Hybrid Finite Difference Research Articles

A Hybrid FDTD–SPICE Method for Predicting the Coupling Response of Wireless Communication System

This article presents a hybrid finite-difference time-domain–simulation program with integrated circuit emphasis (FDTD–SPICE) method for analyzing the system-level coupling responses of the wireless communication system with antenna, metallic enclosures, braided shielded cable, and lumped element, when illuminated by an external electromagnetic pulse (EMP). In the hybrid method, a system-level SPICE model combining antenna and braided coaxial cable is proposed to predict the coupling effects including front-door and back-door couplings. FDTD is used to calculate the induced current on the outer conductor of the coaxial cable, which is then incorporated into the system-level SPICE model as an additional current source. Because the hybrid method avoids meshing the antenna and cable, it has higher computational efficiency than full-wave analysis. A typical microstrip antenna system is selected as a case to demonstrate the accuracy and effectiveness of this proposed method by comparing the numerical results with those obtained by CST. Then, considering the influence of the incident conditions of external EMP, the coupling voltages of the microstrip antenna system are calculated. Furthermore, a typical filter circuit is analyzed to illustrate the practicability of the proposed method. The obtained coupling response information demonstrate that the proposed method is available for designing electromagnetic protection of the inner circuits of the wireless communication system against the impact of external incident wave.

Modeling the deformation of a surfactant-covered droplet under the combined influence of electric field and shear flow

A surfactant-covered droplet subject to both electric field and shear flow is studied using a lattice Boltzmann and finite difference hybrid method, which breaks the limitation of asymptotic approaches that allow only small droplet deformation. It is found that in the electric system where electric field induces circulating flows directed from equator to poles, the presence of surfactants promotes droplet deformation for each electric capillary number (CaE), whereas in the electric system where droplets exhibit a prolate shape and circulating flows are directed from poles to equator, the presence of surfactants hinders droplet deformation at high CaE. We also for the first time show that in the electric system where droplet exhibits an oblate shape, the presence of surfactants almost has no effect on droplet deformation at high CaE. Regardless of electric properties and CaE, the inclination angle of surfactant-covered droplets is always smaller than that of clean droplets.

Computational modeling of three-dimensional thermocapillary flow of recalcitrant bubbles using a coupled lattice Boltzmann-finite difference method

This study analyzes the thermocapillary flow of recalcitrant bubbles within thin channels using a hybrid finite difference lattice Boltzmann method (LBM). It extends a recently developed phase-field LBM to account for temperature effects by coupling the scheme with a fourth-order Runge–Kutta algorithm to solve the governing energy equation. The LBM makes use of a weighted-multiple relaxation-time collision scheme, which has been previously shown to capture high density and viscosity contrasts. This paper makes contributions in two fundamental areas relating to thermocapillary flow. First, it presents and verifies a novel, three-dimensional model to resolve thermocapillary dynamics for practical applications. The verification was undertaken via comparison with analytical solutions for the flow of immiscible fluids in a heated microchannel and for the migration of a droplet in a temperature field. Second, it provides new insight into the inherently three-dimensional nature of recalcitrant bubbles. It was found that the competing inertial and thermal effects allow these bubbles to propagate against the bulk motion of the liquid toward regions of low surface tension.

Development of an Advection-diffusion Model Using Depth-integrated Equations Based on GPU Acceleration

A scalar transport model is developed by adding a depth-averaged advection-diffusion equation to Celeris Advent, which is a Boussinesq-type numerical model that utilizes GPU acceleration. The hybrid finite volume-finite difference method is used to guarantee numerical stability along with the high accuracy of the Boussinesq equation. The advective and diffusive terms are numerically discretized using the finite volume and finite difference methods, respectively. Results of a one-dimensional scalar advection benchmark test showed that the scalar advection by the proposed model was very close to the analytical solution without any remarkable numerical diffusion. In addition, two benchmark tests using experimental data from different hydraulic experiments were numerically reproduced, and the computed results and observed data for scalar transport were found to be in good agreement. The developed model is expected to contribute to real-time disaster prediction for contaminant spills and can assist in preparing countermeasures for these types of disasters.

A general framework of high-resolution hybrid central/WENO numerical scheme for turbulent compressible simulation

This work presents a general framework of finite-difference hybrid scheme which contains a linear central scheme and a nonl-inear WENO scheme. A new optimal-designed shock sensor is used to distinguish the smoothness of flowfield and a binary-type weighting function is used to switch sub-schemes rationally. Based on the above improvements, the effects of different combinations of each component within the hybrid scheme are characterized in linear advection equation and Euler equations. The maximum reference threshold values are provided. Extensive test cases indicate the hybrid scheme’s numerical robustness, low-dissipation, and superior computational efficiency. Specifically, benefited from the high-resolution shock sensor which can accurately perceive shocks without excessive misidentifications, the hybrid scheme can achieve non-oscillatory solutions, and resolve more vortices in smooth regions compared to the original shock-capturing scheme. Meanwhile, the superiority of the hybrid scheme is further confirmed in the Reynolds-averaged Navier–Stokes equations/Lager Eddy Simulations (RANS/LES) for the DLR scramjet combustor case with viscous terms and/or sub-grid scale models are used. The present hybrid framework can be easily implemented within the existing numerical simulation code framework.

An almost second order hybrid scheme for the numerical solution of singularly perturbed parabolic turning point problem with interior layer

In this article, we consider a one dimensional singularly perturbed parabolic convection–diffusion problem with interior turning point. The convection coefficient of the considered problem is vanishing inside the spatial domain and also, exhibits an interior layer. As a result, the exact solution of the considered problem contains an interior layer. A higher order numerical method is constructed and analyzed for the numerical solution of the considered problem. To discretize the time direction, we have used the classical implicit Euler method on a uniform mesh. Also, a hybrid finite difference scheme is employed on a generalized Shishkin mesh condensing in the interior layer region to discretize the spatial domain. Rigorous analysis is performed to show that the proposed method is ε-uniformly convergent of order almost two. The higher accuracy and convergence rate of the proposed scheme are verified via implementing numerical experiments on two test problems. Comparison is done with the scheme proposed in O’Riordan and Quinn (2015) for the considered class of problems.

Efficient BTCS + CTCS Finite Difference Scheme for General Linear Second Order PDE

This work deals with a second order linear general equation with partial derivatives for a two-variable function. It covers a wide range of applications. This equation is solved with a finite difference hybrid method: BTCS + CTCS. This scheme is simple, precise, and economical in terms of time and space occupancy in memory.

Spline approximation method for singularly perturbed differential-difference equation on nonuniform grids

In this paper, a second-order singularly perturbed differential-difference equation involving mixed shifts is considered. At first, through Taylor series approximation, the original model is reduced to an equivalent singularly perturbed differential equation. Then, the model is treated by using the hybrid finite difference scheme on different types of layer adapted meshes like Shishkin mesh, Bakhvalov–Shishkin mesh and Vulanović mesh. Here, the hybrid scheme consists of a cubic spline approximation in the fine mesh region and a midpoint upwind scheme in the coarse mesh region. The error analysis is carried out and it is shown that the proposed scheme is of second-order convergence irrespective of the perturbation parameter. To display the efficacy and accuracy of the proposed scheme, some numerical experiments are presented which support the theoretical results.

Investigation of pull-in behavior of circular nanoplate actuator based on the modified couple stress theory

PurposeThis paper aims to present a nonclassical circular plate model subjected to hydrostatic pressure and electrostatic actuations by considering the modified couple stress theory and the surface elasticity theory. The pull-in phenomenon and nonlinear behavior of circular nanoplate are investigated.Design/methodology/approachThe hybrid differential transformation method (DTM) and finite difference method (FDM) are used to approach the model. The DTM was first applied to the equation with respect to the time, and then the FDM was applied with respect to the radius.FindingsThe numerical results were in agreement with the numerical data in the previous literature. The effects of the length scale parameters, surface parameters, thermal stress, residual stress, hydrostatic pressure and electrostatic actuations of the nonclassical circular plate on the pull-in instability are investigated. The parametric study demonstrated that the pull-in behavior of the circular nanoplate was size dependent.Originality/valueIn this study, the results provide a suitable method in a nonclassical circular plate model. The length scale parameter had an obvious effect on the nonlinear behavior of the circular nanoplate.

A Parallel FDTD/ADI-PE Method for Ultralarge-Scale Propagation Modeling of ILS Signal Analysis

In this letter, we propose a high-accuracy low-cost hybrid finite-difference time-domain (FDTD)/alternating-direction-implicit parabolic equation (ADI-PE) method for ultralarge-scale electromagnetic simulation on a distributed computing platform. The hybrid method offers fast and precise 3-D deterministic radio-wave propagation predictions in a difficult-terrain scenario with specific detailed structures in both near field and far field. Since the typical parallel ADI-PE method suffers from high-frequency data communication between different calculation cores, which greatly discount simulation efficiency in bandwidth-constrained environments, we adopt a Woodbury-formula-based parallel algorithm to find inverse matrixes of tridiagonal matrixes so that implicit and explicit steps of the PE can be finished in local computing cores. Simulation results for the instrument landing system (ILS) demonstrate the capability of the proposed method in achieving the state-of-the-art performance.

The Hybrid Finite Difference and Moving Boundary Methods for Solving a Linear Damped Nonlinear Schrödinger Equation to Model Rogue Waves and Breathers in Plasma Physics

In this paper, the dissipative and nondissipative modulated pulses such as rogue waves (RWs) and breathers (Kuznetsov-Ma breathers and Akhmediev breathers) that can exist and propagate in several fields of sciences, for example, plasma physics, have been analyzed numerically. For this purpose, the fluid dusty plasma equations with taking the kinematic dust viscosity into account are reduced to the linear damped nonlinear Schrödinger equation using a reductive perturbation technique. It is known that this equation is not integrable and, accordingly, does not have analytical solution. Thus, for modelling both dissipative RWs and breathers, the improved finite difference method is introduced for this purpose. It is found that FDM is a good numerical technique for small time interval but for large time interval it becomes sometimes unacceptable. Therefore, to describe these waves accurately, the new improved numerical method is considered, which is called the hybrid finite difference method and moving boundary method (FDM-MBM). This last and updated method gives an accurate and excellent description to many physical results, as it was applied to the dust plasma results and the results were good.

A fully coupled hybrid lattice Boltzmann and finite difference method-based study of transient electrokinetic flows.

Transient electrokinetic (EK) flows involve the transport of conductivity gradients developed as a result of mixing of ionic species in the fluid, which in turn is affected by the electric field applied across the channel. The presence of three different coupled equations with corresponding different time scales makes it difficult to model the problem using the lattice Boltzmann method (LBM). The present work aims to develop a hybrid LBM and finite difference method (FDM)-based model which can be used to study the electro-osmotic flows (EOFs) and the onset of EK instabilities using an Ohmic model, where fluid and conductivity transport are solved using LBM and the electric field is solved using FDM. The model developed will be used to simulate three different problems: (i) EOF with varying zeta-potential on the wall, (ii) similitude in EOF, and (iii) EK instabilities due to the presence of conductivity gradients. Problems (i) and (ii) will be compared with the analytical results and problem (iii) will be compared with the simulations of a spectral method-based numerical model. The results obtained from the present simulations will show that the developed model is capable of studying transient EK flows and of predicting the onset of instability.

An Efficient Low-Dissipation Hybrid Central/WENO Scheme for Compressible Flows

This paper develops a new hybrid finite difference scheme which consists of a nonlinear WENOCU4 scheme to maintain the numerical stability near discontinuities and a fourth-order linear central scheme elsewhere to accurately resolve smooth fluctuations and to speed up the computation. The central scheme is constructed in a robust skew-symmetric form which satisfies energy conservation property. A new efficient discontinuity detector is employed to identify the smoothness of the flowfield. As for the one-dimensional scalar equations, the hybrid scheme behaves almost no attenuation associated with propagation error. The quantitative analysis of the shock-capturing error is investigated. The hybrid scheme also exhibits high-resolution spectral property in the wavenumber space. Extensive cases of Euler equations further demonstrate the high-resolution shock-capturing ability of the detector, remarkable vortices-resolving capacity, and superior computational efficiency of the hybrid scheme. The reduced computational cost of the hybrid scheme is about 30−50% with respect to the baseline scheme.

A second-order adaptive grid method for a nonlinear singularly perturbed problem with an integral boundary condition

In this paper, a nonlinear singularly perturbed problem with an integral boundary condition is studied. A hybrid finite difference method based on the midpoint difference scheme and the upwind difference scheme is constructed. An adaptive grid generation algorithm is generated by equidistributing a monitor function. The convergence analysis of the hybrid difference method on the adaptive grid is derived. It is proved by theory and experiments that the scheme is second-order uniformly convergent, which improves previous results.

Nearshore coastal flow processes using weighted-averaged equations

This work uses the weighted residual method to simulate non-hydrostatic flows in ocean and coastal areas in a vertically-averaged framework. A Vertically-Averaged and Moment equations set is developed. The system is solved through a hybrid finite volume-finite difference numerical scheme to tackle the hyperbolic and elliptic parts of the equations. Data of seven challenging tests are used to evaluate the model ability to reproduce non-linearity, dispersion, wave breaking, bore propagation, sheet flow and wave reflection. The tests comprise propagation of sinusoidal waves over a submerged bar; convergence of the numerical scheme; solitary wave transformation over a dry reef flat, a wet reef flat and an exposed reef crest; collision of two solitary waves; and solitary wave reflection on a vertical wall under non-breaking and breaking conditions. The results highlight the accuracy of the model without prescribing any treatment for wave breaking. The conjunction of long and short waves with wave shoaling, run-up and receding flows is accurately reproduced. The model is considered an alternative tool to Boussinesq-type models to solve non-linear flows in the nearshore region, with the advantage of having an automatic mimic of wave breaking due to the field variables used to produce the weighted residual depth-averaged equations.

A Hybrid Finite Difference WENO-ZQ Fast Sweeping Method for Static Hamilton–Jacobi Equations

In this paper, we propose to combine a new fifth order finite difference weighted essentially non-oscillatory (WENO) scheme with high order fast sweeping methods, for directly solving static Hamilton–Jacobi equations. This is motivated by the work in Xiong et al. (J Sci Comput 45(1–3):514–536, 2010), where a fifth order fast sweeping method base on the classical finite difference WENO scheme is developed. Numerical results in Xiong et al. (2010) show that the iterative numbers of the scheme for some cases are very sensitive to the parameter $$\epsilon $$ , which is used to avoid the denominator to be 0 in the nonlinear weights. Here we propose to use the new fifth order finite difference WENO-ZQ scheme, which was recently developed in Zhu and Qiu (J Comput Phys 318:110–121, 2016), to alleviate this problem. Besides, to save computational cost from WENO reconstructions, a hybrid finite difference linear and WENO scheme is used, which works more robustly. Numerical experiments will be performed to demonstrate the good performance of the new proposed approach.

Single recalcitrant bubble simulation using a hybrid lattice boltzmann finite difference model

In this paper, 2D simulations of a single recalcitrant bubble using a hybrid finite difference lattice Boltzmann method are presented. To solve the flow field, the conservative phase field lattice Boltzmann model of Geier et al. (2015) is employed with a multi-relaxation-time (MRT) scheme which makes it capable of handling multiphase flows with high density and viscosity contrasts. A finite difference approach is applied to obtain the temperature field with a second-order spatial discretization (central) which marches in time with the 2nd order Runge-Kutta marching technique. The well-known continuum surface tension force (CSF) is implemented to define the thermocapillary force which depends on the temperature field. Before delving into the main aim of this work, we first assess the accuracy of the present model by verifying the Laplace law for a static bubble with four different values of surface tension. To further validate the model, thermocapillary migration of a deformable drop, and thermocapillary flow with two superimposed planar fluids are studied as our second and third benchmarks. Comparing the analytical solutions for both velocity and temperature fields with the simulation ones, good agreements are found. We then propose a simple theory with some simplification for the study of the migration of a single recalcitrant bubble, and after that weperform a series of 2D simulations to analyze the effects of density ratios, viscosity ratios, entrance average velocities of the flow, and the values of second derivative of surface tension with respect to the temperature.

Uniformly Convergent New Hybrid Numerical Method for Singularly Perturbed Parabolic Problems with Interior Layers

In this article, we deal with a class of singularly perturbed parabolic convection–diffusion initial-boundary-value problems having discontinuous convection coefficient. Aiming to get better numerical approximation to the solutions of this class of problems, we devise a new hybrid finite difference scheme on a layer-resolving piecewise-uniform Shishkin mesh in the spatial direction, and the time derivative is discretized by the backward-Euler method in the temporal direction. We discuss the stability of the proposed method and establish the parameter-uniform error estimate. Numerical results are also displayed to support the theoretical findings and compared with the existing hybrid scheme to show the improvement in terms of spatial order of convergence. Further, we carry out numerical experiment for the semi-linear parabolic initial-boundary-value problems.

Wave Fields and Nearshore Currents in the Coastal Region Opposite San Mauro Cilento (Italy)

In this paper in order to simulate nearshore currents in computational domains representing the complex morphology of real coastal regions we use a model based on a contravariant integral form of the fully nonlinear Boussinesq equations (FNBE). The contravariant integral form, in which Christoffel symbols are absent, of the continuity equation does not contain the dispersive term. The Boussinesq equation system is numerically solved by a hybrid finite volume-finite difference scheme. The wave breaking is represented by discontinuities of the weak solution of the integral form of the nonlinear shallow water equations (NSWE). The capacity of the proposed model to correctly simulate the wave train propagation on a highly distorted grid is verified against test case present in the literature. The simulation of wave fields and nearshore currents in the coastal region, opposite San Mauro Cilento (Italy) in presence of a system of T-head groins, is numerically reproduced by using the proposed model.

Uniform Hybrid Difference Scheme for Singularly Perturbed Differential-Difference Turning Point Problems Exhibiting Boundary Layers

In this paper, a class of linear second-order singularly perturbed differential-difference turning point problems with mixed shifts exhibiting two exponential boundary layers is considered. For the numerical treatment of these problems, first we employ a second-order Taylor’s series approximation on the terms containing shift parameters and obtain a modified singularly perturbed problem which approximates the original problem. Then a hybrid finite difference scheme on an appropriate piecewise-uniform Shishkin mesh is constructed to discretize the modified problem. Further, we proved that the method is almost second-order ɛ-uniformly convergent in the maximum norm. Numerical experiments are considered to illustrate the theoretical results. In addition, the effect of the shift parameters on the layer behavior of the solution is also examined.