中文摘要：

分析了用基于Lagrange乘子的虚拟区域法数值求解时，翼型后缘存在的奇异问题。为了保持直角坐标网格结构简单及可利用快速算法的特点，提出引入虚拟边界条件控制虚拟流动的方法处理奇异问题。用虚拟区域法数值模拟了翼型不可压对称绕流；并把该方法推广应用到管壁流动的数值模拟，给出了喷管内流场的算例。数值结果表明，虚拟边界条件的引入有助于控制Lagrange乘子的变化，从而改善数值模拟的精度。

英文摘要：

Singularities near the corner of bodies like the trailing edge of an airfoil by the fictitious domain method with Lagrange multipliers are analyzed. Fictitious boundary conditions for controlling fictitious flows inside the body are introduced to deal with singularities and allow the use of fairly structured meshes, and therefore the use of fast solvers. Numerical results of fictitious domain method for solution of incompressible inviscid flows around a symmetric airfoil in a decomposed domain are obtained. A new example of flows in a nozzle is presented. Numerical simulations show that the use of fictitious boundary conditions in the decomposed domain is effective for controlling the magnitude of Lagrange multipliers.