A well-defined grid line-based immersed boundary method for efficient and accurate simulations of incompressible flow

• Published in: Computers & mathematics with applications (1987) Vol. 89; pp. 99 - 115
• Main Authors: Su, Guanting, Pan, Tianyu, Zheng, Mengzong, Li, Qiushi
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.05.2021; Elsevier BV
• Subjects: Algorithms; Boundary conditions; Cartesian coordinates; Circular cylinders; Computational fluid dynamics; Cylinder flow; Direct forcing; Fluid flow; Grid line-based; Immersed boundary method; Incompressible flow; Laminar flow; Reconstruction; Reynolds number; Separation bubble length; Simulation; Steady flow; Surface force; Surface force; Cylinder flow; Grid line-based; Immersed boundary method; Separation bubble length; Direct forcing
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2021.02.013

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.