Numerical simulation of drop formation in micro-channels via VOF/level set methods and immersed boundary methods

Program Code: 

Dr Jong-Leng Liow (

Description of Work: 


Develop immersed boundary methods and VOF/Level set methods for the numerical simulation of multiphase fluid flows in micro-channels.

The use of numerical simulation is a convenient means of understanding the twophase flow in a micro-device. The flow of two or more phases requires the accurate tracking of the fluid interfaces as surface tension is an important physical parameter. Discretisation of the surface tension term often gives rise to parasitic currents or error that can grow with time and distort the results. Currently, the use of the volume of fluid method is a well-known technique for modelling two phase flow problems. An equally promising approach is that of the level set method. It is proposed that it is possible to merge the better attributes of both techniques to bring about a more accurate method for multi-phase flow simulation.

The use of a structured grid for modelling provides efficiency over an unstructured grid. However, there are drawbacks. The structure grid has many unused cells when modelling a micro-device resulting in wastage of memory and calculations on cells with no fluid. The use of a structured grid also gives rise to difficulties in correctly modelling geometries that are not rectangular but curved. Recent work has been done on using the immersed boundary method and extending it to 3-D problems for VOF based codes, using higher order discretisation (pseudo spectral accuracy) and improving the speed and robustness of the solution of the algebraic equations through the use of preconditioning and Krylov methods. Recent advances in the tracking of the liquid-liquid and gas-liquid interface include high order interface reconstruction (Liovic et al. 2006) has not been incorporated into current CFD packages and significant smearing of the interface limits the accuracy of the results. The project will look at building on earlier work in 2D and 3D multi-phase codes for micro-fluidics simulation and incorporating the newer ideas as outlined. The effect of surface tension on the accuracy of the code as well as the 3 phase contact line will be looked at to improve the code for multiple fluid interfaces.

Description of Work:

  • Continue development of a volume of fluid code for multiphase simulation incorporating the immersed boundary method to handle irregular boundaries.
  • Improve the current preconditioned generalized residual method (which is a member of the Krylov subspace method) to provide better stability when solving the algebraic equations with the immersed boundary method coded.
  • Applying the code to study drop and bubble formation in micro-channels where the code is validated through results from experimental work being carried out in the supervisor’s research group.


The prospective student(s) is expected to be able to program in Fortran as this requires the writing of computational fluid dynamics code. An understanding of numerical methods in the solution of the equations of fluid flow will be an asset.