Improvement of the time marching method in a particle method

• MATSUNAGA Takuya

  Department of Systems Innovation, The University of Tokyo

• KOSHIZUKA Seiichi

  Department of Systems Innovation, The University of Tokyo

Bibliographic Information

Other Title

• 粒子法における時間進行法の改良

Abstract

This study concerns the computational accuracy of a particle method for a time-dependent incompressible flow. In recent years, accurate spatial discretization schemes have been developed for a particle method. However, the actual convergence rate in space tends to be much lower than the order of the leading truncation error given by an adopted spatial discretization scheme. This suggests that the Δt-dependent error is comparably significant with respect to the truncation error of the spatial discretization scheme. Under these circumstances, we have developed a new time marching method to improve the computational accuracy by reducing the Δt-dependent error and improving the convergence property. The proposed time marching method is based on the 1st-order fractional step method, just as the conventional methods. However, as opposed to the past studies, the convection term is explicitly included in the provisional velocity calculation, as an Eulerian-based approach. By doing this, the Δt-dependent error caused by the particle movement can be avoided. A numerical test has been carried out using the two-dimensional Taylor-Green vortex problem, where 2nd- and 4th-order spatial discretization schemes are adopted. As a result, the conventional time marching methods gave much lower convergence rate than the order of the spatial discretization scheme. On the other hand, the proposed time marching method showed approximately 2nd- and 4th-order convergence in space with the 2nd- and 4th-order spatial discretization schemes, respectively. Therefore, the proposed method is indicated to highly improve the computational accuracy.

Journal

• Transactions of the JSME (in Japanese)

  Transactions of the JSME (in Japanese) 87 (895), 20-00437-20-00437, 2021

  The Japan Society of Mechanical Engineers

Keywords

• Computational fluid dynamics
• Incompressible flow
• Arbitrary Eulerian Lagrangian method
• Fractional step method
• LSMPS method

Details

• CRID: 1390568937776324480
• NII Article ID: 130008003246
• DOI: 10.1299/transjsme.20-00437
• ISSN: 21879761
• Web Site: https://www.jstage.jst.go.jp/article/transjsme/87/895/87_20-00437/_pdf
• Text Lang: ja
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed