General Prospect of My Research Interests
My research interests lie in developing numerical methods for fluid dynamics. Nonlinear PDEs that govern fluid dynamics arise in many different fields of science and engineering, such as aerodynamics, gas dynamics, magnetohydrodynamics (MHD), laboratory and space plasma physics, radiation hydrodynamics, reactive flows, and geophysical flows. The design of efficient and accurate mathematical approaches for obtaining numerical solutions to such fluid problems is an important endeavor that gives rise to dicult challenges, particularly when those approaches must be designed to exploit modern massively parallel computational resources.
Meeting these challenges is the central concern of my research interests, focusing on developing time-dependent high-order numerical algorithms and methods for simulating a variety of multi-physics fluid problems on large scale parallel, high-performance computing (HPC) architectures.
Scientific Computation on HPC Architectures
My focal research includes conducting applied/computational mathematics research for parallelized, high-order (third-order or higher in both space and time), shock capturing numerical schemes using finite-volume (FV) and finite-difference (FD) adaptive mesh refinement (AMR) algorithms, focusing, in particular, on developing scientific algorithms and codes that are designed to run on future HPC architectures.
Specifically, I am interested in studying the importance of fast convergent, high-order accurate numerical methods and how they are crucial for future high performance exascale computing architectures.
Current Research Topics
Below is the list of several research projects I have been working on. They are all in progress and the websites include ongoing work.
- High-order Schemes using Gaussian Processes for Finite Difference and Finite Volume methods for Computational Fluid Dynamics
- Fourth-order Accurate Piecewise-Cubic Polynomial Methods
- Jacobian-Free Newton-Krylov Implicit Solver
- Slowly-moving Shock
- FLASH: A massively parallel, multi-physics code for computational fluid dynamics in astrophysics