Imposed Boundary Conditions Research Articles

Applications of fractional calculus to thermodynamics analysis of hydromagnetic convection in a channel

The present analysis signifies the impacts of fraction calculus on the MHD analysis of an incompressible fluid flow with entropy generation, viscous dissipation, and joule heating carried out between two endless vertical plates. The left vicinity of the MHD fluid flow channel has a convectively hot MHD fluid with a specific temperature that produces the heat transfer coefficient inside the flow channel. The MHD fluid flow model has been formulated with the fractional order derivative, which is an exciting area of research. The transient form of the system of dimensionless PDEs with imposed boundary conditions is transformed to a fractional order derivative model, which was formerly solved via the Finite Difference Scheme (FDS). The graphical illustrations signify the significance of the transverse magnetic field, viscous dissipation, and Ohamic heating alongside Biot and Bejan numbers. The velocity and temperature illustrations have been shown graphically to observe the influences within the flow channel. With predetermined values of the corresponding dimensionless parameters, the coefficient of skin friction and Nusselt number accompanied by a range of convection constraints are displayed graphically within the flow channel.

Start-Up Multilayer Electro-Osmotic Flow of Maxwell Fluids through an Annular Microchannel under Hydrodynamic Slip Conditions

The present investigation analyzes the transient multilayer electro-osmotic flow through an annular microchannel with hydrophobic walls. The fluids are considered immiscible and viscoelastic, following the Maxwell rheological model. In the problem examined, the linearized Poisson–Boltzmann and Cauchy momentum equations are used to determine the electric potential distribution and the flow field, respectively. Here, different interfacial phenomena are studied through the imposed boundary conditions, such as the hydrodynamic slip and specified zeta potentials at solid–liquid interfaces, the velocity continuity, the electroviscous stresses balance, the potential difference, and the continuity of electrical displacements at the interfaces between fluids. The semi-analytic solution uses the Laplace transform theory. In the results, the velocity profiles and velocity tracking show the oscillatory behavior of flow, which strongly depends on the dimensionless relaxation time. Furthermore, the hydrodynamic slip on the channel walls contributes to the release of energy stored in the fluids due to elastic effects at the start-up of the flow. Similarly, other dimensionless parameters are also investigated. This research aims to predict the parallel flow behavior in microfluidic devices under electro-osmotic effects.

Investigating sound absorption in rail tunnels using wave decomposition

Acoustic noise in trains is a more prevalent problem in tunnels as compared to open track scenarios. This is mainly due to less acoustic radiation relative to increasing contributions of reflections and reverberation. Sound absorbing panels on a tunnel wall and in the track four-foot perform better above 1 kHz with absorption coefficients larger than 0.8. To investigate sound absorption below 1 kHz, we employ wave decomposition into incidence, reflection and absorption components for a section of a given underground tunnel design. A Finite Element (FE) 2D model of a carriage and tunnel is developed, representing a tangent portion of a rail track and including the noise power spectra from the rail-wheel interactions for three different roughness scenarios. The FE model, compared to a Ray Tracing one, provides precisely imposed boundary conditions and the pressure field of the entire tunnel interior. Our results can identify the performance of current panels, absorbing significantly less noise power in the lower frequency range, especially within the 0.3–0.5 kHz interval. The insights from wave decomposition analysis can lead to solutions to increase absorption by changing the reflection pattern below 1 kHz band, improving the passenger comfort during a longer train ride.

A numerical method for sharp-interface simulations of multicomponent alloy solidification

We present a computational method for the simulation of the solidification of multicomponent alloys in the sharp-interface limit. Contrary to the case of binary alloys where a fixed point iteration is adequate, we hereby propose a Newton-type approach to solve the non-linear system of coupled PDEs arising from the time discretization of the governing equations, allowing for the first time sharp-interface simulations of the multialloy solidification. A combination of spatially adaptive quadtree grids, Level-Set Method, and sharp-interface numerical methods for imposing boundary conditions is used to accurately and efficiently resolve the complex behavior of the solidification front. The convergence behavior of the Newton-type iteration is theoretically analyzed in a one-dimensional setting and further investigated numerically in multiple spatial dimensions. We validate the overall computational method on the case of axisymmetric radial solidification admitting an analytical solution and show that the overall method's accuracy is close to second order. Finally, we perform numerical experiments for the directional solidification of a Co-Al-W ternary alloy with a phase diagram obtained from the PANDAT™ database and analyze the solutal segregation dependence on the processing conditions and alloy properties.

A FEM‐PD coupling based on Arlequin approach to impose boundary conditions in peridynamics

AbstractThe peridynamic approach (PD) is a continuous theory that is well suited for solving damage problems. Because of the nonlocal formulation, PD can predict the response of a material and fracture patterns with high probability in high dynamic processes. In PD, some parameters differ from the continuum formulation and have some deviation in discretized PD systems, such as a horizon. A material constant becomes a parameter dependent on the mesh size. A sticking point, which has to be considered, is that an incomplete horizon at the boundaries results in an unphysical variation of the material's stiffness in these regions. Material points at the boundaries do not have an entire nonlocal neighborhood, meaning the points have fewer bonds and are softer than points within the domain. This leads to the so‐called surface effect. The difficulties in applying the classical local initial and boundary conditions happen because of the nonlocal character of the PD. To overcome this problem, several correction techniques have been developed. Nevertheless, a standard method to describe them is not available yet. An alternative approach is the application of the earlier proposed FEM‐PD coupling, which can be seen as a local‐nonlocal coupling method. The damage‐free zones are analyzed by the FEM as classical local theory, while the domain where the fracture is expected is modeled with the PD as a nonlocal theory. Consequently, the reduction of the computational effort as well as the imposing of the conventional local boundary conditions, is achieved. The coupling method is based on the Arlequin method—an energy‐based procedure where the energy of a system is found as a weighted average of both systems. The mechanical compatibility in the overlapping zone of both domains is reached by implementing constraints with the help of the penalty method. In the paper at hand, the focus is on imposing BCs. The proposed method is applied to both static and dynamic applications. The accuracy and convergence behavior is evaluated by analyzing test examples.

Automatically imposing boundary conditions for boundary value problems by unified physics-informed neural network

Automatically imposing boundary conditions for boundary value problems by unified physics-informed neural network

Stream laws in analog tectonic-landscape models

Abstract. The interplay between tectonics and surface processes defines the evolution of mountain belts. However, correlating these processes through the evolution of natural orogens represents a scientific challenge. Analog models can be used for analyzing and interpreting the effect of such interaction. To fulfill this purpose it is necessary to understand how the imposed boundary conditions affect analog models' evolution in time and space. We use nine analog models characterized by different combinations of imposed regional slope and rainfall rates to investigate how surface processes respond to the presence of tectonically built topography (imposed slope) under different climatic conditions (rainfall rate). We show how the combination of these parameters controls the development of drainage networks and erosional processes. We quantify the morphological differences between experimental landscapes in terms of a proposed Se/R ratio, accounting for both observables and boundary conditions. We find few differences between analog models and natural prototypes in terms of parametrization of the detachment-limited stream power law. We observe a threshold in the development of channelization, modulated by a tradeoff between applied boundary conditions.

Buckling analysis of functionally graded plates in thermal environment by using a meshfree method

In material, the pre-stress state caused by temperature variation of the working environment is one of the main reasons which cause buckling in structures. This paper aims to analyse the critical temperature rise to cause buckling in functionally graded material (FGM) under different boundary conditions. Reissner-Mindlin plate theory is employed in this paper with the radial point interpolation method (RPIM). The RPIM has the advantage compared to other meshfree methods in the satisfaction of the Kronecker delta property which allows directly imposing boundary conditions on scattered nodes. Factors affecting to thermal buckling phenomenon are investigated. The accuracy of solutions will be shown by comparing them to reliable results in previous studies

A spectrally discretized wide-angle parabolic equation model for simulating acoustic propagation in laterally inhomogeneous oceans.

Sound waves can be used to carry out underwater activities. Rapidly and accurately simulating sound propagation is the basis for underwater detection. The wide-angle parabolic model has a good computational speed and accuracy and is currently the main numerical model for mid- and low-frequency sound propagation. The classical wide-angle parabolic equation model is discretized by the finite difference method and a low-order difference scheme is generally adopted. In this paper, a wide-angle parabolic equation model based on a spectral method is proposed. The depth operators of each layer are discretized via the Chebyshev spectral method and then assembled into a global matrix for the forward step. Lateral inhomogeneity is addressed by updating the global depth matrix while stepping forward. In the proposed spectral algorithm, both soft and hard seabeds can be accurately simulated by imposing boundary conditions, and the perfectly matched layer technique is used to truncate the unbounded acoustic half-space. Several representative numerical experiments prove the accuracy and efficiency of the proposed algorithm. However, the spectral method requires that the thickness of the layers does not change during the forward step. Thus, the current spectral algorithm cannot simulate waveguides with terrain undulation, which is its main limitation.

Estimation of wavenumber–frequency spectra of wall pressure due to turbulent flow over a flat plate using large-eddy simulation

The wavenumber–frequency spectra (WFS) of turbulent wall pressure fluctuations are used to design underwater acoustic systems, and a method is presented to determine them for flat plate flow using large-eddy simulations (LES). First, the Reynolds averaged Navier–Stokes (RANS) analysis is carried out for flow over the plate using k–ω shear-stress transport model. Flow parameters are extracted from the output of this analysis and used to impose boundary conditions for large-eddy simulations using a smaller domain with finer mesh. Mesh convergence studies are done to establish the adequacy of the proposed meshing scheme for estimating the turbulent boundary layer wall pressures. The stream-wise velocity profiles, turbulence intensities, and power spectra obtained using LES are compared with other computational and experimental results. The time history of fluctuating pressure on the wall at various stream-wise locations is used to estimate the WFS. Estimations are made of the convective ridge as well as sub-convective and low wavenumber portions of the spectrum. The computations are performed at momentum thickness-based Reynolds numbers (Rθ) of 5761, 7988, and 7709. The effect of downstream distance on the WFS is studied by computing it at three downstream locations and shown that the downstream distance has little effect on the WFS once the flow has become fully turbulent. The use of a desktop workstation for the estimation of WFS has not been reported earlier. The results show that the WFS of turbulent pressure due to flow over more complex geometries can be estimated using a similar method.

Isotropic yield surfaces for porous ductile materials: complete geometric representation by a computational homogenisation procedure

PurposeThe present paper aims to explore a computational homogenisation procedure to investigate the full geometric representation of yield surfaces for isotropic porous ductile media. The effects of cell morphology and imposed boundary conditions are assessed. The sensitivity of the yield surfaces to the Lode angle is also investigated in detail.Design/methodology/approachThe microscale of the material is modelled by the concept of Representative Volume Element (RVE) or unit cell, which is numerically simulated through three-dimensional finite element analyses. Numerous loading conditions are considered to create complete yield surfaces encompassing high, intermediate and low triaxialities. The influence of cell morphology on the yield surfaces is assessed considering a spherical cell with spherical void and a cubic RVE with spherical void, both under uniform strain boundary condition. The use of spherical cell is interesting as preferential directions in the effective behaviour are avoided. The periodic boundary condition, which favours strain localization, is imposed on the cubic RVE to compare the results. Small strains are assumed and the cell matrix is considered as a perfect elasto-plastic material following the von Mises yield criterion.FindingsDifferent morphologies for the cell imply in different yield conditions for the same load situations. The yield surfaces in correspondence to periodic boundary condition show significant differences compared to those obtained by imposing uniform strain boundary condition. The stress Lode angle has a strong influence on the geometry of the yield surfaces considering low and intermediate triaxialities.Originality/valueThe exhaustive computational study of the effects of cell morphologies and imposed boundary conditions fills a gap in the full representation of the flow surfaces. The homogenisation-based strategy allows us to further investigate the influence of the Lode angle on the yield surfaces.

The effects of water table fluctuation on LNAPL deposit in highly permeable porous media: A coupled numerical and experimental study

Light Non-Aqueous Phase Liquid (LNAPL) flow on the water table is highly mobile and is sensitive to the fluctuation of groundwater. This process is highly complex and involves the migration of three immiscible phases (i.e. water, LNAPL and air) which need the explicit definition of multiple parameters. A coupled experimental and numerical simulation methodology is performed by using Time Domain Reflectrometer (TDR) and multiphase simulation of a controlled environment to mimic the water table fluctuation and its effect on the LNAPL residual saturation. TDR probes are installed in different locations of a 2D tank (i.e. a cuboid box with relatively low off-plane thickness) and the bulk permittivity of the phases are measured through artificially imposed boundary conditions. The bulk permittivity is then translated into saturation of the three different phases. The translated residual saturations along with the previously measured porous media properties (e.g. porosity and saturated permeability) are then inserted into the numerical simulator (i.e. COMSOL Multiphysics®) and the migration of the three phase in porous media is simulated. The numerical exponents and entry pressures needed for the simulation of the multiphase flow are estimated using the temporal experimental values. The exponents of water LNAPL relative permeability were estimated to be around 2 while the exponents gas LNAPL relative permeability were estimated to be closer to 3. The results, simulated with the optimized parameters, are then evaluated with pictures taken from the transparent face of the 2D tank different stages of the experiment. The temporal evolution of different phase saturation has been compared and validated between the experimental results obtained and interpreted by the TDR probe measurements and the simulations. The relative error stays in the 5 % confidence level for most reported points and only in the highly dynamic flow time steps the error reaches around 12% which are discussed in the text and is accepted due to the highly nonlinear nature of the problem.

Scalar Casimir effects in a Lorentz violation scenario induced by the presence of constant vectors

In this work, we consider a theoretical model that presents a violation of Lorentz symmetry in the approach of quantum field theory. The theoretical model adopted consists of a real massive scalar quantum field confined in the region between two large parallel plates. The violation of Lorentz symmetry is introduced by a CPT-even, aether-like approach, considering a direct coupling between the derivative of the scalar field with two orthogonal constant vectors. The main objective of this paper is to analyze the modification of the Casimir energy and pressure caused by the anisotropy of space–time as a consequence of these couplings. The confinement of the scalar quantum field between the plates is implemented by imposing boundary conditions on them.

A modified equation analysis for immersed boundary methods based on volume penalization: Applications to linear advection–diffusion equations and high-order discontinuous Galerkin schemes

The Immersed Boundary Method (IBM) is a popular numerical approach to impose boundary conditions without relying on body-fitted grids, thus reducing the costly effort of mesh generation. To obtain enhanced accuracy, IBM can be combined with high-order methods (e.g., discontinuous Galerkin). For this combination to be effective, an analysis of the numerical errors is essential. In this work, we apply, for the first time, a modified equation analysis to the combination of IBM (based on volume penalization) and high-order methods (based on nodal discontinuous Galerkin methods) to analyze a priori numerical errors and obtain practical guidelines on the selection of IBM parameters. The analysis is performed on a linear advection–diffusion equation with Dirichlet boundary conditions. Three ways to penalize the immersed boundary are considered, the first penalizes the solution inside the IBM region (classic approach), whilst the second and third penalize the first and second derivatives of the solution. We find optimal combinations of the penalization parameters, including the first and second penalizing derivatives, resulting in minimum errors. We validate the theoretical analysis with numerical experiments for one- and two-dimensional advection–diffusion equations.

Reduced physics model of the tokamak Scrape-Off-Layer for pulse design

The dynamic interplay between the core and the edge plasma has important consequences in the confinement and heating of fusion plasma. The transport of the Scrape-Off-Layer (SOL) plasma imposes boundary conditions on the core plasma, and neutral transport through the SOL influences the core plasma sourcing. In order to better study these effects in a self-consistent, time-dependent fashion with reasonable turn-around time, a reduced model is needed. In this paper we introduce the SOL Box Model, a reduced SOL model that calculates the plasma temperature and density in the SOL given the core-to-edge particle and power fluxes and recycling coefficients. The analytic nature of the Box Model allows one to readily incorporate SOL physics in time-dependent transport solvers for pulse design applications in the control room. Here we demonstrate such a coupling with the core transport solver TRANSP and compare the results with density and temperature measurements, obtained through Thomson scattering and Langmuir probes, of an NSTX discharge. Implications for future interpretive and predictive simulations are discussed.

Solving free-surface problems for non-shallow water using boundary and initial conditions-free physics-informed neural network (bif-PINN)

The physics-informed neural network (PINN) has emerged as an alternative approach for solving a variety of systems, including many fluid dynamics problems. However, the original PINN method suffers from the so called ‘gradient pathology’ where gradients of the residuals from the boundary and initial conditions become stiff, and thus lead to poor results.Inspired by previous works on imposing boundary conditions as hard constraints in PINN, we apply existing techniques in a way that both boundary and initial conditions are incorporated in the governing equations such that the residuals from boundary and initial conditions are no longer required in the loss function, leading to better convergence, lower memory usage and a faster training. For simplicity, our approach is referred to as bif-PINN in this work, but we emphasise that it is an application of existing techniques for solving spatio-temporal PDE system via the PINN framework. We test bif-PINN on several Lagrangian fluid dynamics problems involving either a free-surface or nontrivial vorticity. We first validate the bif-PINN approach on the small amplitude sloshing in an open container where linear solution is valid, and then we increase the amplitude to observe the nonlinear effect. Next, we test bif-PINN on the inviscid Taylor-Green vortex problem which involves nontrivial vorticity and unsteady in the Lagrangian frame where grids can be highly distorted as time increases. Lastly, the bif-PINN approach is applied to the dam break problem which involves fluid impacting on solid wall and a subsequent rebound motion.Results using PINN and bif-PINN are compared, where the original PINN method fails to produce the correct results for all problems involving a free-surface, and a clear advantage in both performance and accuracy for the bif-PINN approach is observed in all cases.

HEAT AND MASS TRANSPORT FOR ELASTICO-VISCOUS FLUID WITH PARTIAL SLIP BOUNDARY OVER A FLAT PERMEABLE PLATE

The elastico-viscous boundary layer fluid motion over a flat permeable plate having slip boundary is considered. The transition of thermal energy and mass transport mechanism has been analyzed. The elastic and viscous characteristic in the fluid is exhibited by Walters Liquid (Model , a non-Newtonian fluid model. The permeable plate at which suction is applied is placed in porous medium. The fluid domain receives thermal energy from the permeable plate. The governing equations of fluid motion with satisfying imposed boundary conditions are reduced to self-similar type by similarity transformation. The finite difference method-based solver ‘bvp4c’ of MATLAB code is employed to perform numerical computation. The impact of different involved flow parameters is illustrated from obtained graphs for discussions from physical point of view.

Boundary and interface methods for energy stable finite difference discretizations of the dynamic beam equation

We consider energy stable summation by parts finite difference methods (SBP-FD) for the homogeneous and piecewise homogeneous dynamic beam equation (DBE). Previously the constant coefficient problem has been solved with SBP-FD together with penalty terms (SBP-SAT) to impose boundary conditions. In this work, we revisit this problem and compare SBP-SAT to the projection method (SBP-P). We also consider the DBE with discontinuous coefficients and present novel SBP-SAT, SBP-P, and hybrid SBP-SAT-P discretizations for imposing interface conditions. To demonstrate the methodology for two-dimensional problems, we also present a discretization of the piecewise homogeneous dynamic Kirchoff-Love plate equation based on the hybrid SBP-SAT-P method. Numerical experiments show that all methods considered are similar in terms of accuracy, but that SBP-P can be more computationally efficient (less restrictive time step requirement for explicit time integration methods) for both the constant and piecewise constant coefficient problems.

Development and implementation of a Direct Surface Description method for free surface flows in OpenFOAM

The solution procedure for two phases in OpenFOAM suffers from unphysical velocity oscillations at the free surface between the two phases. It is likely that this problem also exists in other two-phase Computational Fluid Dynamics (CFD) codes. We aim to solve this by imposing boundary conditions directly on the free surface. We have taken the first step towards a new two-phase solution method by first addressing the water phase alone. It is a free surface modelling method based on merging concepts from two existing methods: (1) A single-phase free surface method and (2) the solution method used in OpenFOAM. The underlying motivation is to enable more accurate estimation of wave induced load distributions from wave crest impacts on offshore structures. This first and foremost requires an accurate prediction of the kinematics near the free surface. We present a solution method with boundary conditions directly on the free surface, thereby the name: Direct Surface Description (DSD). Additionally it is the first time that the isoAdvector algorithm is combined with a single phase free surface method. The implementation is made in OpenFOAM, but may also relevant to other codes as well. First a still water level simulation is presented to illustrate the unphysical behavior of the existing solvers and validate the behaviour of the DSD method. The second test case is a moderately steep stream function wave in intermediate water depth. The DSD method is validated and compared to the existing solution methods of OpenFOAM: interFoam and interIsoFoam . We present a detailed comparison of surface elevations and velocity profiles. This is followed by a convergence study including wave height, velocity and phase shift. Additionally the influence of the Courant–Friedrichs–Lewy (CFL) number is studied. The stream function wave case demonstrates that the DSD method accurately predicts the free surface elevation and velocity fields without free surface undulations or oscillatory velocity fields. The convergence study underlines an increased accuracy of the DSD method. Finally, a 2D and a 3D showcase with breaking waves are presented to show that the DSD method is capable of simulating more complex and realistic cases. • The oscillatory velocities at free surface in OpenFOAM is removed by DSD-method. • Presents a rarely seen comparison of velocity profiles below wave crest and trough. • New DSD-method eliminates the air region leading to decreased CPU time. • Implementation in OpenFOAM makes the method ready for unstructured meshes. • Presents convergence study of velocity and wave heights w.r.t. mesh and CFL number.

Compressive strength of Aluminum-copper alloys at different temperatures

An Al-Cu alloy developed for applications requiring an alloy of moderate strength, weldability and good resistance to sea water, it is an excellent, versatile alloy ideal for many applications. The results obtained show that the level of spring back is strongly related to the imposed boundary conditions. If he is conceivable to overcome this problem by a “practical” tool for single curvature panels, it seems more delicate for double tooling curvature. In conclusion, if the prospects offered by this type of process seem attractive, a vast campaign of digital investigations must be considered in order to define more precisely the limiting radii of curvature that can be achieved without causing problems with spillage or buckling of the stiffeners, especially for double curvature applications. The boundary conditions considered should be able to be reproduced experimentally during shaping. For high strain rate testing, the only usable method to obtain information about the distribution of strains in the specimen is the use of high-speed photography. This method is used to visualize the location of deformations and fracture and also to measure the deformations of the specimen. The use of ultra-fast photography for large-scale tests strain rates can be performed in order to qualitatively study the behavior of materials. The proposed new geometry for the specimen will be modified by the use of high-speed photography.