報告書番号

N05013

タイトル（和文）

非定常乱流解析コードSMART-femの実用性向上（その１） -行列解法の高速化と時間積分の安定化-

タイトル（英文）

Practicality improvement of an unsteady turbulent flow analysis code SMART-fem Part 1: Introduction of fast matrix-solvers and stabilization of time-integration

概要 （図表や脚注は「報告書全文」に掲載しております）

当所で開発したLES乱流解析コードSMART-femに最新の行列解法技法ならびに時間積分法を導入し、実用性を大きく向上させた。ポアソン方程式に起因する行列方程式の解法として従来は要素行列に基づく共役勾配法(CG)を用いていたが、本研究では全体行列に基づくCG法に改修した。この改修により従来法に比べてCPU時間を1/7程度に減少させることができた。さらに、最新の行列解法である代数的マルチグリッド法 (市販ソフト：SMS-AMG, SAMG) をSMART-femに導入し、従来法に比べて２桁程度の高速化を可能とした。また、SMART-femでは非圧縮性条件に補正を加えて圧力振動を抑制しているが、その副作用として長時間の時間積分で誤差が蓄積し、数値不安定が発生する場合がある。これを安定化させるために Almgrenらが提唱する方法（安定化近似投影法）を導入し、その有効性を数値実験で確認した。

概要 （英文）

The practicability of a large-eddy simulation (LES) code, SMART-fem, has been enhanced by introduction of both up-to-date fast matrix solvers and a robust time integration strategy. As for the matrix solvers, it has turned out that a global-matrix based conjugate gradient (CG) method outperforms an element-matrix based CG method, implemented in the original version of SMART-fem, reducing the CPU time by a factor of 6 to 7. Furthermore, it has been also shown that use of algebraic multi-grid solvers (SMS-AMG, SAMG) for the global-matrix equations enables us to drastically reduce the computational costs, approximately by two orders of magnitude in comparison with the original version of SMART-fem. Because the low-order element employed in SMART-fem tends to invoke spatial pressure instability, the global pressure jump term is added into the incompressibility constraint in the SMART-fem to suppress it. As the side-effect, however, the acceleration tends to deviate from the divergence-free condition, possibly leading to numerical blow-up during long time integration. The present numerical experiments have indicated that use of a new type of approximate projection method advocated by Almgren (SIAM Journal on Scientific Computing, 22, pp.1139-1159, 2000) is very effective to eliminate such an accumulation of numerical errors during a long time integration. The introduction of the algebraic multi-grid method as a matrix-solver and a new approximate projection method as a time-integrator has significantly improved the practical aspect of the SMART-fem code in simulating a large-scale turbulent flow.

報告者

キーワード