Tohoku University
Kuya Laboratory
Fluid Dynamics × Quantum Computing

Research

Current research topics

  Upwind schemes, which contain numerical viscosity, are commonly used to perform flow computations stably. However, when upwind schemes are used, it is difficult to perform high-fidelity flow computations due to the non-physical effects of numerical viscosity. We have developed stable and non-dissipative (i.e., no numerical viscosity) numerical schemes, kinetic energy and entropy preserving (KEEP) schemes. Recently, by using the KEEP schemes and an LES (large eddy simulation) wall model, we have succeeded in realizing high-fidelity flow computations (LES) of a whole aircraft configuration (JAXA standard model: JSM). However, many problems still need to be solved in applying high-fidelity flow computations in the design of industrial aerodynamic systems. We are developing novel numerical methods for flow computations to solve those problems.

  流体の数値計算を安定に実施するには数値的な粘性が付加された数値計算手法 (upwind scheme) が一般的に用いられる. しかしupwind schemeを用いた場合には,非物理的に付加された数値粘性の影響で高忠実に数値計算を実施することが困難となる. そこで我々は数値粘性の付加なく安定な数値計算手法 "kinetic energy and entropy preserving (KEEP) scheme" を構築した. 最近ではこのKEEP schemeとLES (large eddy simulation) 壁面モデルを用いることにより,航空機全機 (JAXA standard model: JSM) 周りの高精度流体計算 (LES) の実現に成功している. 産業分野において高精度流体計算を流体機械設計に常用出来るようにするにはまだまだ課題が多く残されており,それらの課題の解決に向けて新たな数値流体計算手法の構築に取り組んでいる.

[Tamaki et al., JCP, 2022, Kuya & Kawai, JCP, 2022, Kuya & Kawai, JCP, 2021, Shima et al., JCP, 2021, Kuya & Kawai, CaF, 2020, Kuya et al., JCP, 2018]

  Numerical methods that can easily and stably perform high-fidelity flow analysis around complex geometries are always required in industry. For example, unstructured-grid finite-volume methods are widely used in industry due to their advantage of being able to create computational meshes around complex geometries. Still, largely distorted computational meshes are likely to induce numerical instability in those methods. As an alternative approach, block-structured Cartesian methods have attracted attention together with immersed boundary methods. Block-structured Cartesian methods can generate computational meshes around complex geometries using only structured grids and have excellent parallel computing efficiency. Recently, we have proposed the "kinetic energy and entropy preserving (KEEP) scheme" that can perform non-dissipative and stable computations on non-conforming block boundaries of block-structured Cartesian meshes without adding numerical dissipation. Using the KEEP schemes, we have stably realized high-fidelity flow computations around complex geometries.

  産業界において複雑形状周りの高精度流体解析を容易かつ安定に行える数値計算手法が常に求められている. 例として,複雑形状周りに計算格子作成が可能であるという利点から,非構造格子有限体積法が産業界で広く用いられている.一方で,非構造格子有限体積法では非常に強く歪んでしまった計算格子において数値計算が不安定になるという問題が常在する. そこで別のアプローチとして,直交格子のみで格子生成が可能かつ並列計算効率にも優れた階層型直交格子法が埋め込み境界法とともに注目されている. 近年我々は階層型直交格子において格子解像度が変化する階層境界においても数値粘性の付加なく非散逸かつ安定に計算が行えるkinetic energy and entropy preserving (KEEP) schemeを提案しており,実際にKEEP schemeを用いることで複雑形状周りの高精度流体解析を安定に行えることを実証している.

[Kuya & Kawai, CaF, 2020]

\begin{align*} {\rm Ising\; model:}\quad & E(\{\sigma_i\}) = \sum_{i} h_i \sigma_i + \sum_{i < j} J_{ij} \sigma_{i} \sigma_j, \quad \sigma_i \in \{-1,1\} \\ \\ {\rm QUBO:}\quad & E(\{q_i\}) = \sum_{i} \sum_{j} Q_{ij} q_{i} q_j, \quad q_i \in \{0,1\} \end{align*}
  Quantum annealing computers are specialized for solving combinatorial optimization problems where a cost function expressed in the form of an ising model or QUBO is minimized. Quantum annealing algorithms have been actively developed and studied in information science, but they have hardly been applied to the field of fluid dynamics. Understanding quantum annealing algorithms enables an entirely different approach to realize flow computations, shape optimization, and machine learning. Although the performance of quantum annealing computers themselves is still in its infancy, we regard quantum annealing computers as one of the next-generation computers and are engaged in research on the applications of quantum annealing computation to the fluid dynamics field.

  量子アニーリングコンピュータはising modelもしくはQUBOと呼ばれる形で表現されるコスト関数を最小化する組合せ最適化問題に特化したマシンとなっている. 量子アニーリング計算に関する研究・開発は情報科学の分野で盛んに行われているが,流体力学分野への応用はほとんど見られない. しかし量子アニーリングアルゴリズムを理解することで今までとは全く異なるアプローチで流体計算や形状最適化,機械学習が可能となる. 量子アニーリングコンピュータ自体の性能もまだまだ発展途上ではあるが,量子アニーリングコンピュータを次世代の計算機の一つとして捉え,量子アニーリング計算の流体力学分野への応用に関する研究に取り組んでいる.

Previous research topics

  Since the flow characteristics of turbulent and laminar flows are very different, accurate predictions of the laminar-turbulent transition phenomenon by flow computation are crucial in fluid machinery design. Although the turbulence model called RANS (Reynolds-averaged Navier-Stokes) is mainly used for numerical simulations of turbulent flows in industry, very simple models are usually used to model turbulent phenomena. We have developed a RANS transition model that incorporates a laminar-turbulent transition model into the Reynolds stress model (RSM). RSM is considered to better reproduce the anisotropic behavior of turbulence than other RANS methods. The proposed RSM transition model shows improved prediction accuracy compared to existing methods.

  乱流と層流では流れの性質が大きく異なるため,層流-乱流遷移現象を数値計算によって正確に予測することは流体機械の設計において非常に重要である. 産業界において乱流の数値計算を行う際にはRANS (Reynolds-averaged Navier–Stokes) と呼ばれる乱流モデルが主に使われているが,乱流現象のモデル化には非常にシンプルなモデルが用いられることが一般的である. そこでレイノルズ応力モデル (RANS手法の中でも乱流の非等方的な振る舞いをより良く再現できると考えられている) に層流-乱流遷移モデルを組み込むことで,既存手法と比較して流体解析精度向上させたRANS遷移モデル (γ-SSG/LRR-ω RSM) を構築している.

[Kuya et al., AIAA J, 2023]


Transonic buffet

Suppression of transonic buffet by VGs

Suppression of transonic shock buffet by vortex generators



Flow separation control of an inverted wing in ground effect

  Transonic shock buffet is an unsteady flow phenomenon characterized by self-sustained oscillations and is one of the most important unresolved issues in the aeronautical field. Also, the flow under a strong adverse pressure gradient is likely to detach from solid surfaces, resulting in a significant reduction of lift (or downforce) of wings. It is known that these aerodynamic phenomena can be effectively suppressed by vortex generators that generate longitudinal vortices in the flow field. The impacts of the vortices generated by vortex generators on the flow fields are experimentally and numerically analyzed.

  遷音速バフェット現象は翼面上で衝撃波が振動する非定常現象であり,航空機空力分野において未だ解明されていない重要な問題の一つである. また強い逆圧力勾配下では流れは固体壁面より剥離してしまうが,流れが剥離すると翼が発生する揚力 (もしくはダウンフォース) は著しく低下する. 流れ場に縦渦を発生させるボルテックスジェネレーターを用いることでこれらの空力現象を効果的に抑制出来ることが知られており,ボルテックスジェネレーターによって生成された渦が流れ場にどのような影響を与えるかの解析を実験および数値計算の両面から行なっている.

[Kuya et al., J Aircr, 2020, Kuya et al., J Fluids Eng, 2010, Kuya et al., J Fluids Eng 2009b, Kuya et al. J Fluids Eng, 2009a]

  Surrogate modeling is one of the optimization tools. Surrogate models approximately predict an unknown relation (i.e., black box) between arbitrary inputs and outputs. While many surrogate models exist, such as polynomial response surface, radial basis function, and kriging, we focused on CoKriging, which can combine high-fidelity data with low-fidelity data to build models efficiently. We proposed CoKriging regression to obtain a smooth approximation even for data containing random noise, such as experimental data.

  代替モデル (surrogate model) は最適設計ツールの一つであり,任意の入力と出力の間の未知の関係(=ブラックボックス)を近似的に予測するものである.代替モデルにはpolynomial response surfaceやradial basis function,krigingと言った多くのモデルが存在するが,我々は高忠実なデータと低忠実なデータを組み合わせて高効率にモデルを得ることが出来るCoKrigingに着目し,実験値のようにランダムなノイズを含んだでデータに対しても滑らかな近似を行えるCoKriging regressionを提案している.

[Kuya et al., AIAA J, 2011]