Interface Problems Research Articles

Polydopamine-engineered design of Nafion-free powder electrode with superhydrophilicity/superaerophobicity and superior adhesive structure for efficient overall water splitting

Absolute exploitation on the intrinsic catalytic property of powder electrocatalysts always faces the obstacles caused by the existing gas–liquid-solid three-phase interface problem and overwhelming dependence on Nafion usage. Herein, a general polydopamine (PDA)-engineering method is developed to construct Nafion-free powder electrode for efficient overall water splitting. The several nanometer scale PDA coating layers that are self-polymerized on catalyst surfaces, enable the superhydrophilicity/superaerophobicity for more exposed electroactive sites and smoother interfacial mass transfer, and meanwhile, render a superior structural stability inside working electrode with equivalent but more homogeneous adhesion compared with that of Nafion-used electrode. At 300 mA cm−2, the CoMoSxOy@PDA exhibits the low overpotential of 311 mV for OER and 343 mV for HER, and meanwhile demonstrates a cell voltage of only 1.89 V for over 200 h of stable operation and almost unaffected catalytic activity even under harsh ultrasonic working conditions. By theory calculations, the reduced reaction energy barrier for oxygen evolution and the optimized adsorption free energy for hydrogen evolution are revealed in depth.

An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation

We consider the reliable implementation of high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems. We construct a reliable algorithm to merge small interface elements with their surrounding elements to automatically generate the finite element mesh whose elements are large with respect to both domains. We propose new basis functions for the interface elements to control the growth of the condition number of the stiffness matrix in terms of the finite element approximation order, the number of elements of the mesh, and the interface deviation which quantifies the mesh resolution of the geometry of the interface. Numerical examples are presented to illustrate the competitive performance of the method.

High-order enforcement of jumps conditions between compressible viscous phases: An extended interior penalty discontinuous Galerkin method for sharp interface simulation

In this paper, we develop a high-order method for the steady two-phase compressible Navier–Stokes equations closed by generic equations of state, adapted to gas–liquid flows. Our framework relies on the extended discontinuous Galerkin method that is tailored here to a general viscous compressible two-phase configuration. While the imposition of interface jumps conditions is commonly recognized as one of the main difficulties to overcome in the context of geometrically unfitted methods, the setting considered in this work makes this aspect even more challenging. To enforce the non-linear coupling conditions at the interface in a sharp manner, we devise a novel strategy combining multiphase Riemann solvers to handle the convective fluxes across the interface and a weighted stabilized Nitsche’s method for the viscous jumps. The weak enforcement of the jumps conditions along with implicit steady-state iterations and cell-agglomeration procedure make the approach robust to treat arbitrary large contrast phase interface problems governed by stiff models, irrespective of the interface location on the mesh. The study is here restricted to static interfaces. Based on the method of manufactured solution, reference solutions are designed. This allows to conduct a detailed numerical study investigating the influence of several numerical parameters. It is shown that to reach optimal error convergence, the use of pressure-velocity-temperature variables set, appropriate all-speed bulk Riemann solver and Symmetric Interior Penalty method combined with tensorial penalty is necessary.

Implementation of the Learner Centered Design method and the personality approach (Case Study: Redesigning The Interface mobile LMS Tel-U)

The Mobile LMS Tel-U is an e-learning platform developed by Telkom University to support the learning process. However, it still requires more demand from Telkom University students. Usability evaluation was conducted on twelve students using the System Usability Scale (SUS), resulting in a score of 46.5. Interviews and observations revealed interface problems on the dashboard, material, grades, and quizzes. This study aims to redesign the mobile LMS Tel-U interface using the Learner-Centered Design method and incorporating a personality approach by categorizing students into introverts and extroverts. Designing based on personality groups acknowledges the differences in interface design preferences and the relationship between personality and e-learning interface design. This approach yields two different interface designs, one for introverted students and one for extroverted students. The LCD method determines student needs in supporting the learning process. The redesigned interface's usability was evaluated using SUS to assess its appropriateness for students' learning needs. The study shows an average increase in usability scores of 80.4. The introverted student group achieved a usability score of 81, while the extroverted student group obtained a score of 80. Thus, the LCD method and personality approach effectively enhance the usability of distance learning applications (e-learning).

A cusp-capturing PINN for elliptic interface problems

In this paper, we propose a cusp-capturing physics-informed neural network (PINN) to solve discontinuous-coefficient elliptic interface problems whose solution is continuous but has discontinuous first derivatives on the interface. To find such a solution using neural network representation, we introduce a cusp-enforced level set function as an additional feature input to the network to retain the inherent solution properties; that is, capturing the solution cusps (where the derivatives are discontinuous) sharply. In addition, the proposed neural network has the advantage of being mesh-free, so it can easily handle problems in irregular domains. We train the network using the physics-informed framework in which the loss function comprises the residual of the differential equation together with certain interface and boundary conditions. We conduct a series of numerical experiments to demonstrate the effectiveness of the cusp-capturing technique and the accuracy of the present network model. Numerical results show that even using a one-hidden-layer (shallow) network with a moderate number of neurons and sufficient training data points, the present network model can achieve prediction accuracy comparable with traditional methods. Besides, if the solution is discontinuous across the interface, we can simply incorporate an additional supervised learning task for solution jump approximation into the present network without much difficulty.

A high order Cartesian grid, finite volume method for elliptic interface problems

We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems with high-contrast and spatially varying coefficients, large discontinuities in the source term, and complex interface geometries. We include a generalized truncation error analysis based on cell-centered Taylor series expansions, which then define stencils in terms of local discrete solution data and geometric information. In the process, we develop a simple method based on Green's theorem for computing exact geometric moments directly from an implicit function definition of the embedded interface. This approach produces stencils with a simple bilinear representation, where spatially-varying coefficients and jump conditions can be easily included and finite volume conservation can be enforced.

Flexural performance of novel ECC-RC composite sandwich panels

To address the shortcomings of precast concrete sandwich panels (PCSPs) such as insufficient load-bearing capacity, poor ductility behavior, and susceptibility to cracking under temperature stress, this study reinforced the face layer of PCSP with engineered cementitious composite (ECC), resulting in the development of novel ECC-RC composite sandwich panels (ECSPs). The flexural performance of ECSP was revealed by way of a four-point bending test and finite element analysis. Test results showed that incorporating ECC into the wythes substantially improved the flexural performance of PCSP, and the maximum crack width of ECSP was well below the corresponding limit requirement when the mid-span deformation reached the serviceability limit state of the panel. ECSP presented a long load-hardening phase owing to the excellent tensile toughness of ECC, and the properties of the reinforcement could be fully utilized in ECSP without causing “over reinforced” damage as seen in PCSP. Finite element analysis demonstrated that the initial cracks of ECSP did not occur at the tensile edge of the panel, indicating excellent durability of ECSP. Based on the test results and finite element analysis, a formula for the flexural carrying capacity of ECSP was proposed, and the corresponding calculation model demonstrated better applicability. It is recommended to use 20 mm thick ECC to reinforce the face layer of ECSP for optimal economic benefits in practical engineering, while paying attention to the interface problem between ECC and concrete.

A highly efficient semi-implicit two-field modeling for thermal contact problems with non-Fourier effects

In this paper, we revisit the thermal interface condition of thermal contact prob- lems with a nonzero thermal resistance. We point out that continuity conditions of the flux at the interfaces, which usually adopt the form of temperature gradient, leads to a paradoxical result if one of the adjacent bodies has zero temperature gradient. Specifically, that using the temperature gradient instead of the real heat flux yields a nonphysical temperature profile and fails to depict the thermal jump in cases with zero temperature gradients. We then show that the two-field (tem- perature and flux) formalism, in lieu of the classical single-field (temperature) naturally resolves this paradox. We propose an easy-to-implement semi-implicit scheme for this two-field formulation. The thermal interface problem is formu- lated in the fashion of differential algebraic equations (DAEs), in which the inter- face conditions are treated as algebraic equations constraining the associated heat process governed by differential equations. Our method can precisely fulfill the interface condition with the magnitude of machine error (10−16) and is computationally more efficient (around 8 to 10× faster) since it only needs to solve a very small Poisson-like system. End-to-end 1D and 2D simulations are presented to demonstrate the versatility and efficacy of our new method.

Analysis of nonconforming IFE methods and a new scheme for elliptic interface problems

In this paper, an important discovery has been found for nonconforming immersed finite element (IFE) methods using the integral values on edges as degrees of freedom for solving elliptic interface problems. We show that those IFE methods without penalties are not guaranteed to converge optimally if the tangential derivative of the exact solution and the jump of the coefficient are not zero on the interface. A nontrivial counter example is also provided to support our theoretical analysis. To recover the optimal convergence rates, we develop a new nonconforming IFE method with additional terms locally on interface edges. The new method is parameter-free which removes the limitation of the conventional partially penalized IFE method. We show the IFE basis functions are unisolvent on arbitrary triangles which is not considered in the literature. Furthermore, different from multipoint Taylor expansions, we derive the optimal approximation capabilities of both the Crouzeix–Raviart and the rotated-Q1 IFE spaces via a unified approach which can handle the case of variable coefficients easily. Finally, optimal error estimates in both H1- and L2-norms are proved and confirmed with numerical experiments.

Trilinear Immersed-Finite-Element Method for Three-Dimensional Anisotropic Interface Problems in Plasma Thrusters

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 existing 3D linear IFE spaces based on tetrahedron meshes, the newly designed trilinear IFE space for the target model simplifies the mesh generation, significantly reduces the number of mesh elements and interface elements, provides much more convenient and efficient ways for finding the intersections between interfaces and mesh edges, and decreases the errors. These advantages lead to much higher efficiency when solving complex anisotropic interface problems in practice. In addition, the proposed method can be easily incorporated into other typical methods based on Cartesian meshes, such as the particle-in-cell method for plasma simulation. Numerical experiments are provided to verify the optimal accuracy, high efficiency, and reliability of the proposed method for solving complex interface problems, as well as its applicability to practical plasma thruster problems.

An Asymptotically Compatible Coupling Formulation for Nonlocal Interface Problems with Jumps

We introduce a mathematically rigorous formulation for a nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization for the weak form of the interface problem. After proving the well-posedness of the weak form, we demonstrate that solutions to the nonlocal interface problem converge to the corresponding local counterpart when the nonlocal data are appropriately prescribed. Several numerical tests in one and two dimensions show the applicability of our technique, its numerical convergence to exact nonlocal solutions, its convergence to the local limit when the horizons vanish, and its robustness with respect to the patch test.

Kernel free boundary integral method for 3D incompressible flow and linear elasticity equations on irregular domains

A second-order accurate kernel-free boundary integral method is presented for Stokes flow and linear elasticity boundary value problems on three-dimensional irregular domains. It solves equations in the framework of boundary integral equations, whose corresponding discrete forms are well-conditioned and solved by the GMRES method. A notable feature of this approach is that the boundary or volume integrals encountered in BIEs are indirectly evaluated by a Cartesian grid-based method, which includes discretizing corresponding simple interface problems with a MAC scheme, correcting discrete linear systems to reduce large local truncation errors near the interface, solving the modified system by a CG method together with an FFT-based Poisson solver. No extra work or special quadratures are required to deal with singular or hyper-singular boundary integrals and the dependence on the analytical expressions of Green’s functions for the integral kernels is completely eliminated. Numerical results are given to demonstrate the efficiency and accuracy of the Cartesian grid-based method.

Time-domain Green’s function associated to the interface problem for the Klein–Gordon equation

In this work we present a representation formula for the Green’s function associated with the source or interface problem for the Klein–Gordon equation from a known result on solution for the non-dispersive wave equation. The results can extend to more general situations, in particular stratified media where the Cagniard-de Hoop method fails for reasons of non-homogeneity of the amplitude and the phase of the exponential in the Laplace transform. Examples and numerical applications are given in two dimensions for the interface problem associated to a dispersive wave equation where the reflected and incident fields are obtained. The calculation of the transmitted field is omitted for the sake of simplicity of the paper. Such a representation formula can be useful to study other qualitative properties of dispersive waves from those known on non-dispersive ones.

Second Order Convergence of a Modified MAC Scheme for Stokes Interface Problems

Stokes flow equations have been implemented successfully in practice for simulating problems with moving interfaces. Though computational methods based on the well-known MAC scheme produce accurate solutions and numerical convergence can be demonstrated using a resolution study, the rigorous convergence proofs are usually limited to particular reformulations and boundary conditions. In this paper, a rigorous error analysis of the marker and cell scheme for Stokes interface problems with constant viscosity in the framework of the finite difference method is presented. Without reformulating the problem into elliptic PDEs, the main idea is to use a discrete Ladyzenskaja-Babuska-Brezzi condition and construct auxiliary functions, which satisfy discretized Stokes equations and possess at least second order accuracy in the neighborhood of the moving interface. In particular, the method, for the first time, enables one to prove second order convergence of the velocity gradient in the discrete $$\ell ^2$$ -norm, in addition to the velocity and pressure fields. Numerical experiments verify the desired properties of the methods and the expected order of accuracy for both two-dimensional and three-dimensional examples.

A Discontinuity and Cusp Capturing PINN for Stokes Interface Problems with Discontinuous Viscosity and Singular Forces

A Discontinuity and Cusp Capturing PINN for Stokes Interface Problems with Discontinuous Viscosity and Singular Forces

An Arbitrary Order Reconstructed Discontinuous Approximation to Biharmonic Interface Problem

An Arbitrary Order Reconstructed Discontinuous Approximation to Biharmonic Interface Problem

HRW: Hybrid Residual and Weak Form Loss for Solving Elliptic Interface Problems with Neural Network

HRW: Hybrid Residual and Weak Form Loss for Solving Elliptic Interface Problems with Neural Network

Comprehensive Review on Thin Film Homojunction Solar Cells: Technologies, Progress and Challenges

With the aim of achieving high efficiency, cost-effectiveness, and reliability of solar cells, several technologies have been studied. Recently, emerging materials have appeared to replace Si-based cells, seeking economic fabrication of solar cells. Thin-film solar cells (TFSCs) are considered strong candidates for this mission, specifically perovskite-based solar cells, reporting competitive power convergence efficiencies reaching up to 25.7%. Substantial efforts have been invested in experimental and research work to surpass the Si-based cells performance. Simulation analysis is a major tool in achieving this target by detecting design problems and providing possible solutions. Usually, a TFSC adopts p-i-n heterojunction architecture by employing carrier transport materials along with the absorber material in order to extract the photogenerated electrons and holes by realizing a built-in electric field. Eventually, this dependency of conventional heterojunction TFSCs on carrier transport layers results in cost-ineffective cells and increases the possibility of device instability and interface problems. Thus, the design of p-n homojunction TFSCs is highly desirable as an essential direction of structural innovation to realize efficient solar cell operation. In this review, a summary of the fundamentals of TFSC materials, recent design and technology progress, and methodologies for improving the device performance using experimental research studies will be discussed. Further, simulation analysis will be provided by demonstrating the latest research work outcomes, highlighting the major achievements and the most common challenges facing thin film homojunction solar cell structures and the methods to improve them.

A Conforming Virtual Element Method Based on Unfitted Meshes for the Elliptic Interface Problem

A Conforming Virtual Element Method Based on Unfitted Meshes for the Elliptic Interface Problem

A face‐centred finite volume method for high‐contrast Stokes interface problems

AbstractA new face‐centred finite volume method (FCFV) for Stokes problems involving sharp interfaces is proposed. Two formulations, based on two strong forms of the Stokes problem, and using different mixed variables, are presented. Particular attention is paid to the symmetry of the resulting system of global equations, and a simple rewriting of the interface boundary condition is proposed to ensure that one of the formulations preserves the symmetry of the linear system that is usually lost when considering material interfaces. Four numerical examples are considered to test the implementation numerically by performing mesh convergence studies, in two and three dimensions. The examples account for discontinuous viscosity as well as the effect of surface tension. The results show that one of the formulations is less sensitive to the numerical stabilisation used in FCFV methods but does not preserve the symmetry of the global system, whereas the other formulation is more sensitive to the stabilisation, but preserves the symmetry of the resulting system of equations. The FCFV method appears as a promising alternative for the simulation of viscous flow involving internal boundaries on conformal meshes. The potential application of the FCFV method for the purpose of geodynamic modelling is discussed.