振動翼を過ぎる非粘性流れの数値解析における時間積分法の誤差評価

抄録

The actual time-accuracy of several time integration schemes is investigated for the unsteady compressible Euler equations. Runge-Kutta, implicit-approximate factorization, and implicit iterative schemes have been applied to several unsteady problems of transonic flows over a pitching airfoil. The flux difference splitting scheme of Roe with the MUSCL algorithm is used for determining numerical fluxes. The Runge-Kutta scheme produces little numerical error in its stable limit. However, no advantage of its third-order accurate form over its second-order accurate form can be found. The Beam-Warming scheme with approximate flux Jacobians is essentially first-order accurate in time and is not suitable for unsteady flow simulations. In order to preserve the accuracy of the numerical solutions, higher-order time-accurate forms as well as Newton-type iterations are necessary for the implicit time integration scheme.