Paradigm shift of Godunov-type finite volume method for compressible flow

2018 Fiscal Year Final Research Report

• Project/Area Number: 17K18838
• Research Category: Grant-in-Aid for Challenging Research (Exploratory)
• Allocation Type: Multi-year Fund
• Research Field: Fluid engineering, Thermal engineering, and related fields
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: Xiao Feng 東京工業大学, 工学院, 教授 (50280912)
• Project Period (FY): 2017-06-30 – 2019-03-31
• Keywords: 数値流体力学 / 圧縮性流体 / 有限体積法 / 衝撃波 / 不連続面 / 流体工学 / 航空宇宙工学 / 計算物理

Outline of Final Research Achievements

The major achievements in this project are summarized as follows.
(1)The guideline for designing new-type high-resolution Godunov schemes based on the BVD (Boundary Variation Diminishing) principle, which requires to minimize the difference in the reconstructed values across cell boundaries, has be established. (2) A class of schemes of great practical significance based on the BVD principle, so-called BVD schemes, have been proposed and verified. (3) High-fidelity shock-capturing schemes without any conventional nonlinear limiter have been developed using properly designed multi-stage BVD algorithms and BVD admissible reconstruction functions. (4) The BVD schemes have been implemented to Euler equations and reactive compressible flow simulations. The BVD schemes show significant advantage in resolving both smooth and discontinuous flow structures, especially in the cases where the contact discontinuities or moving fronts play a crucial role in the dynamic processes.

Free Research Field

数値流体力学

Academic Significance and Societal Importance of the Research Achievements

本研究では，BV値が数値散逸の大小に直結する点に着目し，これまでに類を見ないBV最小化の概念を数値解法開発の原理（BVD原理）として確立させた。BVD原理は，現行のGodunov型有限体積法の欠点を克服する斬新な発想であり，圧縮性流体のみならず，より一般的な双曲型保存則の数値解法の開発に大きな変革をもたらすことに違いがない。本研究は，数値流体力学研究の新しい方向を示し，研究成果は関連分野の新しい理論体系の形成に展開していくであろう。さらに，本研究で提案，実証した新型の数値計算手法は，圧縮性流体の数値解析をはじめ様々な応用問題に大きく資するものであり，産業界にも大きな波及効果を期待出来る。