二维折角管道内超声速流动的多重网格计算

本文应用Euler模型和隐式TVD格式计算了二维折角管道内的超声速流动问题,为了有效地模拟激波和膨胀波系的相互干扰及壁面的反射,本文试将多重网格法和TVD格式结合起来进行数值求解。考虑到目前绝大部分文章采用V-循环多重网格法,我们对多重网格法中的几种多层次循环形式(V-循环、W-循环)进行了比较性的数值计算,旨在从中发现合适的多层次循环求解的形式,以期充分发挥多重网格法在Euler方程求解过程中的效益。同时,本文也是对多重网格法和TVD格式结合求解的一次初步尝试。

A MULTIGRID CALCULATION FOR THE TWO-DIMENSIONAL SUPERSONIC FLOW IN AN ANGLE-SHAPED TUBE

A calculation for the two-dimensional supersonic flow in an angle-shaped tube is presented by using the Euler equations and the implicit TVD (Total Variation Diminishing) scheme. A multigrid algorithm is designed to make more effective modeling of the interaction and reflection of shock waves and rarefaction waves on a body surface. The V-cycle multigrid method has been widely used in most available papers. In this paper, the comparisons of numerical solutions by different cycle forms (V-cycle, W-cycle, etc. ) of the multigrid method are given in order to find a suitable cycle form to accelerate the convergence for solver the Euler equations. In addition, the multigrid solution in the TVD scheme is examined here for the first time.