STABILITY OF THE RAREFACTION WAVE IN THE SINGULAR LIMIT OF A SHARP INTERFACE PROBLEM FOR THE COMPRESSIBLE NAVIER-STOKES/ALLEN-CAHN SYSTEM

This paper is concerned with the global well-posedness of the solution to the compressible Navier-Stokes/Allen-Cahn system and its sharp interface limit in one-dimensional space.For the perturbations with small energy but possibly large oscillations of rarefaction wave solutions near phase separation,and where the strength of the initial phase field could be arbitrarily large,we prove that the solution of the Cauchy problem exists for all time,and converges to the centered rarefaction wave solution of the corresponding standard two-phase Euler equation as the viscosity and the thickness of the interface tend to zero.The proof is mainly based on a scaling argument and a basic energy method.

Magnetic Proximity Effect in an Antiferromagnetic Insulator/Topological Insulator Heterostructure with Sharp Interface

We report an experimental study of electron transport properties of MnSe/(Bi,Sb)_2Te_3 heterostructures,in which MnSe is an antiferromagnetic insulator,and(Bi,Sb)_2Te_3 is a three-dimensional topological insulator(TI).Strong magnetic proximity effect is manifested in the measurements of the Hall effect and longitudinal resistances.Our analysis shows that the gate voltage can substantially modify the anomalous Hall conductance,which exceeds 0.1 e^(2)/h at temperature T=1.6 K and magnetic field μ_0H=5 T,even though only the top TI surface is in proximity to MnSe.This work suggests that heterostructures based on antiferromagnetic insulators provide a promising platform for investigating a wide range of topological spintronic phenomena.

Sharp interface direct forcing immersed boundary methods： A summary of some algorithms and applications

Body-fitted mesh generation has long been the bottleneck of simulating fluid flows involving complex geometries. Immersed boundary methods are non-boundary-conforming methods that have gained great popularity in the last two decades for their simplicity and flexibility, as well as their non-compromised accuracy. This paper presents a summary of some numerical algori- thms along the line of sharp interface direct forcing approaches and their applications in some practical problems. The algorithms include basic Navier-Stokes solvers, immersed boundary setup procedures, treatments of stationary and moving immersed bounda- ries, and fluid-structure coupling schemes. Applications of these algorithms in particulate flows, flow-induced vibrations, biofluid dynamics, and free-surface hydrodynamics are demonstrated. Some concluding remarks are made, including several future research directions that can further expand the application regime of immersed boundary methods.

A sharp interface approach for cavitation modeling using volume-of-fluid and ghost-fluid methods

This paper describes a novel sharp interface approach for modeling the cavitation phenomena in incompressible viscous flows. A one-field formulation is adopted for the vapor-liquid two-phase flow and the interface is tracked using a volume of fluid（VOF） method. Phase change at the interface is modeled using a simplification of the Rayleigh-Plesset equation. Interface jump conditions in velocity and pressure field are treated using a level set based ghost fluid method. The level set function is constructed from the volume fraction function. A marching cubes method is used to compute the interface area at the interface grid cells. A parallel fast marching method is employed to propagate interface information into the field. A description of the equations and numerical methods is presented. Results for a cavitating hydrofoil are compared with experimental data.

Remarks on Sharp Interface Limit for an Incompressible Navier-Stokes and Allen-Cahn Coupled System

The authors are concerned with the sharp interface limit for an incompressible Navier-Stokes and Allen-Cahn coupled system in this paper.When the thickness of the diffuse interfacial zone,which is parameterized by ε,goes to zero,they prove that a solution of the incompressible Navier-Stokes and Allen-Cahn coupled system converges to a solution of a sharp interface model in the L^(∞)(L^(2))∩L^(2)(H^(1))sense on a uniform time interval independent of the small parameterε.The proof consists of two parts:One is the construction of a suitable approximate solution and another is the estimate of the error functions in Sobolev spaces.Besides the careful energy estimates,a spectral estimate of the linearized operator for the incompressible Navier-Stokes and Allen-Cahn coupled system around the approximate solution is essentially used to derive the uniform estimates of the error functions.The convergence of the velocity is well expected due to the fact that the layer of the velocity across the diffuse interfacial zone is relatively weak.

The Fictitious Domain Method with Sharp Interface for Elasticity Systems with General Jump Embedded Boundary Conditions

In framework of the fictitious domain methods with immersed interfaces for the elasticity problem,the present contribution is to study and numerically validate the jump-integrated boundary conditions method with sharp interface for the vector elasticity system discretized by a proposed finite volume method.The main idea of the fictitious domain approach consists in embedding the original domain of study into a geometrically larger and simpler one called the fictitious domain.Here,we present a cell-centered finite volume method to discretize the fictitious domain problem.The proposed method is numerically validated for different test cases.This work can be considered as a first step before more challenging problems such as fluid-structure interactions or moving interface problems.

Combination of direct-forcing fictitious domain method and sharp interface method for dielectrophoresis of particles

In this paper, we combine the direct-forcing fictitious domain （DF/FD） method and the sharp interface method to resolve the problem of particle dielectrophoresis in two dimensions. The flow field and the motion of particles are solved with the DF/FD method, the electric field is solved with the sharp inter- face method, and the electrostatic force on the particles is computed using the Maxwell stress tensor method. The proposed method is validated via three problems： effective conductivity of particle compos- ite between two planar plates, cell trapping in a channel, and motion of particles due to both conventional and traveling wave dielectrophoretic forces.

A High Order Sharp-Interface Method with Local Time Stepping for Compressible Multiphase Flows

In this paper,a new sharp-interface approach to simulate compressible multiphase flows is proposed.The new scheme consists of a high order WENO finite volume scheme for solving the Euler equations coupled with a high order pathconservative discontinuous Galerkin finite element scheme to evolve an indicator function that tracks the material interface.At the interface our method applies ghost cells to compute the numerical flux,as the ghost fluid method.However,unlike the original ghost fluid scheme of Fedkiw et al.[15],the state of the ghost fluid is derived from an approximate-state Riemann solver,similar to the approach proposed in[25],but based on a much simpler formulation.Our formulation leads only to one single scalar nonlinear algebraic equation that has to be solved at the interface,instead of the system used in[25].Away from the interface,we use the new general Osher-type flux recently proposed by Dumbser and Toro[13],which is a simple but complete Riemann solver,applicable to general hyperbolic conservation laws.The time integration is performed using a fully-discrete one-step scheme,based on the approaches recently proposed in[5,7].This allows us to evolve the system also with time-accurate local time stepping.Due to the sub-cell resolution and the subsequent more restrictive time-step constraint of the DG scheme,a local evolution for the indicator function is applied,which is matched with the finite volume scheme for the solution of the Euler equations that runs with a larger time step.The use of a locally optimal time step avoids the introduction of excessive numerical diffusion in the finite volume scheme.Two different fluids have been used,namely an ideal gas and a weakly compressible fluid modeled by the Tait equation.Several tests have been computed to assess the accuracy and the performance of the new high order scheme.A verification of our algorithm has been carefully carried out using exact solutions as well as a comparison with other numerical reference solutions.The material interface is resolved sharply and accurately without spurious oscillations in the pressure field.

A sharp-interface immersed boundary method for simulating high-speed compressible inviscid flows

This paper presents a robust sharp-interface immersed boundary method for simulating inviscid compressible flows over stationary and moving bodies.The flow field is governed by Euler equations,which are solved by using the open source library OpenFOAM.Discontinuities such as those introduced by shock waves are captured by using Kurganov and Tadmor divergence scheme.Wall-slip boundary conditions are enforced at the boundary of body through reconstructing flow variables at some ghost points.Their values are obtained indirectly by interpolating from their mirror points.A bilinear interpolation is employed to determine the variables at the mirror points from boundary conditions and flow conditions around the boundary.To validate the efficiency and accuracy of this method for simulation of high-speed inviscid compressible flows,four cases have been simulated as follows:supersonic flow over a 15°angle wedge,transonic flow past a stationary airfoil,a piston moving with supersonic velocity in a shock tube and a rigid circular cylinder lift-off from a flat surface triggered by a shock wave.Compared to the exact analytical solutions or the results in literature,good agreement can be achieved.

Modeling of the Saltwater Intrusion Using the Level Set Method. Application to Henry’s Problem

The salt intrusion phenomenon is caused by overexploitation of aquifers in coastal areas. This physical phenomenon has been the subject of numerous studies and numerous methods have been proposed, with the aim of protecting the quality of the water in these aquifers. This work proposes a two-dimensional saline intrusion model using the sharp interface approach and the level set method. It consists of a parabolic equation modeling the underground flow and a hyperbolic Equation (the level set equation) which makes it possible to track the evolution of the interface. High-order numerical schemes such as the space scheme WENO5 and the third-order time scheme TVD-RK were used for the numerical resolution of the hyperbolic equation. To limit the tightening of the contour curves of the level set function, the redistanciation or reinitialization algorithm proposed by Sussma et al. (1994) was used. To ensure the effectiveness and reliability of the proposed method, two tests relating to the standard Henry problem and the modified Henry problem were performed. Recall that Henry’s problem uses the variable density modeling approach in a confined and homogeneous aquifer. By comparing the results obtained by the level set method with reinitialization (LSMR) and those obtained by Henry (1964), and by Simpson and Clement (2004), we see in the two test cases that the level set method reproduces well the toe, the tip and the behaviour of the interface. These results correspond to the results obtained by Abarca for Henry’s problem with constant dispersion coefficients. The results obtained with LSMR, reproduced the interface with a slight spacing compared to those obtained by Henry. According to Abarca (2006), this spacing is due to the absence of the longitudinal and transversal dispersion coefficients in the model.

An Efficient Neural-Network and Finite-Difference Hybrid Method for Elliptic Interface Problems with Applications

A new and efficient neural-network and finite-difference hybrid method is developed for solving Poisson equation in a regular domain with jump discontinuities on embedded irregular interfaces.Since the solution has low regularity across the interface,when applying finite difference discretization to this problem,an additional treatment accounting for the jump discontinuities must be employed.Here,we aim to elevate such an extra effort to ease our implementation by machine learning methodology.The key idea is to decompose the solution into singular and regular parts.The neural network learning machinery incorporating the given jump conditions finds the singular solution,while the standard five-point Laplacian discretization is used to obtain the regular solution with associated boundary conditions.Regardless of the interface geometry,these two tasks only require supervised learning for function approximation and a fast direct solver for Poisson equation,making the hybrid method easy to implement and efficient.The two-and three-dimensional numerical results show that the present hybrid method preserves second-order accuracy for the solution and its derivatives,and it is comparable with the traditional immersed interface method in the literature.As an application,we solve the Stokes equations with singular forces to demonstrate the robustness of the present method.

A Hybrid Scheme of Level Set and Diffuse Interface Methods for Simulating Multi-Phase Compressible Flows

We propose a hybrid scheme combing the level set method and the multicomponent diffuse interface method to simulate complex multi-phase flows.The overall numerical scheme is based on a sharp interface framework where the level set method is adopted to capture the material interface,the Euler equation is used to describe a single-phase flow on one side of the interface and the six-equation diffuse interface model is applied to model the multi-phase mixture or gas-liquid cavitation on the other side.An exact Riemann solver,between the Euler equation and the six-equation model with highly nonlinear Mie-Gr¨uneisen equations of state,is developed to predict the interfacial states and compute the phase interface flux.Several numerical examples,including shock tube problems,cavitation problems,air blast and underwater explosion applications are presented to validate the numerical scheme and the Riemann solver.

On the Isotropic-Nematic Phase Transition for the Liquid Crystal

In this paper,we study the isotropic-nematic phase transition for the nematic liquid crystal based on the Landau-de Gennes Q-tensor theory.We justify the limit from the Landau-de Gennes flow to a sharp interface model:in the isotropic region, Q≡0;in the nematic region,the Q-tensor is constrained on the manifolds={s_(+)(n −1/3 I),n∈S^(2)}with s_(+) positive constant,and the evolution of alignment vector field obeys the harmonic map heat flow,while the interface separating the isotropic and nematic regions evolves by the mean curvature flow.This problem can be viewed as a concrete but representative case of the Rubinstein-Sternberg-Keller problem introduced in Rubinstein et al.(SIAM J.Appl.Math.49:116-133,1989;SIAM J.Appl.Math.49:1722-1733,1989).

Ultrafast flash memory with large self-rectifying ratio based on atomically thin MoS_(2)-channel transistor

Flash memory with high operation speed and stable retention performance is in great demand to meet the requirements of big data.In addition,the realisation of ultrafast flash memory with novel functions offers a means of combining heterogeneous components into a homogeneous device without considering impedance matching.This report proposes a 20 ns programme flash memory with 10^(8) self-rectifying ratios based on a 0.65 nm-thick MoS_(2)-channel transistor.A high-quality van der Waals heterojunction with a sharp interface is formed between the Cr/Au metal floating layer and h-BN tunnelling layer.In addition,the large rectification ratio and low ideality factor(n=1.13)facilitate the application of the MoS_(2)-channel flash memory as a bit-line select transistor.Finally,owing to the ultralow MoS_(2)/h-BN heterojunction capacitance(50 fF),the memory device exhibits superior performance as a high-frequency(up to 1 MHz)sine signal rectifier.These results pave the way toward the potential utilisation of multifunctional memory devices in ultrafast two-dimensional NAND-flash applications.

Phase Field Models Versus Parametric Front Tracking Methods: Are They Accurate and Computationally Efficient?

We critically compare the practicality and accuracy of numerical approximations of phase field models and sharp interface models of solidification.Here we focus on Stefan problems,and their quasi-static variants,with applications to crystal growth.New approaches with a high mesh quality for the parametric approximations of the resulting free boundary problems and new stable discretizations of the anisotropic phase field system are taken into account in a comparison involving benchmark problems based on exact solutions of the free boundary problem.