A well-defined grid line-based immersed boundary method is presented for efficient and accurate simulation of unsteady, incompressible flow using non-body conformal, Cartesian grids. Near the fluid–solid interface, the spatial discretization of Navier–Stokes equations is modified to enforce desired boundary conditions in a well-defined manner. Desired modifications can be stably derived using a one-dimensional reconstruction scheme along grid line directions. Eligible grid points and corresponding stencils for reconstruction are determined as grid-IB relationship is described using a grid line-based algorithm. The present method is globally second-order accurate in space and time. For the laminar flow around a circular cylinder, perfect agreement with benchmark numerical studies conducted on body conformal grids is achieved. A strictly linear relationship between the separation bubble length and the Reynolds number within the steady flow regime is reported. Capable of treating a fluid–solid interface with arbitrary geometric complexity, the present method is qualified for efficient simulation of real-world flow problems without necessarily sacrificing accuracy.

提出了一种定义明确的基于网格线的沉浸边界方法，可使用非人体保形笛卡尔网格高效，准确地模拟不稳定，不可压缩的流动。在流体-固体界面附近，对Navier-Stokes方程的空间离散进行了修改，以明确定义的方式实施所需的边界条件。可以使用沿着网格线方向的一维重构方案来稳定地导出期望的修改。确定合格的网格点和用于重建的相应模板，因为使用基于网格线的算法描述了网格IB关系。本方法在空间和时间上是全局二阶精确的。对于圆柱体周围的层流，可以实现与在人体保形网格上进行的基准数值研究的完美一致性。据报道，在稳定流动范围内，分离气泡的长度与雷诺数之间存在严格的线性关系。该方法能够处理任意几何复杂性的流固界面，适用于有效模拟现实世界中的流动问题而不必牺牲精度的情况。