时间推进积分方程法求解非定常跨声速流动

本文提出了一种求解非定常跨声速流动的新方法——时间推进积分方程法,此法克服了时间线化积分方程法的限制,能较好地模拟激波的运动。本文首先用一维波(?)问题——模型问题阐明此法的基本思想,然后将它应用于二维非定常跨声速流动中。本文还首次引入拟速度位的概念,使时间推进积分方程式得到简化,尾涡条件和Kutta条件更易处理。数值计算表明时间推进积分方程法是合理可靠的。

TIME MARCHING INTEGRAL EQUATION METHOD FOR THE SOLUTIONS OF UNSTEADY TRANSONIC FLOWS

Time marching integral equation method(TMIEM) has been developed here which eliminates the limitation of the time-linearized integral equation method in that the latter method can not satisfactorily simulate the shock wave motion and which keeps the advantages of the fast convergence and less computer CPU time of the steady integral equation method and the time-linearized integral equation method. The fundamental ideas of TMIEM are discussed at first by dealing with a model problem-initial and boundary value problem of one-dimensional wave equation Then the method is implemented for two-dimensional unsteady transonic flows. To make the trailing vortex condition easy to treat and simplify the time marching integral equation, a quasi-velocity-potential has been first introduced here.Some typical flows over airfoils have been calculated using TMIEM to justify the new method and the calculated results are compared with other numerical results and experimental data. The three types of shock wave motion observed by Tijdeman and Seebass by experiment have been calculated successfully using TMIEM , which is a good verification for TMIEM. The preliminary numerical calculations show that the time marching integral equation method can satisfactorily solve the problems of the shock wave motion since it eliminates the limitation of the time-linearized integral equation method and is a reasonable and reliable me'thod for unsteady transonic flows.