コロケート格子有限体積法によるマクスウェル流体の構成式の離散化手法

Abstract

本研究では, 粘弾性流体を表すモデルの一つである非圧縮性マクスウェル流体の基礎方程式を2次元コロケート格子上で有限体積法により計算する手法を検討した. 著者らが提案したコロケート格子を用いる非圧縮性ニュートン流体の解法を改良し, マクスウェル流体の構成式を基礎方程式に加え, 運動方程式中の応力項を計算する際の流速の参照点を空間的にコンパクトにする手法を提案し, 非物理的な数値振動を抑制できることを数値実験により確認した. さらに, 流速の発散を制御可能なC-HSMAC 法を圧力解法に用いることにより, 通常のSMAC法で発生する可能性のある応力の数値振動を抑制できることを確認した. 最後に, 簡単な数値実験を通じて, 提案された計算手法によりマクスウェル流体の弾性的な挙動を定性的に再現できることを示した.

In this study, numerical methods for the basic equations of the Maxwell fluid, which is one of the viscoelastic fluids, were investigated on the two-dimensional collocated grid system by the finite volume method. On the basis of the numerical method proposed by the authors previously, that for the stress terms in the momentum equations were proposed in this study. By the proposed numerical method, the stress terms are calculated with the spatially compact velocity distribution, and it was demonstrated by the numerical experiments that the method can avoid the unphysically oscillated results. Additionally, for the pressure calculation, the C-HSMAC method which controls the divergence of the velocity was applied to the Maxwell fluid and in the numerical experiments it was shown that the method prevented the numerical oscillation of stresses which may happen by using the SMAC method. Furthermore, the proposed method was applied to the numerical experiments in which the elastic character is dominant. As a result of the computations, it was demonstrated that the proposed method and the C-HSMAC method enable to qualitatively predict the elastic behaviors of the Maxwell fluid.