithm development for computational fluid dynamics
Current Research
· Extremely Fast Practical 3D CFD Solver: It aims to develop an agglomeration multigrid method that accelerates convergence of Reynolds-Averaged Navier-Stokes solvers for fully unstructured practical large-scale 3D geometries within the framework of NASA’s FUN3D CFD code. Essential components to achieve the goal are being developed: a fast and robust agglomeration scheme, consistent and accurate coarse grid discretization, and efficient parallel implementation.
· A Final Answer to Viscous Discretization: A very useful general principle for constructing robust and accurate diffusion schemes is proposed, which is applicable to all discretization methods and all types of grids. Resulting diffusion schemes have good high-frequency damping and very efficiently integrated with advection schemes. Extensions to high-order methods, advection-diffusion equations, and the Navier-Stokes equations are currently under way.
· A Future Tradition on Viscous Simulations: It aims to develop a radically new methodology for achieving practically fast and accurate viscous simulations that have never been achieved. The idea is to solve the diffusion equation as a first-order hyperbolic system. It enables the use of exceptionally large time steps and a simultaneous computation of accurate diffusive flux (viscous stresses and heat fluxes). The idea is now being extended to and the Navier-Stokes equations.
· Beautiful Hypersonic Computations: A class of robust Euler fluxes, called the rotated-hybrid Riemann solvers, are developed to combat anomalies in CFD codes that arise particularly in hypersonic computations. The developed Euler fluxes have been shown to be very robust and capable of producing accurate flow solutions for various well-known 2D test cases. Sophisticated extensions to 3D are currently pursued.
Publications
· H. Nishikawa, A General Principle for Constructing Diffusion Schemes, 40th AIAA Fluid Dynamics Conference and Exhibit, June 2010.
· H. Nishikawa, A First-Order System Approach for Diffusion Equation. II: Unification of Advection and Diffusion, Journal of Computational Physics, in press.
· H. Nishikawa, B. Diskin, and J. L. Thomas, A Critical Study of Agglomerated Multigrid Methods for Diffusion, AIAA Journal, in press.
· B. Diskin, J. L. Thomas, E, J. Nielsen, H. Nishikawa and J. A. White, Comparison of Node-Centered and Cell-Centered Unstructured Finite-Volume Discretizations. Part I: Viscous Fluxes, AIAA Journal, in press.
· 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.
· H. Nishikawa, Adaptive-Quadrature Fluctuation-Splitting Schemes for the Euler Equations, International Journal for Numerical Methods in Fluids, 57, pp. 1-12, 2008.
· 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.
· 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.
· H. Nishikawa and B. van Leer, Optimal Multigrid Convergence by Elliptic/Hyperbolic Splitting, Journal of Computational Physics, 190, pp. 52-63, 2003.
· P. L. Roe and H. Nishikawa, Adaptive Grid Generation by Minimising Residuals, International Journal for Numerical Methods in Fluids, 40: 121-136, 2002.