Research Field (Topics & Description)

Topics: Compressible Stokes, Navier-Stokes equations; convection, convection-diffusion equations:
               existence, regularity, corner singularity expansions, stress intensity factors, etc.
               Numerical Analysis: Finite Element Methods: stability, error estimates,
               Adaptive Mesh Refinement Technique: a posteriori error estimate, local error indicator.

Description: In fluid mechanics, flows separations, internal recirculations and discontinuities are technologically and mathematically important issues to be resolved. Such phenomena are often generated by sharp corners and edges of body contours of flow regions like diriven cavities. Most problems in aerodynamics or hydrodynamics do not show precise resolutions or required solutions due to their complexities. Therefore it is very important to identify and resolve precise informations of fluid flows near singular boundaries.
    My research lies in studying the singular behaviors and the regularities for the solutions of the compressible viscous Navier-Stokes system(CNSS) on domains with corners and showing the stability and convergence (error estimate) of the corresponding discrete problems by suitable weak formulation and simulating the numerical solutions by designing the FEM code.