控制体有限元方法中的一种高阶插值格式

HIGH-ORDER INTERPOLATION SCHEME OF CVFEM

针对控制体有限元方法对流动方向不平行于坐标轴方向的回流问题数值模拟采用各种迎风格式都容易产生假扩散的问题，本文给出了一种由插值单元及其迎风相邻单元所确定的高阶插值格式。通过对Ｒｅ＝１０００时三种不同形状的二维四边形空穴流模拟，表明该格式与局部斜迎风格式的适当组合可有效地减小控制体有限元方法对回流问题数值模拟的假扩散。

Even though all upwind schemes of Control-Volume Finite-Element Method (CVFEM) enhance the accuracy for simulation of advection-dominated fluid flows,but lead to severe false diffusion for flows oblique or skew to the axis direction.A high-order polynomial interpolation scheme is proposed,based on the locally skewed upwind scheme and an upwind neighbor element of the interpolated element.The numerical tests of lid-driven cavity flow in three different geometric fields for Re =1000,and with 41×41 uniform grids,proved that the proposed high-order scheme can almost achieve the bench-mark solutions that previous researchers obtained with much more refined grids.