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| Biofluid Dynamics | Supersonics & Hypersonics | Compliant Wall Technique | Coal Processing | Forest Fire |
| Course Projects | Publications | Symposiums & Seminars | Useful Links |
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I am developing a numerical method suitable for the simulation of fluid-structure interaction, especially biological fluid dynamics. This method is called the immersed interface method, which is a Cartesinan grid method. It has the same methematical formulation as Peskin's immersed boundary method, namely structures immersed in a fluid being modeled as momentum forcing, and therefore has the robustness and efficiency of Peskin's immersed boundary method. The momentum forcing appears in the singular form of the Dirac delta function in the Navier-Stokes equations. Instead of approxmating the Dirac delta function by discretized smooth functions in Peskin's immersed boundary method, the immersed interface method directly incorporates jump conditions caused by the singular forcing into numerical schemes. By doing so, it can achieve higher order accuracy locally and better mass conservation enclosed by a no-penetration boundary. Also, the sharpness of an interface does not depend on grid resolutions.
The applicability of the immersed interface method depends on whether the necessary jump conditions are known. Recently, I derived the jump conditions of all first-, second- and third-order spatial derivatives of the velocity and the pressrue as well as first- and second-order temporal derivatives of the velocity for the 3D incompressible Navier-Stokes equations subject to singular force. Please refer to my manuscript submitted to "SIAM Journal of Scientific Computing" for the derivation. Using these jump conditions, the immersed interface method can be applied to the simulation of 3D incompressible viscous flows with local first- or second-order spatial and temporal discretization accuracy.
I have implemented the immersed interface method to simulate 2D flows with immersed boundaries moved and deformed by driving force or prescribed with known motion. Taylor-Couette flow, flow induced by a relaxing balloon, flow past single and multiple cylinders, and flow around a hovering flapping wing are sucessfully simulated by the method. Please refer to my manuscript submitted to "Journal of Computatinal Physics" for the simulations. The simulation results demonstrated that: (1) second-order accuracy in the infinity norm for both the velocity and the pressure has been achieved; (2) computational cost is dominated by the pressure Poisson solver and the addition of an object boundary introduces relatively insignificant cost.
Right now, I am developing a 3D code. A broad range of biofluid dynamics problems can be simulated using the 2D and 3D codes, including insect flight, aquatic animal locomotion, and bacteria swimming.
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This was a one-year post-doctoral research from July 2002 to June 2003 with
Professor Pino Martin at Mechanical and Aerospace Engineering Department of Princeton
University.
Shock/turbulent-boundary-layer interaction and chemistry/turbulent-boundary-layer
interaction were targeted for investigation through numerical simulation.
The simulation code uses a third-order WENO scheme for the convective flux,
a fourth-order central finite difference for viscous flux and a third-order data-parallel
lower-upper (DPLU) relaxation method for the unsteady terms.
The code was parallelized with MPI.
Linear stability analysis of compressible boundary layers was carried out
for code validation.
Genuine periodic boundary conditions toward temporal simulation were analyzed
theoretically, and they were assessed by extended temporal simulation with forcing.
A rescaling inflow method was proposed for spatial simulation of supersonic
flows over complex geometries.
Grids for complex geometries were analytically mapped to Cartesian grids
to be clustered near walls and corners.
Non-reflecting boundary conditions were formulated in curvilinear coordinates
and then implemented in conjunction with a buffer domain technique.
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This was my Ph.D. research under the supervision of Professor John Lumley at
Mechanical and Aerospace Engineering Department of Cornell University.
Turbulent channel flow in the presence of a compliant wall was simulated
numerically.
The compliant wall was modeled as a spring-supported plate.
An immersed boundary method implemented in a spectral-like compact finite
difference scheme was tried and then given up.
A time-dependent coordinate transformation was used to eliminate the
compliant wall deformation in the computational domain.
The generalized NS equations were solved using the spectral method.
The code was validated by reproducing results of the linear stability
theory for compliant channels.
The data were analyzed through statistical tools, flow visualization and
POD.
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| This was my M.E. research at Thinghua University. A synthetic model was established for coal devolatilization and gasification moving-beds heated by cycling ash from fluidized-beds in a heat-electricity-gas plant. The model predicts gas production rate, gas component content and interior conditions of the moving-beds. |
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| This was my B.S. research at the University of Science and Technology of China. Thermal buoyant flow in cross-wind was simulated numerically to mimic a special case in a forest fire. The code uses SIMPLE algorithm and $\kappa-\epsilon$ turbulence model. The inlet boundary conditions were related to the fire field combustion. |
| A synthetic model to predict moisture content of forest surface coverage was summarized. The model considers factors such as coverage constitution, topology, environment and weather. It is quasi-empirical. |
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| Numerical Simulation of Coupled Convection and Conduction in a Partly-Filled Pipe |
| Numerical Experiments of 2D Incompressible Inviscid Flow |
| Numerical Simulation of Propagation of a 1D Premixed Flame |
| Numerical Simulation of Combustion of Sprayed Oil in Air |
| Optimization of Series-connected Heat Exchangers |
| Optimization of a Coal Gasification Model |
| Optimization of Portfolio Selection with LP and QP |
| Training of a Neural Network for Coal Gasification Process |
| System Design of Forest-Fire-Behavior Software |
| Design of Software Little-Paint with C++ |
| Implementation of a Binary Priority Queue with Java |
| Implementation of a Suffix Tree with Java |
| Implementation of an Octal Tree for 3D Data Interpolation |
| Technical Improvement Proposal for a Chain Boiler |
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