Articles written in Sadhana
Volume 31 Issue 6 December 2006 pp 697-707
In this paper we present a level set-based algorithm for the solution of incompressible two-phase flow problems. The technique is applied to the numerical simulation of impact of two surge fronts resulting from the collapse of liquid columns. The incompressible Navier-Stokes equations are solved using a projection method based on forward Euler time-stepping. The Hamilton-Jacobi type equation for the transport of level set function is carried out by a high resolution fifth-order accurate WENO scheme. For efficient implementation of the WENO scheme we have proposed grid staggering for the level set function. The solution of the pressure Poisson equation is obtained using an efficient preconditioned conjugate gradient method. It is shown that the present formulation works very well for large density and viscosity ratios. For the purpose of validation, we have simulated small-amplitude free sloshing of liquid in a container and the well-known two-dimensional broken-dam problem of Martin and Moyce. Simulations of impact of surge fronts have been carried out and the results are discussed.
Volume 34 Issue 2 April 2009 pp 271-298
In this paper, we discuss the results of a series of tests carried out to assess the level set methodology for capturing interfaces between two immiscible ﬂuids. The tests are designed to investigate the accuracy of convection process, the preservation of interface shape, and the mass conservation properties of individual ﬂuids. These test cases involve the advection of interfaces of different shapes exposed to translation, rotation, deformation, and shear ﬂow. Prescribed solenoidal velocity ﬁelds are used and no attempt is made to couple the advection of the level set function with the momentum equations. For the solution of level set equation we have employed ﬁrst-order upwind scheme, MacCormack method, second-order ENO scheme, and ﬁfth-order WENO scheme. Our studies show that the level set method perform well when higher-order schemes are used for the solution of advection equation. However, for certain type of shearing and vortical velocity ﬁelds mass conservation is an issue on coarser meshes even with higher order schemes. Finer mesh must be used in such situations to reduce numerical diffusion.