A sharp interface immersed boundary method for moving geometries with mass conservation and smooth pressure variation

Abstract

Improper mass conservation and spurious pressure fluctuations are considered as two serious limitations of the immersed boundary method (IBM) for modeling flow over moving/deformable bodies. Earlier attempts to overcome these issues were usually mathematically involved and computationally expensive. In one of our recent work (Kumar M, Roy S, Ali MS. An efficient immersed boundary algorithm for simulation of flows in curved and moving geometries. Comput Fluids 2016; 129: 159–178.), a simple and robust methodology is demonstrated for the sharp interface immersed boundary method which imposes proper boundary conditions for pressure and velocity in the cells intercepted by the solid boundary. In the present paper the mass conservation and pressure fluctuations of the proposed scheme are investigated in detail and the results are presented. The proposed methodology is shown not to add any computational overhead for both fixed and moving boundary problems. An overall second order accuracy is maintained in the discretization and the interpolation schemes. Validation and verification studies have been presented. The achieved results show a second order accurate mass conservation and also exhibit smooth behavior of pressure near the moving surfaces. Species concentration equation is solved to quantify the accuracy in mixing calculations. The present IBM scheme is also used to predict the terminal velocity of objects falling in a quiescent fluid medium under the actions of gravity.