A well-defined grid line-based immersed boundary method for efficient and accurate simulations of incompressible flow - Su, Guanting; Pan, Tianyu; Zheng, Mengzong; Li, Qiushi (Computers & mathematics with applications (1987), 2021)
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. •The forcing term is introduced as a second-order tensor.•The grid line-based method is well-defined in two and three dimensions.•A grid line-based algorithm for grid-IB relationship description is presented.•Steady separation bubble length varies with Re in a strictly linear manner.•Perfect agreement with studies that use body conformal grids is obtained.