非定常圧縮性流れに対する陰的保存スキームの近似流束ヤコビアンの評価と検証

概要

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A high-order space-accurate scheme of hyperbolic conservation laws usually requires data obtained at five grid points. An implicit version of the scheme constitutes an expensive pentadiagonal system on the left-hand side of the scheme when the scheme is written in ⊿-form of the algorithm. In order to make the left-hand side of the scheme an efficient tridiagonal system, various types of approximation are often applied to flux-Jacobian matrices on the left-hand side of the scheme. In this paper, these approximations are examined and assessed with respect to actually permissible Courant number, shock and contact-discontinuity profiles, and numerical accuracy of the solution using a one-dimensional shock tube problem. The effect of subiteration procedure at each time step, which is introduced in the developed scheme, is also assessed. The results show that implicit schemes with subiteration are favorable in terms of both stability and accuracy of the solution.
一般社団法人日本機械学会の論文
1997-04-25