General view
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Sequential methods for coupled flow-mechanics
The co-conducted process of solid deformation and fluid flow constructs a unified system that deformation and flow can effect each other.
Finite element method and finite volume method are two most popular methods in numerical analysis for solid deformation and fluid dynamics.
In the aspect of fluid dynamics, two different types of partial differential equations (PDEs), elliptic PDE and hyperbolic PDEs, are analyzed. They are both related to conservation laws and imply much of physical substance. One of the bottlenecks in the subject is the existing of discontinous surfaces (fractures), which is so-called fractured porous media.
Many challenges appear when performing the discretization processes of geometry and PDEs, also know as mesh paratition and discretized PDEs. Unstructured grid is a type of conformal grid using to paratition the studied physical domain, while the discreized forms of PDEs are difficult than that in the situation of structured grids.
Sequential methods is efficient for solving the coupled system of elliptic-hyperbolic PDEs. In this case, I developed a solver that can solve elliptic PDE first and then hyperbolic PDE in many iterative steps until satisfied the convergence criterion.
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Solid deformation (elliptic PDE)
The phenomenon related to solid mechanics, especially elasticity and fracture mechanics for solid media, structural stability analysis in practical applications. Numerical analysis and theortical approaches were used in my works, for instance, finite element method, data analysis and complex variable theory, etc.
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Flow problem (elliptic PDE)
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Transport problem (coupled elliptic-hyperbolic PDEs)
In the field of fluid dynamics, I only involve several topics in it, in which my works mainly on computational fluid dynamics (CFD) for fractured porous media, and transport problem, such as two-phase flow. A simulator that solving the coupled systems of hyperbolic-elliptic equations was implemented by C++. The solving strategy is sequential implicit algorithm, where the pressure and saturation can be calculated through enough iterations.