Multiphysics Problems Research Articles

Investigations concerning the effects of thermal radiation, induced magnetic field, and chemical reaction on MHD flow through a permeable medium

This paper focuses on the effects of heat radiation and chemical reactions on naturally occurring convective MHD flow that conducts electricity when there is an induced magnetic field present between two vertical walls having a porous medium between them. An analytical method is adopted to investigate the impacts of all pertinent parameters concerning the presented multi-physics problem. With the aid of relevant conversions, the nonlinear PDEs are remodeled into nonlinear ODEs.The effects of radiation parameters, Hartmann number, Hall current, chemical reaction and porosity parameters are scrutinized on velocity components, induced magnetic field, and current density. The results predict that the temperature profile decreases as the radiation factor rises, whereas the induced magnetic field would exhibit the opposite pattern. The profiles of component velocity get more intense for high rates of the porosity parameter. Additionally, profiles of induced magnetic field surges with elevated chemical reaction parameter values have been noted. The presented approach is very promising for multi-physics phenomena like chemical reactors and solar thermal devices.

Extended isogeometric analysis of multi-material and multi-physics problems using hierarchical B-splines

Extended isogeometric analysis of multi-material and multi-physics problems using hierarchical B-splines

Actin based motility unveiled: How chemical energy is converted into motion

Actin-based motility is a complex process in which the actin-polymerization is the primary force-generating motor machinery. It can produce protrusive forces through actin filaments polymerization and cross-link during lamellipodia protrusion in migrating cells and it is responsible for the intracellular motion of certain pathogens in infected host cells. We propose a multi-physics model for actin-based motility, stemming from continuity equations that account for the actin chemical kinetics. Thermodynamic restrictions are identified, moving from the multiplicative decomposition of the deformation gradient into chemical and elastic parts. Constitutive theory and chemical kinetics are prescribed to finally write governing equations for the multi-physics problem. The field equations are solved numerically with the finite element method. As a proof of concept, a one-dimensional model for actin-based motility of bacteria pathogens is studied.

3D frictional contact of graded magneto-electro-elastic film-substrate system under electromagnetic fields

The 3D frictional contact model of graded magneto-electro-elastic (MEE) film-substrate system under electromagnetic fields is presented. The semi-analytical method (SAM) is used to solve this multi-physical contact problem. Firstly, the frequency response functions (FRFs) for every layer of MEE material subjected to unit mechanical, electric and magnetic loads are derived. Conjugate gradient method (CGM) is then employed to obtain contact responses with Discrete convolution-fast Fourier transformation (DC-FFT) speeding related calculations. Finally, multilayered model is used to approximate graded film with two types of grads, exponentially varying grad (EVG) and volume-fraction varying grad (FVG), the effects of the type and thickness of graded film and the friction coefficient are investigated. The results show that EVG film with gradient index less than one or FVG film with smaller volume fraction of piezoelectric phase at the surface are preferred for the MEE film-substrate systems.

A Modified Constitutive Model for Shape Memory Polymers Based on Nonlinear Thermo-Visco-Hyperelasticity with Application to Multi-Physics Problems

Shape memory polymers (SMPs) as a class of smart material have provided diverse attributes recently used in different applications. Raising the usage of SMPs, especially in more sensitive environments, such as the human body or similar high-risk circumstances, highlights the necessity of more accurate simulations. Suitable constitutive modeling is the foundation of an accurate simulation. Not only should such modeling consider precise details to diminish errors, but also it must provide a robust and powerful procedure to calibrate the material parameters. To achieve these goals, in this paper a modified constitutive model for SMPs based on the concept of internal state variables and rational thermodynamics is proposed in large deformation. Taking its basis from the nonlinear hyperelasticity and viscoelasticity, the model can provide a more accurate prediction of SMPs response. In comparison to other available constitutive models based on viscoelastic approach, the number of material parameters is smaller. Furthermore, performing a new approach for material parameters extraction, two different SMP materials were calibrated. The proposed model’s capability was assessed by comparing the model outputs with experimental results in diverse conditions such as different temperature rates and applied stretch ratios. The user-friendly implementation process of this model in multi-physics software based on the finite element method can be counted as another advantage of the proposed model. Hence, to simulate smart systems containing SMP elements, three multi-physics analyses in various fields and conditions were performed, and the importance of conducting such multi-physics phenomena has been discussed.

Intelligent modeling with physics-informed machine learning for petroleum engineering problems

The advancement in big data and artificial intelligence has enabled a novel exploration mode for the study of petroleum engineering. Unlike theory-based solution methods, the data-driven intelligent approaches demonstrate superior flexibility, computational efficiency and accuracy for dealing with complex multi-scale, and multi-physics problems. However, these intelligent models often disregard physical laws in pursuit of error minimization, which leads to certain uncertainties. Therefore, physics-informed machine learning approaches have been developed based on data, guided by physics, and supported by machine learning models. This study summarizes four embedding mechanisms for introducing physical information into machine learning models, including input databased embedding, model architecture-based embedding, loss function-based embedding, and model optimization-based embedding mechanism. These “data + physics” dualdriven intelligent models not only exhibit higher prediction accuracy while adhering to physic laws, but also accelerate the convergence to improve computational efficiency. This paradigm will facilitate the guide developments in solving petroleum engineering problems toward a more comprehensive and efficient direction. Cited as: Xie, C., Du, S., Wang, J., Lao, J., Song, H. Intelligent modeling with physics-informed machine learning for petroleum engineering problems. Advances in Geo-Energy Research, 2023, 8(2): 71-75. https://doi.org/10.46690/ager.2023.05.01

Reduced Order Modeling of Nonlinear Vibrating Multiphysics Microstructures with Deep Learning-Based Approaches

Micro-electro-mechanical-systems are complex structures, often involving nonlinearites of geometric and multiphysics nature, that are used as sensors and actuators in countless applications. Starting from full-order representations, we apply deep learning techniques to generate accurate, efficient, and real-time reduced order models to be used for the simulation and optimization of higher-level complex systems. We extensively test the reliability of the proposed procedures on micromirrors, arches, and gyroscopes, as well as displaying intricate dynamical evolutions such as internal resonances. In particular, we discuss the accuracy of the deep learning technique and its ability to replicate and converge to the invariant manifolds predicted using the recently developed direct parametrization approach that allows the extraction of the nonlinear normal modes of large finite element models. Finally, by addressing an electromechanical gyroscope, we show that the non-intrusive deep learning approach generalizes easily to complex multiphysics problems.

Large surface deformation due to thermo-mechanical effects during cryopreservation by vitrification - mathematical model and experimental validation.

This study presents a simplified thermal-fluids (TF) mathematical model to analyze large surface deformations in cryoprotective agents (CPA) during cryopreservation by vitrification. The CPA deforms during vitrification due to material flow caused by the combined effects of thermal gradients within the domain, thermal contraction due to temperature, and exponential increase in the viscosity of the CPA as it is cooled towards glass transition. While it is well understood that vitrification is associated with thermo-mechanical stress, which might lead to structural damage, those large deformations can lead to stress concentration, further intensifying the probability to structural failure. The results of the TF model are experimentally validated by means of cryomacroscopy on a cuvette containing 7.05M dimethyl sulfoxide (DMSO) as a representative CPA. The TF model presented in this study is a simplified version of a previously presented thermo-mechanics (TM) model, where the TM model is set to solve the coupled heat transfer, fluid mechanics and solid mechanics problems, while the TF model omits further deformations in the solid state. It is demonstrated in this study that the TF model alone is sufficient to capture large-body deformations during vitrification. However, the TF model alone cannot be used to estimate mechanical stresses, which become significant only when the deformation rates become so small that the deformed body practically behaves as an amorphous solid. This study demonstrates the high sensitivity of deformation predictions to variation in material properties, chief among which are the variations of density and viscosity with temperature. Finally, this study includes a discussion on the possibility of turning on and off the TF and TM models in respective parts of the domain, in order to solve the multiphysics problem in a computationally cost-effective manner.

Time-Dependent Numerical Modelling of Acoustic Cavitation in Liquid Metal Driven by Electromagnetic Induction

The numerically simulated method of using electromagnetic field from an alternating current is a patented method to create in liquid metal, under the conditions of resonance, acoustic waves of sufficient strength to cause cavitation and implosion of gas bubbles, leading to beneficial degassing and grain refinement. The modelling stages of electromagnetics are described below along with acoustics in liquids, bubble dynamics, and their interactions. Sample results are presented for a cylindrical container with liquid aluminium surrounded by an induction coil. The possibility of establishing acoustic resonance and sustaining the bubble oscillation at a useful level is demonstrated. Limitations of the time-dependent approach to this multi-physics modelling problem are also discussed.

An adaptive wavelet method for nonlinear partial differential equations with applications to dynamic damage modeling

Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet-based technique to solve a coupled system of nonlinear partial differential equations (PDEs) while resolving features on a wide range of spatial and temporal scales. The algorithm exploits the multiresolution nature of wavelet basis functions to solve initial-boundary value problems on finite domains with a sparse multiresolution spatial discretization. By leveraging wavelet theory and embedding a predictor-corrector procedure within the time advancement loop, we dynamically adapt the computational grid and maintain accuracy of the solutions of the PDEs as they evolve. Consequently, our method provides high fidelity simulations with significant data compression. We present verification of the algorithm and demonstrate its capabilities by modeling high-strain rate damage nucleation and propagation in nonlinear solids using a novel Eulerian-Lagrangian continuum framework.

Simulation for magnetic force impact on nanomaterial transportation through a porous closed curved container as a multi physics problem

It is a practical application to use porous zones for cooling systems of magnetic sensors. The importance of MHD (Magnetohydrodynamic) on the irreversibility of liquid within a chamber consisting of porous zone has been incorporated in current article. CVFEM (Control Volume based Finite Element Method) has been employed to model the simplified model obtained after employing the vorticity formula. Outputs indicated that the intensity of nanomaterial circulation increases as Ra increases, while it decreases with the inclusion of a magnetic field, which converts the heat transmission mode to conduction, and due to the appearance of a stretching eddy, the heat plume is removed. A reduction in permeability reflects an increase in the exergy drop, which means greater thermal irreversibility. A nonessential impact on the Bejan number (Be) distribution was reported with altering Darcy number (Da) if the buoyancy force was negligible. Regardless of the changing maximum magnitude of Be, augmenting Da results in lower Be. Due to the dependence of Nusselt number (Nu) on the inner surface temperature, Hartmann number (Ha) has a reverse relation with Nu, which means a lower cooling rate with the inclusion of Ha.

Conformable finite element method for conformable fractional partial differential equations

<abstract><p>The finite element (FE) method is a widely used numerical technique for approximating solutions to various problems in different fields such as thermal diffusion, mechanics of continuous media, electromagnetism and multi-physics problems. Recently, there has been growing interest among researchers in the application of fractional derivatives. In this paper, we present a generalization of the FE method known as the conformable finite element method, which is specifically designed to solve conformable fractional partial differential equations (CF-PDE). We introduce the basis functions that are used to approximate the solution of CF-PDE and provide error estimation techniques. Furthermore, we provide an illustrative example to demonstrate the effectiveness of the proposed method. This work serves as a starting point for tackling more complex problems involving fractional derivatives.</p></abstract>

An efficient AMG based composite solver for the fully coupled solution of the large scale ion flow field problem

• The authors provide more details for the mathematical description of the ion flow field problem and explain the irregularity introduced by the Kapzov hypothesis. • The comparison of the iteration costs under the unipolar and the bipolar cases are present to verify the efficiency of the present method. • The misleading statement about the scalability is rephrased. • The capitalization problems and other typos are revised according to the reviewers’ comments. As the configuration of the HVDC transmission line model becomes more complex, the size of the discretized ion flow field problem grows up to an extremely large degree and the computational time needed for solving the linear system is unacceptable. The algebraic multigrid method(AMG) is a well-known preconditioner for its theoretically optimal performance in solving the elliptic equation. In the present work, the Poisson equation is pre-processed by the classical AMG method and the transport part is preconditioned by the Petrov-Galerkin AMG. These two preconditioners are applied to approximate the ideal preconditioner of the Poisson-Continuity coupled system derived from the block LU factorization. The composite preconditioner significantly improves the convergence of the Krylov iterative solver and the ion flow field problem with million degrees of freedom is solved in less than 20 min. The present work brings a novel and general scheme to improve the efficiency of the traditional algorithm for the multi-physics problems.

Electromagnetic-Thermal Analysis With FDTD and Physics-Informed Neural Networks

This article presents the coupling of the finite-difference time-domain (FDTD) method for electromagnetic field simulation, with a physics-informed neural network based solver for the heat equation. To this end, we employ a physics-informed U-Net instead of a numerical method to solve the heat equation. This approach enables the solution of general multiphysics problems with a single-physics numerical solver coupled with a neural network, overcoming the questions of accuracy and efficiency that are associated with interfacing multiphysics equations. By embedding the heat equation and its boundary conditions in the U-Net, we implement an unsupervised training methodology, which does not require the generation of ground-truth data. We test the proposed method with general 2-D coupled electromagnetic-thermal problems, demonstrating its accuracy and efficiency compared to standard finite-difference based alternatives.

Electromagnetic-Thermal Modeling of Nonlinear Magnetic Materials

A nonlinear electromagnetic (EM)-thermal coupled solver is developed for modeling ferromagnetic materials widely used in electric motors. To accurately predict machine performance, the time-domain finite element method is employed to solve this multiphysics problem. By adopting the nonlinear B-H models to account for hysteresis effects, magnetic core losses are computed as the major sources of power dissipation for magnetic materials. The resulting temperature change is then obtained and its effect on the magnetic properties is subsequently evaluated. Due to different time scales of EM field variations and heat transfer processes, different time step sizes are adopted to enhance the simulation speed. During thermal time marching, the EM solver is invoked adaptively based on material property changes, and EM losses are calculated and updated through extrapolation, resulting in an efficient EM-thermal coupling scheme. Numerical examples are presented to validate the accuracy and capabilities of the proposed EM-thermal co-simulation framework.

Numerical modelling of braided ceramic fiber seals by using element differential method

• A multi-physical coupled model is proposed for the braided ceramic fiber seals. • The coupled fields contain the process of heat conduction, seepage and deformation. • Element differential method (EDM) is used to solve the multi-physical problems. • The material-dependent parameters in model are obtained by an inverse procedure. • Compared to FEM, EDM is more easy and efficient dealing with the coupled model. A new kind of dynamic seal with braided ceramic fibers has been designed to seal the movable panels in the scramjet engines, which are used for the propulsion of hypersonic vehicle. The braided ceramic fiber structure can provide buffer forces when the seals are subjected to the external dynamical preloads. However, it also makes the seals difficult to analyze. Up to now, the analysis of the seals still uses 1D models so that one cannot implement the coupled analysis of seals and their surrounding structures and flows. In this paper, a novel 2D and 3D mechanics-thermal-seepage coupled model is proposed to describe these seals, which provides a possibility for the aforementioned coupled analysis. Meanwhile, a strong-form numerical method, element differential method (EDM) is employed to discretize the governing equations of the coupled model due to its efficiency and robustness. Three examples are given. The first one is to invert the material-dependent parameters of three kinds of seal strips from the experimental data by Levenberg-Marquardt (LM) algorithm. Other two implement the analyses of 3D square and circular cross-section seals, respectively, which verify that EDM is more efficient than FEM in seal analysis when using the same mesh sizes.

Designing an object-oriented architecture for the finite element simulation of structural elements

This paper reports the development of an architecture and software implementation of the library of classes for the finite-element analysis of problems in the theory of elasticity with an open-source code. The practical necessity of such systems is due to the fact that in modern equipment there are new types of materials whose structural elements' calculation has certain features. As a result, it is necessary to update the relevant scientific software or even devise a new one. A flexible software architecture is designed to reduce the time and complexity of such updates. Existing implementations of the method of finite elements with open source have been analyzed: it was revealed that there are no systems aimed at the most flexible and user-friendly architecture. The system of abstract classes proposed in the current work corresponds to known SOLID principles of object-oriented design and makes it possible to scale the already developed analysis program for new tasks in an easy and understandable way. To test the quality of the developed system from the point of view of software engineering, the maintainability index and cyclomatic complexity code metrics were used. The values of these metrics for the modules of the PyFEM system core vary in the following ranges: from 1 to 18 for the maintainability index, and from 22 to 100 for cyclomatic complexity. PyFEM testing was performed on the task of determining the stressed-strained state of the turbine rotor blade. Due to the ease of implementation, it was possible to build a set of effective and intuitive classes that make it possible to solve numerically the static and dynamic problems in the theory of elasticity. The developed class library can be used in the development of both universal and specialized software designed to analyze multiphysics problems.

Variationally consistent homogenization of electrochemical ion transport in a porous structural battery electrolyte

In this paper, we develop a multi-scale modeling framework for a multiphysics problem characterized by electro-chemically coupled ion transport in a Structural Battery Electrolyte (SBE). The governing equations of the problem are established by coupling Gauss law with mass conservation for each mobile species. By utilizing variationally consistent homogenization, we are able to establish a two-scale model where both the macro-scale and sub-scale equations are deduced from a single-scale problem. Investigations of the sub-scale RVE problem show that the transient effects are negligible for the length scales relevant to the studied application, which motivates the assumption of micro-stationarity. In the special case of linear constitutive response, we get a numerically efficient solution scheme for the macro-scale problem that is based on a priori upscaling. As a final step, we demonstrate the numerically efficient solution scheme by solving a 2D macro-scale problem using upscaled constitutive quantities based on a 3D RVE.

Computational study of the Transmission pole during downburst using ANSYS, considering fluid-structure interactions

A downburst is described as a strong downdraft that causes a devastating wind outburst on or near the earth surface. Such occurrences are more common during thunderstorms. Downbursts generally impinge on the ground and convect radially in all directions from the point of contact. Downbursts have been widely documented as a regular cause of high voltage electrical transmission tower and pole failures in numerous nations. The flow dynamics of impinging jets are investigated using numerical models, with applicability to downburst-related high intensity winds. The downburst is simulated using three primary viscous models (, , and RANS). These three viscous models are used to simulate downburst in two dimensions. The RANS viscous model is used for further investigation. To determine the temporal variant characteristics of a downburst, both steady and transient state simulations are performed. The flow is quasi-periodic, with vortex rings formed by the initial jet instability impinging on the surface, where they find an unstable separation reattachment of the boundary layer. Fluid-structure interactions (FSI) are multiphysics problems that cannot be handled using single physics equations. To determine the impacts of downburst on transmission poles, a 2-D steel pole 8 metres high with a fixed base is put near the downburst. Downburst pressure is measured on a transmission pole. The stresses and deflections caused by the pressure distribution on the tower due to varying fluid domain dimensions and jet velocities on the transmission poles are determined using one way coupling, from 2-D transmission pole geometry to 3-D transmission pole geometry.

Waveform Relaxation with Asynchronous Time-integration

We consider Waveform Relaxation (WR) methods for parallel and partitioned time-integration of surface-coupled multiphysics problems. WR allows independent time-discretizations on independent and adaptive time-grids, while maintaining high time-integration orders. Classical WR methods such as Jacobi or Gauss-Seidel WR are typically either parallel or converge quickly. We present a novel parallel WR method utilizing asynchronous communication techniques to get both properties. Classical WR methods exchange discrete functions after time-integration of a subproblem. We instead asynchronously exchange time-point solutions during time-integration and directly incorporate all new information in the interpolants. We show both continuous and time-discrete convergence in a framework that generalizes existing linear WR convergence theory. An algorithm for choosing optimal relaxation in our new WR method is presented. Convergence is demonstrated in two conjugate heat transfer examples. Our new method shows an improved performance over classical WR methods. In one example, we show a partitioned coupling of the compressible Euler equations with a nonlinear heat equation, with subproblems implemented using the open source libraries DUNE and FEniCS .