東大数値解析セミナー(UTNAS)
- 投稿者
- 齊藤 宣一(東京大学大学院数理科学研究科)
- 日程
- 2020年12月15日(火) 16:30-18:00
- 会場
- オンライン
| 本文 |
東京大学大学院数理科学研究科と情報理工学系研究科では,本年度も数値解析セミナーを定期的(月に1,2回程度)に開催致します. 多くの皆様のご参加をお待ち申し上げます. |
| 講演者 | Ming-Cheng Shiue (National Chiao Tung University) |
| 題目 | Iterated pressure-correction projection methods for the 2d Navier-Stokes equations based on the scalar auxiliary variable approach |
| 概要 |
In this talk, the first-order iterated pressure-correction projection methods based on the scalar auxiliary variable approach is proposed and studied for the 2d Navier-Stokes equations and Boussinesq equations.
In the literature, enormous amounts of work have contributed to the study of numerical schemes for computing the Navier-Stokes equations. In general, two of the main numerical difficulties for solving Navier-Stokes equations are the incompressible condition and the nonlinear term. One of the approaches to deal with the incompressible condition is the so-called projection. The typical projection method only needs to solve the Poisson type of equations depending on the nonlinear term's treatment, which is efficient. However, the pressure-correction projection methods suffer from the splitting error, leading to spurious numerical boundary layers and the limitation of accuracy in time. In the literature, an iterated pressure-correction projection method has been proposed to overcome the difficulty. As for the nonlinear term treatment, it is better to treat the nonlinear term explicitly so that one only requires to solve the corresponding linear system with constant coefficients at each time step. However, such treatment often results in a restricted time step due to the stable issue. Recently, the scalar auxiliary variable approach has been constructed to have an unconditional energy stable numerical scheme. In this work, a new iterated pressure-correction projection method based on the scalar auxiliary variable's simple choice is proposed. We find that this new scheme can enjoy two properties, including reducing the splitting errors and having unconditional energy stability. The proofs of the energy stability and error convergence are provided and analyzed. Finally, numerical examples are provided to illustrate the theoretical work. This is joint work with Tony Chang. |
| 備考 |
聴講をご希望される方は， 下記詳細 web の「備考」中に記載のある事前参加登録ページで参加登録をお願いいたします．
登録した方にのみ，講演の1時間前に，ZoomミーティングのURLを送付します． ただし，応用数学合同オンラインセミナーのコアメンバーの方は，すでに登録済ですので，再度の登録の必要はありません. |
お問い合わせ先
齊藤 宣一
e-mail: norikazu__AT__g.ecc.u-tokyo.ac.jp