Hybrid Numerical Methods Research Articles

Advancing Hybrid Numerical Methods for Nonlinear Stochastic Differential Equations: Applications in Complex Systems

The focus of this work is to consider composite numerical techniques for the approximation of SDEs with nonlinear coefficients in the drift and diffusion terms. SDEs, crucial for modeling systems with stochastic components, contain nonlinear terms that cause analytical solvability, numerical stiffness, and sensitivity to noise. These difficulties pose a problem for traditional techniques such as Euler-Maruyama or Milstein schemes, specifically in stiff or very nonlinear systems. Accompanying exact methods are numerical methods that include a deterministic synthesis of drift terms and a stochastic interpolation of diffusion terms with the purpose of increasing precision and stability and optimizing used computing time. Discussed approaches include implicit-explicit (IMEX) schemes, spectral collocation methods, and machine learning-assisted techniques. IMEX methods handle stiffness in nonlinear drift terms implicitly, while explicitly handling stochastic diffusion. Spectral-collocation methods utilize high-order polynomial approximations for accuracy in discretization where solutions are smooth and defined in a bounded domain. The combination of these techniques and machine learning extends SDE analysis and concentrates on SDE nonlinearities as well as adaptive solution strategies. They find use in every area of discipline, such as stochastic volatility models in finance, population dynamics in biology, and turbulent fluid flows in engineering. Simulation results show that hybrid schemes outperform other methods in terms of accuracy, stability, and computational expense. This work outlines how the integration of the suggested methods can overcome the shortcomings of the classic approaches so as to enable progression in solving complex, high-dimensional, and nonlinear stochastic problems. Subsequent studies will continue to investigate additional adaptive frameworks and more domain-specific and machine learning-based improvements to expand the spectrum of hybrid use.

Modeling of a metal hydride energy storage tank dynamics using hybrid numerical, experimental, and machine learning methods

This study presents an integrated analysis combining numerical simulations, experimental investigations, and machine learning models to simulate the performance of metal hydride systems for hydrogen storage under various conditions by using a LaNi5 metal hydride cylindrical tank of 500 NL capacity, with a focus on PCM thermal enhancements and surface water heating and cooling. Numerical simulations offer insights into thermal and reaction dynamics, while experimental data are used for model validation and supplemented with additional numerical data for training a FFNN model to predict dynamic hydrogen flow, surface temperature, and surface heat flux. The obtained mean RMSEs for charging/discharging experimental data is 2.8 SOC% for the state of charge and 0.3 °C for surface temperatures. The study compares the effectiveness of water cooling and heating in metal hydride surface across different temperatures, highlighting their impact on the efficiency of hydrogen absorption and desorption processes. Energy consumption is shown to be non-linear; during charging, heat flux peaks before decreases rapidly within around 0.2 h. During discharging, heat flux rises steadily. The study also explores the impact of adding copper fins to the PCM covering metal hydride system, revealing significant improvements in charging and discharging efficiency, specifically, the integration of 16 copper fins led to a notable decrease in complete charging time from approximately 6.5 h to just over 5.2 h, and in complete discharging time from around 4.5 h to under 3.96 h. Using PCM, the highest heat flux is 5 times less during charge and 2 times less during discharge than that for water cooling mode.

A Closed-Form Inverse Kinematic Analytical Method for Seven-DOF Space Manipulator with Aspheric Wrist Structure

The seven-degree-of-freedom space manipulator, characterized by its redundant and aspheric wrist structure, is extensively used in space missions due to its exceptional dexterity and multi-joint capabilities. However, the non-spherical wrist structure presents challenges in solving inverse kinematics, as it cannot decouple joints using the Pieper criterion, unlike spherical wrist structures. To address this issue, this paper presents a closed-form analytical method for solving the inverse kinematics of seven-degree-of-freedom aspheric wrist space manipulators. The method begins by identifying the redundant joint through comparing the volumes of the workspace with different joints fixed. The redundant joint angle is then treated as a parametric joint angle, enabling the derivation of closed-form expressions for the non-parametric joint angles using screw theory. The optimal solution branch is identified through a comparative analysis of various self-motion manifold branches. Additionally, a hybrid approach, combining analytical and numerical methods, is proposed to optimize the parametric joint angle for a trajectory tracking task. Simulation results confirm the effectiveness of the proposed method.

Simultaneous space–time Hermite wavelet method for time-fractional nonlinear weakly singular integro-partial differential equations

An innovative simultaneous space–time Hermite wavelet method has been developed to solve weakly singular fractional-order nonlinear integro-partial differential equations in one and two dimensions with a focus whose solutions are intermittent in both space and time. The proposed method is based on multi-dimensional Hermite wavelets and the quasilinearization technique. The simultaneous space–time approach does not fully exploit for time-fractional nonlinear weakly singular integro-partial differential equations. Subsequently, the convergence analysis is challenging when the solution depends on the entire time domain (including past and future time), and the governing equation is combined with Volterra and Fredholm integral operators. Considering these challenges, we use the quasilinearization technique to handle the nonlinearity of the problem and reconstruct it to a linear integro-partial differential equation with second-order accuracy. Then, we apply multi-dimensional Hermite wavelets as attractive candidates on the resulting linearized problems to effectively resolve the initial weak singularity at t=0. In addition, the collocation method is used to determine the tensor-based wavelet coefficients within the decomposition domain. We elaborate on constructing the proposed simultaneous space–time Hermite wavelet method and design comprehensive algorithms for their implementation. Specifically, we emphasize the convergence analysis in the framework of the L2 norm and indicate high accuracy dependent on the regularity of the solution. The stability of the proposed wavelet-based numerical approximation is also discussed in the context of fractional-order nonlinear integro-partial differential equations involving both Volterra and Fredholm operators with weakly singular kernels. The proposed method is compared with existing methods available in the literature. Specifically, we highlighted its high accuracy and compared it with a recently developed hybrid numerical approach and finite difference methods. The efficiency and accuracy of the proposed method are demonstrated by solving several highly intermittent time-fractional nonlinear weakly singular integro-partial differential equations.

Hybrid intelligent and numerical methods to estimate the transmission coefficients of rectangular floating breakwaters

ABSTRACT Breakwaters are used to reduce incoming wave energy at harbors and shorelines. This paper presents a comparison of novel two-dimensional hybrid intelligent models for the idealization of the effects of waves on the performance of moored rectangular floating breakwaters (FBs). Fluid structure interactions (FSIs) were idealized by airy-type monochromatic regular waves generated in a numerical wave tank. The coupled Volume of Fluid-Fast Fictitious Domain (VOF-FFD) interpolation method was used to evaluate FB motions. Different forms of Least Squares Support Vector Machine Methods (LSSVMs) that utilized 183 data streams were used to model FB performance for different wave height-to-water depth ratios, dimensional aspect ratios, and specific length-to-water depth ratios. Of those, 80% were used to train the model and 20% to test it. Parametric studies have shown that during training a Least Squares Support Vector Machine Method-Bat Algorithm (LSSVM-BA) with R2 = 0.8725, MAE = 0.0276, and RMSE = 0.0488 presents the most appropriate model for the evaluation of FB performance. Notwithstanding this, during testing a Least Squares Support Vector Machine Method-Cuckoo Search (LSSVM-CS) Algorithm with corresponding values of 0.6841, 0.0519, and 0.0708 performs better.

Hybrid numerical methods for modelling multi-physics mass transport in coal

It is a challenging task to predict and analyse the transient flow physics in unconventional complex geological formations such as coal seams. This is due to the multi-scale multi-physics nature of processes taking place in coal seam gas reservoirs. Therefore, numerical tools allowing the incorporation of various flow physics inherent to coal into the simulation routine are of particular importance. At the pore-scale, the rock images obtained by micro-computed tomography are frequently used for flow modelling in porous or fractured media by direct numerical simulations (Lattice Boltzman method or by solving Navier Stokes equations) or by utilising so-called pore-network modelling. Both methods have advantages and drawbacks, while their hybridisation may allow us avoid some of the major pitfalls. Due to a limited number of research dedicated to image-based pore-scale modelling in coal, we develop a hybrid numerical model that combines the Hagen-Poiseuille analytical solution and the volume of fluid advection scheme for fluid flow in fractures with the continuum Darcy flow in the coal matrix. The explicit coupling of fluid flow across the fracture-matrix domains is implemented via corresponding source terms in the governing equations. Besides, additional physics including sorption and matrix swelling-shrinkage phenomena are introduced into the numerical model. The hybrid solver is validated against analytical solutions and a previously developed Darcy-Brinkman-Stokes framework, which has similar functionality for modelling fluid flow in coal seams. To validate the developed model and show its capability to capture multi-scale multi-physics flow in coal, several illustrative simulations are conducted using synthetic and realistic digital images of coal. As a result, the accuracy of the hybrid solver was within 4% when compared to the Darcy-Brinkman-Stokes framework for flow simulation on realistic geometry. Besides, the non-parallelised hybrid model outperformed the parallelised direct numerical simulation, being more than 90 times faster in terms of computational time. The findings are beneficial for conducting larger core-scale simulations of multi-scale multi-physics flow in coal seams with potential applications to natural gas production, hydrogen storage, and carbon dioxide geosequestration.

Particle Swarm Optimization of Resonant Sonic Crystals Noise Barriers

The study of technological materials made by meticulously arranging acoustic elements has received a lot of attention over the past three decades with the goal of generating improved acoustic properties, often going beyond the behavior of materials found in nature. These are frequently referred to as acoustic metamaterials, and because of the way wave propagation phenomena is managed, they exhibit unusual properties. Improvements in noise mitigation techniques of acoustic systems based on metamaterials principles have been made effectively and precisely using combined or hybrid numerical methods and improved numerical formulations. These noise mitigation properties should be optimized by modifying topology and inner elements properties, which requires a huge search space. This work focuses on metamaterials called sonic crystals with Helmholtz resonators, and its innovative insulation properties as noise barriers are optimized with the Particle Swarm Optimization (PSO). This evolutionary algorithm provides a mono objective solution for the multi-dimensional search space inspired in animal behavior looking for food and communicating between each other. In order to assess the results obtained by the proposed approach, the presented PSO algorithm is compared with a Genetic Algorithm (GA): the results show that the PSO algorithm provides a better solution that pursues the objective of satisfying the acoustic comfort without exceeding the imposed practical constraints.

A high-fidelity solver based on hybrid numerical methods on unstructured grids for incompressible multiphase flows

A high-fidelity solver is developed on the unstructured grids to simulate incompressible multiphase flows with free surface based on volume of fluid (VOF) method. In this framework, the velocity is defined by both volume integrated average (VIA) and point value (PV) as computational variables which are updated simultaneously by volume-average/point-value multi-moment (VPM) method at each time step. Compared with our previous work, a node-based finite element (FE) method is used instead of cell-centered finite volume (FV) method for the discretization of pressure Poisson equation, which provides a new pattern that can naturally treat with the velocity and pressure coupling. It does not require Rhie–Chow interpolation or the use of a Petrov–Galerkin finite element formulation with tunable parameters to circumvent the well-known instability conditions. Moreover, we propose a novel balanced-force formulation with FE discretization to accommodate the surface tension force, which effectively eliminates the large numerical errors associated with the non-orthogonality of unstructured grids. In VOF method, the volume fraction is defined as VIA to identify the moving interface which is updated by solving advection equation through the FV formulation. The resulting model that combines hybrid discretizations, rigorously preserves the mass and momentum conservation, substantially improves the numerical accuracy and robustness of pressure field, and significantly suppresses the spurious velocity to nearly machine error even for multiphase flows with large density ratios. Various numerical examples have been presented to demonstrate the excellent capabilities of present solver which can provide high-fidelity solutions for practical applications in presence of largely deformed interface and highly complex geometry.

Probabilistic Resource Assessment of The Ulumbu Geothermal Field, East Nusa Tenggara, Indonesia

DOI:10.17014/ijog.9.2.183-193A resource assessment of the Ulumbu Geothermal Field, East Nusa Tenggara, Indonesia, is proposed here. The fundamental issue of reserve estimation is determining the optimum capacity to be installed (field size) that affects the decision-making in geothermal projects. The reservoir numerical model and heat stored method are the most appropriate tools for geothermal resource assessment. Therefore, the hybrid numerical simulation and heat stored methods, coupled with the probabilistic approach, are applied to Ulumbu. Based on the calibrated numerical model, the estimation of the reservoir is divided into the steam zone and liquid reservoir. The energy reserve of the Ulumbu is estimated by Monte Carlo simulation with the results P10-P50-P90 are 71 MWe, 95 MWe, and 127 MWe, respectively

The FEM‐BCI methods in EMC applications

AbstractThe paper reviews the finite element method‐boundary condition iteration family of hybrid numerical methods and shows their use in some electromagnetic problems arising in electromagnetic compatibility applications, ranging from static and quasi static to dynamic ones.

An efficient soil water balance model based on hybrid numerical and statistical methods

Most soil water balance models only consider downward soil water movement driven by gravitational potential, and thus cannot simulate upward soil water movement driven by evapotranspiration especially in agricultural areas. In addition, the models cannot be used for simulating soil water movement in heterogeneous soils, and usually require many empirical parameters. To resolve these problems, this study derives a new one-dimensional water balance model for simulating both downward and upward soil water movement in heterogeneous unsaturated zones. The new model is based on a hybrid of numerical and statistical methods, and only requires four physical parameters. The model uses three governing equations to consider three terms that impact soil water movement, including the advective term driven by gravitational potential, the source/sink term driven by external forces (e.g., evapotranspiration), and the diffusive term driven by matric potential. The three governing equations are solved separately by using the hybrid numerical and statistical methods (e.g., linear regression method) that consider soil heterogeneity. The four soil hydraulic parameters required by the new models are as follows: saturated hydraulic conductivity, saturated water content, field capacity, and residual water content. The strength and weakness of the new model are evaluated by using two published studies, three hypothetical examples and a real-world application. The evaluation is performed by comparing the simulation results of the new model with corresponding results presented in the published studies, obtained using HYDRUS-1D and observation data. The evaluation indicates that the new model is accurate and efficient for simulating upward soil water flow in heterogeneous soils with complex boundary conditions. The new model is used for evaluating different drainage functions, and the square drainage function and the power drainage function are recommended. Computational efficiency of the new model makes it particularly suitable for large-scale simulation of soil water movement, because the new model can be used with coarse discretization in space and time.

An integrated particle model for fluid–particle–structure interaction problems with free-surface flow and structural failure

Discrete Element Method (DEM) and Smoothed Particles Hydrodynamics (SPH) are integrated to investigate the macroscopic dynamics of fluid–particle–structure interaction (FPSI) problems. With SPH the fluid phase is represented by a set of particle elements moving in accordance with the Navier–Stokes equations. The solid phase consists of physical particle(s) and deformable solid structure(s) which are represented by DEM using a linear contact model and a linear parallel contact model to account for the interaction between particle elements, respectively. To couple the fluid phase and solid particles, a local volume fraction and a weighted average algorithm are proposed to reformulate the governing equations and the interaction forces. The structure is coupled with the fluid phase by incorporating the structure’s particle elements in SPH algorithm. The interaction forces between the solid particles and the structure are computed using the linear contact model in DEM. The proposed model is capable of simulating simultaneously fluid–structure interaction (FSI), particle–particle interaction and fluid–particle interaction (FPI), with good agreement between complicated hybrid numerical methods and experimental results being achieved. Finally, a specific test is carried out to demonstrate the capability of the integrated particle model for simulating FPSI problems with the occurrence of structural failure.

Hybrid numerical methods combining discretized multidimensional and segmented-quasi-one-dimensional models for simulating thermofluid systems

Purpose – The purpose of this paper is to first present the key features of hybrid numerical methods that enable cost-effective simulations of complex thermofluid systems, and then demonstrate the formulation and application of such a method. Design/methodology/approach – A hybrid numerical method is formulated for simulations of a closed-loop thermosyphon operating with slurries of a micro-encapsulated phase-change material suspended in distilled water. The slurries are modeled as homogeneous mixtures, with inputs of effective properties and overall heat-loss coefficients. Combinations of an axisymmetric two-dimensional (2D) control-volume finite-element method and a segmented-quasi-one-dimensional (1D) model are used to achieve cost-effective simulations. Proper matching of the solutions at the interfaces between adjacent axisymmetric 2D and quasi-1D zones is ensured by incorporating and heuristically determining suitable lengths of pre- and post-heating (and also pre- and post-cooling) sections. Findin...

Occupational exposure of personnel operating military radio equipment: measurements and simulation

Technical literature provides numerous studies concerning radiofrequency exposure measurements for various radio communication devices, but there are few studies related to exposure of personnel operating military radio equipment. In order to evaluate exposure and identify cases when safety requirements are not entirely met, both measurements and simulations are needed for accurate results. Moreover, given the technical characteristics of the radio devices used in the military, personnel mainly operate in the near-field region so both measurements and simulation becomes more complex. Measurements were made in situ using a broadband personal exposimeter equipped with two isotropic probes for both electric and magnetic components of the field. The experiment was designed for three different operating frequencies of the same radio equipment, while simulations were made in FEKO software using hybrid numerical methods to solve complex electromagnetic field problems. The paper aims to discuss the comparative results of the measurements and simulation, as well as comparing them to reference levels specified in military or civilian radiofrequency exposure standards.

A Hierarchy of Hybrid Numerical Methods for Multiscale Kinetic Equations

In this paper, we construct a hierarchy of hybrid numerical methods for multi-scale kinetic equations based on moment realizability matrices, a concept introduced by Levermore, Morokoff, and Nadiga in [Phys. Fluids, 10 (1998), pp. 3214--3226]. Following such a criterion, one can consider a hybrid scheme where the hydrodynamic part is given either by the compressible Euler or Navier--Stokes equations, or even with more general models, such as the Burnett or super-Burnett systems.

Multiscale Fluid Mechanics and Modeling

In recent years, there has been a tremendous growth of activity on multiscale modeling and computation. In particular, the multiscale hybrid numerical methods are those that combine multiple models defined at fundamentally different length and time scales within the same overall spatial and temporal domain. For examples, a framework of hybrid continuum and molecular dynamics multiscale method has been developed to simulate micro- and nanoscale fluid flows, which combines the continuum computational fluid dynamics (CFD) or the mesoscopic lattice Boltzmann method for the bulk flow region and the atomistic molecular dynamics for the interface region. The similar idea of constrained variation has also been used in developing multiscale fluid turbulent models for constrained dynamic subgrid-scale stress model, Reynolds stress constrained large eddy simulation (RSC-LES) for wall-bounded turbulent flows with massive separation and heat flux constrained large eddy simulation. For RSC-LES, our model is able to solve the traditional log-layer mismatch problem in RANS/LES approaches and can predict mean velocity, turbulent stress and skin friction coefficients more accurate than pure dynamic large eddy models and traditional detached eddy simulation using the same grid resolution. Our results demonstrate the capability of multiscale simulation methods for complex fluid systems and the necessity of physical constraints on the multiscale methods.

CONTINUOUS y-FUNCTION HYBRID METHODS FOR DIRECT SOLUTION OF DIFFERENTIAL EQUATIONS

The aim of this study is to produce consistent two-step y-function hybrid numerical methods for a direct solution of general second-order differential equations. The basis function is interpolated at both grid and off-grid points and its associated differential system are collocated at all grid points. The method developed is continuous, consistent and symmetric. The results show that the proposed method is better when compared with existing methods.

Hybrid numerical methods to solve shallow water equations for hurricane induced storm surge modeling

In this paper an efficient numerical method based on hybrid finite element and finite volume techniques to solve hurricane induced storm surge flow problem is presented. A segregated implicit projection method is used to solve the 2D shallow water equations on staggered unstructured meshes. The governing equations are written in non-conservation form. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centered finite volume method. The nonlinear wave equation is solved by the node-based Galerkin finite element method. This staggered-mesh scheme is distinct from other conventional approaches in that the velocity components and auxiliary variables are stored at cell centers and vertices, respectively. The present model uses an implicit method, which is very efficient and can use a large time step without losing accuracy and stability.The hurricane induced wind stress and pressure, bottom friction, Coriolis effect, and tidal forcing conditions are implemented in this model. The levee overtopping option is implemented in the model as well. Hurricane Katrina (2005) storm surge has been simulated to demonstrate the robustness and applicability of the model.

Improved Two-Dimensional Dynamic Stall Prediction with Structured and Hybrid Numerical Methods

A joint comprehensive validation activity on the structured numerical method elsA and the hybrid numerical method TAU was conducted with respect to dynamic stall applications. To improve two-dimensional prediction, the influence of several factors on the dynamic stall prediction was investigated. The validation was performed for three deep dynamic stall test cases of the rotor blade airfoil OA209 against experimental data from two-dimensional pitching airfoil experiments, covering low-speed and high-speed conditions. The requirements for spatial discretization and for temporal resolution in elsA and TAU are shown. The impact of turbulence modeling is discussed for a variety of turbulence models ranging from one-equation Spalart–Allmaras-type models to state-of-the-art, seven-equation Reynolds stress models. The influence of the prediction of laminar/turbulent boundary layer transition on the numerical dynamic stall simulation is described. Results of both numerical methods are compared to allow conclusions to be drawn with respect to an improved prediction of dynamic stall.

Hybrid Multiscale Methods II. Kinetic Equations

In this work we consider the development of a new family of hybrid numerical methods for the solution of kinetic equations which involves different scales. The basic idea is to couple macroscopic and microscopic models in all cases in which the macroscopic model does not provide correct results. The key aspect in the development of the algorithms is the choice of a suitable hybrid representation of the solution and a merging of Monte Carlo methods in nonequilibrium regimes with deterministic methods in equilibrium ones. This approach permits us to treat efficiently both the microscopic and the macroscopic scales. Applications to the Boltzmann–BGK equation are presented to show the performance of the new methods.