Practical
Applications

Reservoir Simulation
Reservoir simulation is the art of combining physics, mathematics, reservoir engineering, and computer programming to develop a tool for predicting hydrocarbon reservoir performance via various operating strategies. It is an important decisionmaking tool. For example, engineers use it to obtain information pertaining to the processes that take place in oil reservoirs. Such information enables an analysis of the various recovery strategies in order to effect optimal oil recovery. The crucial part of reservoir simulations is to solve largescale discretized PDEs (highly coupled, nonsymmetric, and indefinite) over and over again. However, this is also the most timeconsuming process of any modern petroleum reservoir simulator (more than 75%). The complexity of the geometry and of the physical model, heterogeneity, and size of reservoir model are continuing to grow, which makes these linear systems more difficult to solve using standard direct or iterative solvers. 
A typical reservoir.

The FASP method takes full
advantage of the underlying physical and analytic properties of the
mathematical model.


SPE 10
Benchmark
Two phases (water and oil): 1.1
million cells, 5 wells.

Reference: X. Hu, W. Liu, G. Qin, J.
Xu, Y. Yan, and C. Zhang (2011);
X. Hu, J. Xu, and C.
Zhang (2013) 

Fluid Structure Interaction
Fluidstructure interaction (FSI) aims at understanding the
interaction between moving structure and fluid and how their
interaction affects the interface between them. FSI has a wide
range of applications in many areas including hemodynamics and
wind/hydro turbines simulation. FSI problems are
computationally challenging. The computational domain of FSI
consists of fluid and structure subdomains. The position of the
interface between fluid domain and structure domain is time
dependent. Therefore, the shape of the fluid domain is one of
the unknowns, increasing the nonlinearity of the FSI problems.

Examples of fuel cells: (left)
cardiac simulation; (right) 2D Turek benchmark

Numerical solutions of FSI are roughly classified into
partitioned approaches and monolithic approaches. Partitioned
approaches employ singlephysics solvers to solve the fluid
and structure problems separately and then couple them by the
interface conditions. Monolithic approaches solve the fluid
and structure problems simultaneously. Monolithic approaches
are considered more stable, although it is accompanied with
larger linear systems and higher computational cost.


Turek FluidStructure Interaction Benchmark

References: J. Xu and K. Yang (2014) 
Hydroelectric generator simulation involves the moving fluid
domain, which is due to the rotation and deformation of the
blade of the generator. Therefore, efficient monolithic
solver for the couple system is difficult to construct.
In order to simulation fluid coupled with rotating structures,
like hydroturbine in hydroelectric generators, we develop a
new ALE method to update the fluid mesh so that it can handle
arbitrary rotation.


Moving mesh for real hydroelectric generator

Artificial heart is a kind of effective treatment for heart
failure, which is the finial battlefield of cardiovascular
disease. The artificial heart significantly changes the
hemodynamics of the aorta. The main difficulty of artificial
heart simulation is the complex interaction between blood, aorta
and artificial heart.

Artificial heart in vessel


Hemodynamics near the artificial heart

References:
Q. Zhang, B. Gao, K. Gu, Y. Chang, J. Xu and P. Deuflhard (2014)


Magnetohydrodynamics
The magnetohydrodynamics (MHD) model describes the dynamics of charged fluids in the presence of electromagnetic fields. A principle application of MHD is the modeling of plasma physics, ranging from plasma confinement for thermonuclear fusion to astrophysical plasma dynamics. MHD is also used to model the flow of liquid metals, for example, in magnetic pumps, liquid metal blankets in fusion reactor concepts, and aluminum electrolysis. 
Tokamak



Liddriven cavity, Re=400, Rm=400: (left) stream line of the
velocity; (right) distribution of the total magnetic field
Liddriven cavity, Re=400, Rm=400: number of iterations

Reference: K. Hu, Y. Ma, and J.
Xu (2015); K. Hu, X. Hu,
Y. Ma, and J. Xu (2015)


Energy Storage
Lithiumion batteries are rechargeable,
and they are characterized by lithium ions that move from the negative
electrode to the positive electrode during discharge and then back
again during charging.


References: J.
Wu, V. Srinivasan, X, and CY, Wang (2002); J. Wu, J. Xu, and H. Zou (2006). 
A fuel cell is a device that converts a
fuel’s chemical energy from a fuel into electricity through a chemical
reaction with oxygen or another oxidizing agent. Hydrogen is the most
commonly used fuel for this purpose, but hydrocarbons such as natural
gas and alcohols like methanol are sometimes used.

Examples of fuel cells.



Fast convergence
within 21 iterations versus oscillatory/nonconvergent iterations using
commercial CFD software.

References:
P.Sun,
G. Xue, CY. Wang, and Xu (2008); P.Sun,
G. Xue, CY. Wang, and Xu (2009); P.Sun,
CY. Wang, and Xu (2010). 

Subsurface Flow Simulation
Subsurface flow, in hydrology, is the flow of water beneath the earth’s surface that constitutes part of the water cycle. 

Reference:
J. Cheng, X.
Huang, S. Shu, J. Xu, C. Zhang, S. Zhang, and Z. Zhou
(2013) 