A sharp interface cartesian grid method for simulating flows with complex moving boundaries

A Cartesian grid method for computing flows with complex immersed, moving b oundaries is presented. The flow is computed on a fixed Cartesian mesh and the solid boundaries are allowed to move freely through the mesh. A mixed E ulerian-Lagrangian framework is employed, which allows us to treat the imme rsed moving boundary as a sharp interface. The incompressible Navier-Stokes equations are discretized using a second-order-accurate finite-volume tech nique, and a second-order-accurate fractional-step scheme is employed for t ime advancement. The fractional-step method and associated boundary conditi ons are formulated in a manner that property accounts for the boundary moti on. A unique problem with sharp inter-face methods is the temporal discreti zation of what are termed "freshly cleared" cells, i.e., cells that are ins ide the solid at one time step and emerge into the fluid at the next time s tep. A simple and consistent remedy for this problem is also presented. The solution of the pressure Poisson equation is usually the most time-consumi ng step in a fractional step scheme and this is even more so for moving bou ndary problems where the flow domain changes constantly. A multigrid method is presented and is shown to accelerate the convergence significantly even in the presence of complex immersed boundaries. The methodology is validat ed by comparing it with experimental data on two cases: (1) the flow in a c hannel with a moving indentation on one wall and (2) vortex shedding from a cylinder oscillating in a uniform free-stream. Finally, the application of the current method to a more complicated moving boundary situation is also demonstrated by computing the flow inside a diaphragm-driven micropump wit h moving valves. (C) 2001 Elsevier Science.