Xiaoming He

Xiaoming He
Missouri University of Science and Technology | Missouri S&T · Department of Mathematics

PhD

About

133
Publications
18,073
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
3,294
Citations
Additional affiliations
May 2009 - August 2010
Florida State University
Position
  • PostDoc Position
August 2010 - present
Missouri University of Science and Technology
Position
  • Professor (Assistant)

Publications

Publications (133)
Article
Full-text available
This paper focuses on the unconditionally optimal error estimates of a fully discrete decoupled scheme for two-phase magnetohydrodynamic (MHD) model with different viscosities and electric conductivities, by using the zero-energy-contribution (ZEC) method for the temporal discretization and mixed finite elements for the spatial discretization. Base...
Data
We visualized and quantified the nanogel particle transport in porous media in a 3D glass porous media. The video shows the particles (red) flow through the glass (black) packed micromodel.
Article
Understanding the transport and retention of elastic nanogel and microgel particles in porous media has been a significant research subject for decades, essential to the application of enhanced oil recovery (EOR). However, a lack of dynamic adsorption and desorption studies, in which the kinetics in porous media are seldom investigated, hinders the...
Article
In this paper, we propose and analyze a finite-element method of variational data assimilation for a second-order parabolic interface equation on a two-dimensional bounded domain. The Tikhonov regularization plays a key role in translating the data assimilation problem into an optimization problem. Then the existence, uniqueness and stability are a...
Article
Accurately solving the anisotropic interface problem is one of the difficulties in aerospace plasma applications. Based on cubic Cartesian meshes, this paper develops a trilinear nonhomogeneous immersed finite element (IFE) method for solving the complex anisotropic 3D elliptic interface model with nonhomogeneous flux jump. Compared with the existi...
Article
Full-text available
In this paper, we first propose and analyze a steady state Dual-Porosity-Navier–Stokes model, which describes both Dual-Porosity flow and free flow (governed by Navier–Stokes equation) coupled through four interface conditions, including the Beavers–Joseph interface condition. Then we propose a domain decomposition method for efficiently solving su...
Article
This paper presents fully kinetic particle simulations of plasma charging at lunar craters with the presence of lunar lander modules using the recently developed Parallel Immersed-Finite-Element Particle-in-Cell (PIFE-PIC) code. The computation model explicitly includes the lunar regolith layer on top of the lunar bedrock, taking into account the r...
Article
Full-text available
In this article, we consider a phase field model with different densities and viscosities for the coupled two-phase porous media flow and two-phase free flow, as well as the corresponding numerical simulation. This model consists of three parts: a Cahn-Hilliard-Darcy system with different densities/viscosities describing the porous media flow in ma...
Article
Full-text available
In this paper, we develop and analyze a finite element projection method for magnetohydrodynamics equations in Lipschitz domain. A fully discrete scheme based on Euler semi‐implicit method is proposed, in which continuous elements are used to approximate the Navier–Stokes equations and H(curl) conforming Nédélec edge elements are used to approximat...
Article
In this article, we first establish a new flow-coupled binary phase-field crystal model and prove its energy law. Then by using some newly introduced variables, we reformulate this three-phase model into an equivalent form, which makes it possible to construct a fully discrete linearized decoupling scheme with unconditional energy stability and sec...
Article
In this work, a decoupled and iterative finite element method is developed and analyzed for steady-state generalized Boussinesq equations, in which both the viscosity and thermal conductivity depend on the temperature. By utilizing the solutions obtained in the previous iteration step, the coupled system is reduced to Navier-Stokes equations with t...
Article
Weak scaling performance of a recently developed fully kinetic, 3-D parallel immersed-finite-element particle-in-cell framework, namely PIFE-PIC, was investigated. A nominal 1-D plasma charging problem, the lunar photoelectron sheath at a low Sun elevation angle, was chosen to validate PIFE-PIC against recently derived semi-analytic solutions of a...
Article
In this article, we develop and analyze a novel fully discrete decoupled finite element method to solve a flow-coupled ternary phase-field model for the system consisting of three immiscible fluid components. Based on the L2-gradient flow approach, the conserved Allen–Cahn type dynamics is used to describe the free interface motion, where multiple...
Article
In this article we consider the numerical modeling and simulation via the phase field approach for coupled two-phase free flow and two-phase porous media flow of different densities and viscosities. The model consists of the Cahn-Hilliard-Navier-Stokes equations in the free flow region and the Cahn-Hilliard-Darcy equations in porous media that are...
Article
Full-text available
A multigrid multilevel Monte Carlo (MGMLMC) method is developed for the stochastic Stokes–Darcy interface model with random hydraulic conductivity both in the porous media domain and on the interface. Three interface conditions with randomness are considered on the interface between Stokes and Darcy equations, especially the Beavers–Joesph interfac...
Conference Paper
View Video Presentation: https://doi.org/10.2514/6.2022-1988.vid This paper presents a kinetic particle simulation study of the plasma charging and dust transport near the uneven lunar surface terrain. A fully-kinetic 3-D finite-difference (FD) particle-in-cell (PIC) code is utilized to simulate the plasma interaction with uneven surface terrain. T...
Article
In this article, we present a time-dependent dual-porosity–Navier–Stokes model with four interface conditions, including Beavers–Joseph interface condition, to describe a coupling system of complex porous media and conduit networks. This system has many applications, such as the flow simulation problems for a multistage fractured horizontal wellbor...
Preprint
Full-text available
In this article we consider the numerical modeling and simulation via the phase field approach of two-phase flows of different densities and viscosities in superposed fluid and porous layers. The model consists of the Cahn-Hilliard-Navier-Stokes equations in the free flow region and the Cahn-Hilliard-Darcy equations in porous media that are coupled...
Article
The phase-field method has been widely used to study the rapid solidification processes such as additive manufacturing. To lower the computational cost, many simplifications and modifications were made to the original set of phase-field equations for alloy solidification. However, how those simplifications affect the modeling outcome is not well st...
Article
For highly coupled nonlinear incompressible magnetohydrodynamic (MHD) system, a well-known numerical challenge is how to establish an unconditionally energy stable linearized numerical scheme which also has a fully decoupled structure and second-order time accuracy. This paper simultaneously reaches all of these requirements for the first time by d...
Article
This article presents the derivation of semianalytic solutions to a new 1-D photoelectron sheath model near the lunar surface. The plasma species include the cold solar wind protons, drifting Maxwellian solar wind electrons, and Maxwellian photoelectrons emitted from the surface. The semianalytic model is then numerically solved to obtain profiles...
Article
Full-text available
In this paper, we establish the fully decoupled numerical methods by utilizing scalar auxiliary variable approach for solving Cahn–Hilliard–Darcy system. We exploit the operator splitting technique to decouple the coupled system and Galerkin finite element method in space to construct the fully discrete formulation. The developed numerical methods...
Article
MSC: 35K61 76T99 76S05 76D07 Keywords: Navier-Stokes Cahn-Hilliard Darcy Diffuse interface model Well-posedness Superposed free flow and porous media a b s t r a c t We study a diffuse interface model for two-phase flows of similar densities in superposed free flow and porous media. The model consists of the Navier-Stokes-Cahn-Hilliard system in fr...
Article
In this paper, we demonstrate the convergence analysis of Robin-Robin domain decomposition method with finite element discretization for Stokes-Darcy system with Beavers-Joseph interface condition, with particular attention is paid to the case which is convergent for small viscosity and hydraulic conductivity in practice. Based on the techniques of...
Article
This paper presents an adaptive Kriging based method to perform uncertainty quantification (UQ) of the photoelectron sheath and dust levitation on the lunar surface. The objective of this study is to identify the upper and lower bounds of the electric potential and that of dust levitation height, given the intervals of model parameters in the 1-D p...
Conference Paper
This paper presents a modeling and simulation study of the photoelectron sheath near uneven lunar surface. A fully kinetic 3-D finite-difference (FD) particle-in-cell (PIC) code is utilized to simulate the plasma interaction with local uneven surface terrain on the lunar surface in 2-D photoelectron sheaths. The code is first validated using a 1-D...
Article
Full-text available
We consider in this paper numerical approximations of a phase field model for twophase ferrofluids, which consists of the Navier-Stokes equations, the Cahn-Hilliard equation, the magnetostatic equations, and the magnetic field equation. By combining the projection method for the Navier-Stokes equations and some subtle implicit-explicit treatments f...
Article
In this paper, we develop a sparse grid stochastic collocation method to improve the computational efficiency in handling the steady Stokes-Darcy model with random hydraulic conductivity. To represent the random hydraulic conductivity, the truncated Karhunen-Loève expansion is used. For the discrete form in probability space, we adopt the stochasti...
Article
In order to simulate the Kaufman-type discharge problems, a fully decoupled iterative method with anisotropic immersed finite elements on Cartesian meshes is proposed, especially for a three-dimensional (3D) non-axisymmetric anisotropic hybrid model which is more difficult than the axisymmetric or isotropic models. The classical hybrid model, which...
Article
The advantages of the barycentric rational interpolation (BRI) introduced by Floater and Hormann include the stability of interpolation, no poles, and high accuracy for any sufficiently smooth function. In this paper we design a transformed BRI scheme to solve two dimensional fractional Volterra integral equation (2D-FVIE), whose solution may be no...
Preprint
This paper presents a recently developed particle simulation code package PIFE-PIC, which is a novel three-dimensional (3-D) Parallel Immersed-Finite-Element (IFE) Particle-in-Cell (PIC) simulation model for particle simulations of plasma-material interactions. This framework is based on the recently developed non-homogeneous electrostatic IFE-PIC...
Article
Full-text available
This paper develops a two-dimensional implicit particle-in-cell model, which considers algorithms without and with magnetic field, based on the anisotropic immersed-finite-element method. The direct implicit particle-in-cell (DIPIC) algorithm is utilized to track the movement of electrons and ions, while the anisotropic immersed-finite-element meth...
Article
In this article a generalized finite difference method (GFDM), which is a meshless method based on Taylor series expansions and weighted moving least squares, is proposed to solve the elliptic interface problem. This method turns the original elliptic interface problem to be two coupled elliptic non-interface subproblems. The solutions are found by...
Article
Full-text available
In this paper, the discrete unified gas kinetic scheme (DUGKS), which is a novel direct kinetic method, is developed for a reformulated BGK-Vlasov-Poisson system in all electrostatic plasma regimes characterized by a wide range of Knudsen number and normalized Debye length. The current scheme is constructed for multiscale plasma simulation, while t...
Article
Full-text available
In this paper, we propose a discontinuous finite volume element method to solve a phase field model for two immiscible incompressible fluids. In this finite volume element scheme, discontinuous linear finite element basis functions are used to approximate the velocity, phase function, and chemical potential while piecewise constants are used to app...
Article
In this article a domain decomposition method is proposed to solve a time-dependent Navier-Stokes-Darcy model with Beavers-Joseph interface condition and defective boundary condition. Robin boundary conditions between the Navier-Stokes domain and Darcy domain are constructed by directly re-organizing the terms in the three interface conditions, inc...
Article
Full-text available
In this paper, we consider numerical approximations for solving the nonlinear magnetohydrodynamical system, that couples the Navier–Stokes equations and Maxwell equations together. By combining the projection method and some subtle implicit–explicit treatments for nonlinear coupling terms, we develop a fully decoupled, linear and unconditionally en...
Article
In this paper, we consider numerical approximations for solving the magneto-hydrodynamic equations, which couples the Navier–Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is the time discretization, i.e., how to develop suitable temporal discretizations for the nonlinear terms in order to prese...
Article
Full-text available
Anisotropic diffusion is important to many different types of common materials and media. Based on structured Cartesian meshes, we develop a three‐dimensional non‐homogeneous immersed finite element (IFE) method for the interface problem of anisotropic diffusion, which is characterized by an anisotropic elliptic equation with discontinuous tensor c...
Article
In this paper, we propose a diffuse interface model and finite element approximation for two-phase magnetohydrodynamic (MHD) flows with different viscosities and electric conductivities. An energy stable scheme, which is based on the finite element method for the spatial discretization and first order semi-implicit scheme combined with convex split...
Article
Unconventional shale or tight oil/gas reservoirs that have micro-/nano sizes of the dual-scale matrix pore throats with micro-fractures may result in different fluid flow mechanisms compared with conventional oil/gas reservoirs. Microfluidic model, as a potential powerful tool, has been used for decades for investigating fluid flow at pore-scale in...
Article
We propose and analyze an efficient ensemble algorithm with artificial compressibility for fast decoupled computation of multiple realizations of the stochastic Stokes‐Darcy model with random hydraulic conductivity (including the one in the interface conditions), source terms, and initial conditions. The solutions are found by solving three smaller...
Article
In this paper, we propose and analyze two stabilized mixed finite element methods for the dual‐porosity‐Stokes model which couples the free flow region and microfracture‐matrix system through four interface conditions on an interface. The first stabilized mixed finite element method is a coupled method in the traditional format. Based on the idea o...
Article
In this paper, we develop a new square phase-field crystal model using the L2-gradient flow approach, where the total mass of atoms is conserved through a nonlocal Lagrange multiplier. We construct a fast, provably unconditionally energy stable, second-order scheme by using the recently developed SAV approach with the stabilization technique, where...
Preprint
In this article we develop a multi-grid multi-level Monte Carlo (MGMLMC) method for the stochastic Stokes-Darcy interface model with random hydraulic conductivity both in the porous media domain and on the interface. Because the randomness through the interface affects the flow in the Stokes domain, we investigate the coupled stochastic Stokes-Darc...
Article
Full-text available
In this paper, we study a finite element approximation for a linear, first-order in time, unconditionally energy stable scheme proposed in [7] for solving the magneto-hydrodynamic equations. We first reformulate the semi-discrete scheme to the fully discrete version and then carry out a rigorous stability and error analysis for it. We show that the...
Article
This paper aims at designing an observer-based feedback law which locally stabilizes the solution to the two dimensional Navier–Stokes equations with mixed boundary conditions. We consider a finite number of controls acting on a portion of the boundary through Robin boundary conditions and construct a linear Luenberger observer based on the point o...
Article
In this paper, we consider numerical approximations for a model of smectic-A liquid crystal flows in its weak flow limit. The model, derived from the variational approach of the de Gennes free energy, is consisted of a highly nonlinear system that couples the incompressible Navier-Stokes equations with two nonlinear order parameter equations. Based...
Article
The electromagnetic field, which is governed by Maxwell's equation, plays a key role in plasma simulation. In this article, we first derive the interface conditions when we rewrite the interface Maxwell's equation, whose problem domain involves complex media such as objects of different materials, into a parabolic–hyperbolic type of interface model...
Article
A fully kinetic particle-in-cell model combined with a nonhomogeneous interface immersed finite element field solver is presented for simulations of the plasma charging at the lunar terminator. This model explicitly includes the lunar regolith layer and the bedrock in the simulation domain, taking into account of regolith layer thickness and permit...
Article
This paper presents a new mathematical model and an analytical solution to the pressure transient equation of a uniform-flux which fully penetrates the vertical well in a two-layer petroleum reservoir with crossflow. This new model and solution provide an accurate and fast tool to (1) evaluate a vertical well performance in a two-layer reservoir; (...
Article
Full-text available
We analyze a parallel, noniterative, multiphysics domain decomposition method for decoupling the Stokes–Darcy model with multistep backward differentiation schemes for the time discretization and finite elements for the spatial discretization. Based on a rigorous analysis of the Ritz projection error shown in this article, we prove almost optimal L...
Article
In this paper, we consider the numerical approximation for a phase field model of the coupled two-phase free flow and two-phase porous media flow. This model consists of Cahn–Hilliard–Navier–Stokes equations in the free flow region and Cahn–Hilliard–Darcy equations in the porous media region that are coupled by seven interface conditions. The coupl...
Article
Full-text available
In this paper, we consider numerical approximations for solving the nonlinear magneto-hydrodynamical system, that couples the Navier-Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is about the time marching problem, i.e., how to develop suitable temporal discretizations for the nonlinear terms i...
Article
Surface evolution is an unavoidable issue in engineering plasma applications. In this article an iterative method for modeling plasma-surface interactions with moving interface is proposed and validated. In this method, the plasma dynamics is simulated by an immersed finite element particle-in-cell (IFE-PIC) method, and the surface evolution is mod...
Article
In this paper, we present a stabilized finite volume element method with the conforming finite element triples P1-P0-P1 and P1-P1-P1 for approximating the velocity, pressure, and hydraulic head of a coupled Stokes-Darcy problem. The proposed method is convenient to implement, computationally efficient, mass conserving, optimally accurate, and able...
Article
In this paper, the droplet formation process at a low capillary number in a flow focusing micro-channel is studied by performing a three-dimensional phase field benchmark based on the Cahn-Hilliard Navier-Stokes equations and the finite element method. Dynamic moving contact line and wetting condition are considered, and generalized Navier boundary...
Article
Full-text available
In this paper, we propose a novel, thermodynamically consistent phase field model to simulate the deformation and breakup of a ferrodroplet that is immersed in a viscous medium and subject to an applied uniform magnetic field. Instead of using the magnetic body force in the traditional Rosensweig model, the key idea of this model is to propose a ne...
Article
A novel Immersed-Finite-Element Particle-in-Cell (IFE-PIC) simulation tool is presented in this paper for plasma surface interaction where charged plasma particles are represented by a number of simulation particles. The Particle-in-Cell (PIC) method is one of the major particle models for plasma simulation, which utilizes a huge number of simulati...
Article
We present a particle-in-cell (PIC) method using a nonhomogeneous immersed-finite-element (IFE) field solver for modeling dielectric surface charging of complex-shaped objects in plasmas. The IFE solver allows PIC codes using a Cartesian mesh applied to simulations involving arbitrarily shaped objects with a similar accuracy as that using a body-fi...
Article
We consider the problem of local exponential stabilization of the nonlinear Boussinesq equations with control acting on portion of the boundary. In particular, given a steady state solution on an bounded and connected domain , we show that a finite number of controls acting on a part of the boundary through Neumann/Robin boundary conditions is suff...
Article
In this paper, we propose and numerically solve a new model considering confined flow in dual-porosity media coupled with free flow in embedded macrofractures and conduits. Such situation arises, for example, for fluid flows in hydraulic fractured tight/shale oil/gas reservoirs. The flow in dual-porosity media, which consists of both matrix and mic...