## Discontinuous Galerkin Methods for Phase Transitional Flows

### Organization:

*Funded by: *CSC Fellowship Cina

*PhD: Lulu Tian*

Supervisor: Jaap van der Vegt

*Collaboration*: Hans Kuerten, Bernard Geurts, Yan Xu ; University of Science and Technology of China (USTC)

### Description:

The numerical simulation of phase transitional flows requires an accurate description of the physical phenomena at the interface between the different phases and the capturing of the generally thin interfaces in between the phases for which we will use the diffuse interface method. In addition, the equations governing phase transitional flows frequently have a hyperbolic-elliptic character for which many of the numerical schemes developed for hyperbolic partial differential equations are not suitable.

In this project a new discontinuous Galerkin finite element method will be developed for hyperbolic-elliptic partial differential equations governing phase transitional flows. Due to its local element wise discretization the discontinuous Galerkin method is well suited for local mesh refinement, which will be used to improve the capturing of the phase transition interface in the diffusive interface method.

Publications: