Sharp-interface Method Research Articles

Modeling process–structure–property relationship in organic photovoltaics using a robust diffuse interface approach

Organic photovoltaics (OPVs) can potentially provide a cost-efficient means of harnessing solar energy. However, optimum OPV performance depends on understanding the process–structure–property (PSP) correlation in organic semiconductors. In the working of bulk-heterojunction OPVs, the morphology plays a crucial role in device performance. In order to understand PSP linkage, a theoretical framework has been developed. We first established process–structure correlations by generating a range of morphologies with various blend ratios of donor and acceptor organic semiconductors for various annealing periods. Second, we calculated the effective electronic properties corresponding to the simulated structures using a diffuse interface approach that is numerically more robust and straightforward than the classical sharp interface method. This novel framework, wherein both the process–structure and the structure–property relationship have been established using the diffuse interface approach, completes the theoretical PSP linkage, allowing the optimization of process parameters for device applications. The theoretical PSP linkage is then benchmarked qualitatively with experimental results on a model P3HT:PCBM system. We have been able to identify the morphological characteristics that maximize device performance. This work is carried out in the broad overview of the integrated computational materials engineering framework wherein the processing parameters are optimized by determining the process–structure–property relationships.

Pseudo-transient ghost fluid methods for the Poisson-Boltzmann equation with a two-component regularization

The Poisson Boltzmann equation (PBE) is a well-established implicit solvent continuum model for the electrostatic analysis of solvated biomolecules. The numerical solution of the nonlinear PBE is still a challenge due to its exponential nonlinear term, strong singularity by the source terms, and distinct dielectric regions. In this paper, a new pseudo-transient approach is proposed, which combines an analytical treatment of singular charges in a two-component regularization, with an analytical integration of nonlinear term in pseudo-time solution. To ensure efficiency, both fully implicit alternating direction implicit (ADI) and unconditionally stable locally one-dimensional (LOD) methods have been constructed to decompose three-dimensional linear systems into one-dimensional (1D) ones in each pseudo-time step. Moreover, to accommodate the nonzero function and flux jumps across the dielectric interface, a modified ghost fluid method (GFM) has been introduced as a first order accurate sharp interface method in 1D style, which minimizes the information needed for the molecular surface. The 1D finite-difference matrix generated by the GFM is symmetric and diagonally dominant, so that the stability of ADI and LOD methods is boosted. The proposed pseudo-transient GFM schemes have been numerically validated by calculating solvation free energy, binding energy, and salt effect of various proteins. It has been found that with the augmentation of regularization and GFM interface treatment, the ADI method not only enhances the accuracy dramatically, but also improves the stability significantly. By using a large time increment, an efficient protein simulation can be realized in steady-state solutions. Therefore, the proposed GFM-ADI and GFM-LOD methods provide accurate, stable, and efficient tools for biomolecular simulations.

A sharp-interface immersed smoothed point interpolation method with improved mass conservation for fluid-structure interaction problems

To solve the problem of inaccurate boundary identification and to eliminate the spurious pressure oscillation in the previously developed immersed smoothed point interpolation method (IS-PIM), a new sharp-interface IS-PIM combining mass conservation algorithm, called Sharp-ISPIM-Mass, is proposed in this work. Based on the so called sharp-interface method, the technique of quadratic local velocity reconstruction has been developed by combining with the mass conservation algorithm, which enables the present method improve the accuracy of the velocity field and satisfy the mass conservation condition near the boundary field. So the proposed method would not encounter the problem of spurious mass flux. In addition, a new form of FSI force evaluation considering pressure and viscous force to perform a whole function from the fluid domain to fictitious fluid domain is introduced, which makes the present method obtain more accurate results of FSI force than the original one. Through the numerical studies of a number of benchmark examples, the performance of the Sharp-ISPIM-Mass has been examined and illustrated.

An Accurate Sharp Interface Method for Two-Phase Compressible Flows at Low-Mach Regime

An accurate numerical approach is presented for computing two-phase flows with surface tension at low-Mach regime. To develop such a model, where slight compressible effects are taken into account as well as correct thermodynamical closures, both the liquid and the gas are considered compressible and described by a precise compressible solver. A low-Mach correction has been implemented to eliminate excessive numerical dissipation. The interface between two-phase flows is captured by the level set method that is considered to be sharp. The interface capturing issue of the level set method within the Eulerian framework is the key point of the two-phase flow simulations, and in this work we propose a high-order coupled time-space approach for interface advection. Several numerical test-cases have been employed to validate the present numerical approach and enlighten its good performance.

A sharp interface method for an immersed viscoelastic solid

The immersed boundary–finite element method (IBFE) is an approach to describing the dynamics of an elastic structure immersed in an incompressible viscous fluid. In this formulation, there are generally discontinuities in the pressure and viscous stress at fluid–structure interfaces. The standard immersed boundary approach, which connects the Lagrangian and Eulerian variables via integral transforms with regularized Dirac delta function kernels, smooths out these discontinuities, which generally leads to low order accuracy. This paper describes an approach to accurately resolve pressure discontinuities for these types of formulations, in which the solid may undergo large deformations. Our strategy is to decompose the physical pressure field into a sum of two pressure–like fields, one defined on the entire computational domain, which includes both the fluid and solid subregions, and one defined only on the solid subregion. Each of these fields is continuous on its domain of definition, which enables high accuracy via standard discretization methods without sacrificing sharp resolution of the pressure discontinuity. Numerical tests demonstrate that this method improves rates of convergence for displacements, velocities, stresses, and pressures as compared to the conventional IBFE method. Further, it produces much smaller errors at reasonable numbers of degrees of freedom. The performance of this method is tested on several cases with analytic solutions, a nontrivial benchmark problem of incompressible solid mechanics, and an example involving a thick, actively contracting torus.

A sharp-interface method for the simulation of shock-induced vaporization of droplets

A sharp-interface method is developed to calculate the vaporization of droplets in high-speed flows. The levelset method is used to track the liquid-gas interface. A sharp-interface approach using an interfacial Riemann solver based ghost fluid method (RS-GFM) is developed to couple the liquid and gas flow-fields at the interface. The interfacial Riemann problem accounts for surface tension and phase change effects, which affect the jump in pressure and the normal velocity fields across the interface. The current RS-GFM also accounts for the jump in viscous stresses at the interface caused by the Marangoni effect. The resulting sharp-interface approach captures all the first-order physical effects at play in shock-induced droplet vaporization. The method is validated by comparing the current results with benchmark experimental and numerical results. Finally, 2D and 3D simulations of shock-droplet interactions are performed to quantify the shock-induced vaporization rate of the droplets, under the influence of viscosity and surface tension.

A 3D conservative sharp interface method for simulation of compressible two-phase flows

A three-dimensional (3D) conservative sharp interface (CSI) method, which combines 3D cut-cell methods and finite volume methods in the arbitrary Lagrangian-Eulerian framework, is proposed to simulate compressible inviscid two-phase flows. The 3D cut-cell method allows to reconstruct interfaces on a Cartesian mesh and update unstructured interface cells in the vicinity of the interface, making the reconstructed interface always coinciding with the cell faces of the interface cells. The complexity in generating 3D interface cells is significantly reduced by exploiting the symmetry and rotational symmetry of fluid positions in a cut cell. Compared to our previous two-dimensional work (Lin et al. (2017) [17]), the occurrence of large interface cells is also avoided by using the new strategy of cell assembly. With the help of the 3D cut-cell method, a second-order finite volume method in the arbitrary Lagrangian-Eulerian framework can be used nearly in the whole domain, except for the interface cells with under-resolved interfaces or topology changes, at which a first-order finite volume method is used instead. The convergence of the 3D CSI method is examined by studying the Rayleigh collapse of a gas bubble in water, and second-order accuracy has been obtained for the interface evolution. Simulation of shock-induced bubble collapse demonstrates that the axisymmetricity of the interface is well preserved in the 3D computation. Moreover, the 3D CSI methods are also given experimental validation, including the interaction of a shock with 3D curved gas-gas interface and droplet deformation after shock impact. In all cases, a good agreement has been achieved with the experimental data, with respect to the interface evolution and flow features.

Numerical approach for generic three‐phase flow based on cut‐cell and ghost fluid methods

SummaryIn this paper, we introduce numerical methods that can simulate complex multiphase flows. The finite volume method, applying Cartesian cut‐cell is used in the computational domain, containing fluid and solid, to conserve mass and momentum. With this method, flows in and around any geometry can be simulated without complex and time consuming meshing. For the fluid region, which involves liquid and gas, the ghost fluid method is employed to handle the stiffness of the interface discontinuity problem. The interaction between each phase is treated simply by wall function models or jump conditions of pressure, velocity and shear stress at the interface. The sharp interface method “coupled level set (LS) and volume of fluid (VOF)” is used to represent the interface between the two fluid phases. This approach will combine some advantages of both interface tracking/capturing methods, such as the excellent mass conservation from the VOF method and good accuracy of interface normal computation from the LS function. The first coupled LS and VOF will be generated to reconstruct the interface between solid and the other materials. The second will represent the interface between liquid and gas.

A new and improved cut-cell-based sharp-interface method for simulating compressible fluid elastic–perfectly plastic solid interaction

In this work, a new integrated, conservative and consistent cut-cell-based sharp-interface method is developed to simulate compressible multi-material problems with various interfaces. In the proposed method, the material interfaces are represented by quadratic-curve cut faces evolved with the help of the level set equation. Multiple level set functions are applied to address multiple interfaces. The system is mainly developed in Eulerian coordinates with the cut faces moving in a Lagrangian manner, thus, it benefits from a Lagrangian moving interface in terms of accuracy and handles large deformations more conveniently than those works in a Lagrangian framework. Clear improvements in robustness and accuracy over the modified ghost fluid method can be observed in various 2D test cases.

A robust sharp interface method for SPH

Based on our previous sharp interface method (SIM) for smoothed particle hydrodynamics (SPH) [Zhang M and Deng X-L. A sharp interface method for SPH. Journal of Computational Physics 2015; 302 469–484], a robust SIM for SPH is developed. According to Lagrangian nature of SPH, the interface is located between two types of SPH particles. It is different from the previous method, in which the initial interface is defined by the user. The main consequence of the interface definition in the current method is that minimum value of level set function is around half the initial inter-particle distance. Therefore the calculation of level set function becomes more robust. The interface status is determined by jump conditions at the interface. Then the interface status is extended to the ghost fluid particles. Various benchmark tests are given to show the performance of the robust SIM for SPH. Comparing with the previous SIM for SPH, current method is more robust and accurate in the simulation of low-speed multiphase flows of high density ratios with clear interface.

Adaptive Cartesian cut-cell sharp interface method (aC3SIM) for three-dimensional multi-phase flows

A sharp interface method has been developed for treating interfacial discontinuities in compressible multi-phase fluids on three-dimensional Cartesian cut-cell grids. The evolution of the interfacial discontinuities in the Cartesian grid is captured by the level-set method. The intersections between interfacial fronts and Cartesian grids are interpolated using level-set function values at the vertices of Cartesian grids. Triangular surfaces are then constructed on the interfacial fronts. A novel cell merge method is used for complex topological changes. Jump conditions across discontinuous interfaces are enforced by reconstruction of interfacial flow variables using a constrained least-squares method. The inviscid flux across internal faces of the same fluid is calculated by the local Lax–Friedrichs flux. Manufactured solutions for interfaces are suggested for validation of the reconstruction method. Laplace’s law test results show that the present method drastically reduces the parasite currents compared to conventional interface treatment methods. Bubble rise problems also show the validity and accuracy of the proposed sharp interface method for immiscible two-phase fluids.

Numerical study of the shear-thinning effect on the interaction between a normal shock wave and a cylindrical liquid column

Based on adaptive mesh refinement, the SIM (Sharp-Interface Method) is utilized to numerically study the interaction between a shock wave and a liquid column as well as the evolution of the flow field. The SIM consists of the LSM (Level Set Method) and the GFM (Ghost Fluid Method). The LSM tracks the gas-liquid interface, and the GFM generates the virtual domains near the interface based on the gas-liquid interface condition. The hybridized GFM has been developed by integrating the Riemann GFM and the modified GFM together, which ensures the accuracy of the interface Riemann problem in the small deformation region of the interface while ensuring that the large interface deformation can be processed correctly. By comparing with the experimental results and the numerical results in previous literature, the good agreement shows that the above algorithm can accurately simulate the interactions between shock waves and liquid columns along with achieving the evolutions of the sharp gas-liquid interfaces. Based on the algorithm above, the interactions between the shock waves and the inviscid, the Newtonian, and the shear-thinning liquid columns are simulated, respectively. The numerical results indicate that the viscous effect can cause the bending of the liquid column and large deformation in the high shearing region. However, the shear thinning effect alleviates the bending and the deformation of the liquid column in the high shear region.

Coupling the fictitious domain and sharp interface methods for the simulation of convective mass transfer around reactive particles: Towards a reactive Sherwood number correlation for dilute systems

We suggest a reactive Sherwood number model for convective mass transfer around reactive particles in a dilute regime. The model is constructed with a simple external-internal coupling and is validated with Particle-Resolved Simulation (PRS). The PRS of reactive particle-fluid systems requires numerical methods able to handle efficiently sharp gradients of concentration and potential discontinuities of gradient concentrations at the fluid-particle interface. To simulate mass transfer from reactive catalyst beads immersed in a fluid flow, we coupled the Sharp Interface Method (SIM) to a Distributed Lagrange Multiplier/Fictious Domain (DLM/FD) two-phase flow solver. We evaluate the accuracy of our numerical method by comparison to analytic solutions and to generic test cases fully resolved by boundary fitted simulations. A previous theoretical model that couples the internal diffusion-reaction problem with the external advection-diffusion mass transfer in the fluid phase is extended to the configuration of three aligned spherical particles representative of a dilute particle-laden flow. Predictions of surface concentration, mass transfer coefficient and chemical effectiveness factor of catalyst particles are validated by DLM-FD/SIM simulations. We show that the model captures properly the effect of an internal first order chemical reaction on the overall respective reactive Sherwood number of each sphere depending on their relative positions. The proposed correlation for the reactive Sherwood number is based on an existing non-reactive Sherwood number correlation. The model can be later used in Euler/Lagrange or Euler/Euler modelling of dilute reactive particle-laden flows.

Application of Multiphase Flow Analysis based on Sharp Interface Method to Prediction of Behavior of Engine Oil

Application of Multiphase Flow Analysis based on Sharp Interface Method to Prediction of Behavior of Engine Oil

A computational model for molten corium spreading and solidification

When the core is breached during a severe nuclear accident, a molten mixture of nuclear fuel, cladding, and structural supports is discharged from the reactor vessel. This molten mixture of ceramic and metal is often referred to as “corium”. Predicting the flow and solidification of corium poses challenges for numerical models due to the presence of large Peclet numbers when convective transport dominates the physics. Here, we utilize a control volume finite-element method (CVEM) discretization to stabilize the advection dominated flow and heat transport. This CVFEM approach is coupled with the conformal decomposition finite-element method (CDFEM), which tracks the corium/air interface on an existing background mesh. CDFEM is a sharp-interface method, allowing the direct discretization of the corium front. This CVFEM-CDFEM approach is used to model the spreading of molten corium in both two- and three-dimensions. The CVFEM approach is briefly motivated in a comparison with a streamwise upwind/Petrov-Galerkin (SUPG) stabilized finite-element method, which was not able to suppress spurious temperature oscillations in the simulations. Our model is compared directly with the FARO L26 corium spreading experiments and with previous numerical simulations, showing both quantitative and qualitative agreement with those studies.

A radial basis function based ghost cell method with improved mass conservation for complex moving boundary flows

A sharp interface immersed boundary method is presented for simulating flows around moving boundaries with arbitrary complex geometries. A time semi-implicit finite difference method is used to solve the incompressible Navier–Stokes equations on a fixed, staggered Cartesian grid. The boundary conditions at the immersed interface are enforced by a ghost cell method. Tracking complex moving boundaries and suppressing pressure oscillations are two major challenges in the sharp interface method. In this work, a polynomial radial basis function (PRBF) is introduced to the ghost cell method to implicitly represent and reconstruct the arbitrary immersed boundaries. In addition, a simple and robust signed identification strategy is used to determine the phase state of the grid cells. To suppress violent pressure oscillations on the moving boundaries, a fractional area representation (FAR) method, together with a mass force term, is introduced to the pressure Poisson equation. This FAR method not only retains the desirable property of consistent discretization in the ghost cell method but also takes advantage of the mass conservation property of the cut cell method. The proposed method is validated using five test cases, including the flow around a hydrofoil, in-line oscillation of a cylinder in a static fluid, uniform flows around a transversely oscillating cylinder, twin oscillating cylinders, and a pitching hydrofoil. The present results are in good agreement with the reference results, which validates the accuracy and capability of the proposed method.

Numerical and analytical study of laminar film condensation in upward and downward vapor flows

Laminar film condensation in upward and downward vapor flows is numerically investigated by using a sharp-interface level-set method to track the condensate film surface and accurately calculating the phase-change mass flux under the saturation temperature condition at the interface. An analytical model for steady laminar film condensation in upward as well as downward vapor flows is developed to validate the present numerical results. As the vapor velocity increases, the condensation rate is observed to decrease in upward vapor flows whereas it increases in downward vapor flows. The effects of vapor velocity and wall temperature on laminar film condensation in upward and downward vapor flows are investigated.

FROM IIM TO AUGMENTED IIM: A POWERFUL TOOL FOR COMPLEX PROBLEMS USING CARTESIAN MESHES

The immersed interface method (IIM) ?rst proposed in is an accurate numerical method for solving elliptic interface problems on Cartesian meshes. It is a sharp interface method that was intended to improve accuracy of the immersed boundary (IB) method. The IIM is second order accurate in the maximum norm (pointwise, strongest) while the IB method is ?rst order accurate. The ?rst IIM paper is one of the most downloaded one from the SIAM website and is one of the most cited papers. While IIM provided a way of accurate discretization of the partial differential equations (PDEs) with discontinuous coefficients, the augmented IIM ?rst proposed in made the IIM much more efficient and faster by utilizing existing fast Poisson solvers. More important is that the augmented IIM provides an efficient way for multi-physics models with different governing equations, problems on irregular domains, multi-scales and multi-connected domains. A brie?y introduction of the augmented strategy including some recently progress is presented in this article.

An efficient, high-order method for solving Poisson equation for immersed boundaries: Combination of compact difference and multiscale multigrid methods

A new efficient and high-order accurate sharp-interface method for solving the Poisson equation on irregular domains and non-uniform meshes is presented. The approach is based on a combination of a fourth-order compact finite difference scheme and a multiscale multigrid (MSMG) method. The key aspect of the new method is that the regular compact finite difference stencil is modified at the irregular grid points near the immersed boundary to obtain a sharp interface solution while maintaining the formal fourth-order accuracy. The MSMG method is designed based on the standard multigrid V-cycle technique to solve the system of equations derived from the fourth-order compact discretization, while the corresponding multigrid relaxation, restriction and prolongation operators are properly constructed for non-uniform grids with immersed boundaries. The contribution of the present work is the design of a fourth-order-accurate Poisson solver whose accuracy, efficiency and computational cost are independent of the complexity of the geometry and the presence or not of an immersed boundary. The new method is demonstrated and validated for a number of problems including smooth and jagged boundaries. The test cases confirm that the new method is fourth-order accurate in the maximum norm whether an immersed boundary is present or not and on uniform or non-uniform meshes. Furthermore, the computational efficiency of the new method is demonstrated with regard to convergence rate and run time, which shows that the MSMG method is equally efficient for domains with immersed boundaries as for simple domains. The new compact difference method is evaluated by comparison with the standard fourth-order (non-compact) finite difference approximation in terms of both accuracy and computational efficiency. The new compact difference scheme yields indeed more accurate numerical solutions. The striking difference between the two schemes is the much higher computational efficiency: The number of V-cycles needed to reach the discretization error is significantly lower for the new compact method compared to the standard difference scheme. As a result, the new compact scheme requires only a fraction of the computer time for convergence in comparison to the standard fourth-order difference scheme.

An in-cell reconstruction finite volume method for flows of compressible immiscible fluids

We present a hybrid capturing/tracking method for finite volume solvers of compressible flows involving two immiscible fluids that are described by equations of states for ideal gases. The approach is an extension of the two-dimensional level set based in-cell-reconstruction method originally proposed by Smiljanovski et al. [1] for deflagration waves to three-dimensional flows involving interfaces between two immiscible fluids with surface tension forces. The interface motion is captured by an extension to the conservative, un-split geometric volume-of-fluid technique of Owkes and Desjardins [2]. The resulting method is a sharp interface method that avoids time-step restrictions or merging/mixing rules due to cut-cells by using cell-face-aperture averaged waves to update the volume averaged states of cells containing the interface directly. The method furthermore avoids the use of any mixed states in discretization stencils, by reconstructing the pure fluid states in each mixed cell, explicitly enforcing the jump conditions across the interface. Simulations of compressible flows that involve the interaction of shocks with interfaces between immiscible fluids are performed to demonstrate the performance of the proposed method.