Generalized numerical formulation for multi-moment constrained high resolution schemes for practical use

2014 Fiscal Year Final Research Report

• Project/Area Number: 24560187
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Fluid engineering
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: XIAO Feng 東京工業大学, 総合理工学研究科(研究院), 准教授 (50280912)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 高精度数値解法 / 圧縮性流体 / 浅水波モデル / 保存解法 / マルチ・モーメント制約 / WENO再構築 / 衝撃波 / 数値振動

Outline of Final Research Achievements

(1) A generalized numerical formulation has been developed to provide a base for designing new schemes with various constraints. The guideline to choose the proper multi-moment constraints for the desired numerical properties has been investigated through both theoretical and numerical analysis. (2) A novel 4th order high resolution scheme, MCV-WENO4, has been proposed and verified to be of advantage in comparison with other existing methods. (3) An efficient and conservative collocation method, Gauss-Legendre point based conservative collocation (GLPCC) method, has been proposed by using the collocation constraints. A three-point scheme of fifth-order accuracy has been adopted to develop the global shallow-water model on the cubed sphere grid. (4) A multi-moment finite volume method has been developed on unstructured grids with arbitrary mesh elements, which provides a numerical framework that well balances accuracy, efficiency and robustness for practical applications.

Free Research Field

数値流体力学