Research Agenda
Multiphase flow occurs in many natural and engineering settings and daily life. Kinematics and dynamics of the fluids flow are much difficult to study compare to the ones of single phase case. Simulation in general multiphase flow setting requires independent solution of each phase as well as simultaneous consideration of interfacial solution. Furthermore phase transition makes picture even complicated.
My research concerns theoretical and its computational validation for fluids mixing and interfacial instabilities. There are there are 3 widely studied subjects in fluid instabilities: 1) shock wave driven Richtmeyer-Meshkov instability, 2) constant force driven Rayleigh-Taylor Instability 3) temperature gradient driven Kelvin-Helmholz instability. All the topics have show its face in many real world application, for instances, fusion, supernova, nuclear reaction, global atmosphere movement etc. My research can find its applications in Richtmeyer-Meshkov instability or more favorably in Rayleigh-Taylor instability.
I investigated two-phase flow setting from a Theory of Averaged Equations point of view but not from micro scale continuum fluid mechanics point of view. In other words, rather than point-wise solution of fluid dynamics, I researched macroscopic behavior of two-phase fluids motion, like, mixing length growth rate, center of mixing region dynamics etc.
I am interested in modeling of physical process in random field (RF) setting. Namely Modeling of Randomness in Continuum Mechanics. Here I need to clarify a few things before I proceed. The principle of Quantum Physics, Natural process is inherently random, does not contain set of my research topics. My research is standing on the ground of continuum fluid mechanics which assume to have pretty regular solution. My basics assumption for modeling of randomness is lack of knowledge or uncertainty from lack of information. In other words I effort to obtain, so to say, macro-macro solution in probabilistic sense. Hence my solution stands on top of statistical aggregates. There are many application that we cannot predict its solution in deterministic fashion, porous media flow is one of the famous engineering problems in this category. Fluid through porous formation has applications in groundwater hydrology, environmental remediation, and problems of petroleum engineering and many other areas. I analyzed tracer flow, miscible identical two-phase flow, through random porous media using stochastic method for curved geometries as well as a planar case.
I also worked on groundwater simulator. It is a full two-phase, water as a wetting phase and air as a non-wetting phase, simulation with capillary effect considered. A fully coupled air and water underground flow model was developed under IPARS framework. IPARS (Integrared Accurate Parallel Reservoir Simulator) is a underground flow simulation framework developed by researchers at TICAM (Texas Institute of Computational and Applied Mathematics), University of Texas at Austin.
As is mentioned in previous paragraph, many physical systems require mathematical description of partial differential equation (PDE) with coefficients or terms of random field. Scientists often call it stochastic differential equations. If only one term or coefficient in PDE is random , the solution of the system must be random. Therefore the mathematical system doesn't give us any deterministic answer to our question. However we can deduce probable solution under probability law with given statistics of random fields. Through modeling we could obtain answer meaningful only in statistical sense but essential information for a specific case of the problems.
My primary work in this area was applying the Interior-Point method to flash calculation of reservoir simulation. By flash calculation, one wants to find phase equilibrium in multiphase fluids setting. Multiphase flow and phase change can make Newtonian iteration to this nonlinear algebraic system hard to solve and often fail due to bad initial guess and unknown number of phases at certain flow simulation stage.
For inequality constraint optimization problems, there are two widely adapted methods: (1) SQP, (2) Interior-Point. Because of the unpredictable nonlinearity of the equality and inequality constraints, nonlinear interior-point methods are more suitable than SQP algorithm. I applied Newton-Damped Nonlinear Interior-Point algorithm for Gas-Oil-Water three phase flow system.
One of the unique characteristics of flow through porous media is the scale- effect: fluid transport and mixing depends on the history of fluid flow. Non-local dispersion is the key factor which describe this phenomenon. I designed a numerical scheme, mixed finite elements method in the lowest order Raviar-Thoma spave, that is, finite volume methods for an parabolic type integro-differential equation in one dimesional case. I have done convergence study in the context of Lax-Richtnyer Theory. I showed that the scheme is stable, the integro-differential equation has parabolic and hyperbolic nature depends on the kernel operator.