In a broad sense, my research includes the development of mathematical models (usually in the form of partial differential equations) for complex physical processes, the design of numerical algorithms to solve these equations, and the exploration of underlying physics by analyzing the numerical results. The ultimate goal is to understand our physical world.
Currently, my research includes the following three physical problems: the moving contact line problem where a fluid wets a solid surface, interfacial flows of viscoelatic fluids, and icing.
To track the moving boundaries, such as the deformable fluid-fluid interface and the rigid fluid-particle interface, I have used the arbitrary Lagrangian-Eulerian, level-set, and phase-field methods.
To solve the partial differential equations, I have used the finite difference, finite volume, finite element (including the discontinuous Galerkin), and spectral methods, depending on the nature of the problems.
Of course, programming is required to develop computer codes to compute the numerical results. I use FORTRAN, MATLAB, C, and C++.