Arbitrary Lagrangian Eulerian Formulation Research Articles

An ALE formulation for the geometric nonlinear dynamic analysis of planar curved beams subjected to moving loads

This paper presents an arbitrary Lagrangian-Eulerian (ALE) formulation based on the consistent corotational method for the geometric nonlinear dynamic analysis of planar curved viscoelastic beams subjected to moving loads. In the ALE description, the beam nodes can be moved in arbitrarily specified ways to describe the moving loads’ material positions accurately. The pure deformation and the deformation rate of the element are measured in a curvilinear coordinate system fixed on a curved reference configuration that follows the rotation and translation of a corotational frame. Based on Hamilton’s principle, the global elastic force vector, the global internal damping force vector, the global inertia force vector, and the global external damping force vector are derived using the same shape functions to ensure the consistency and independence of the element. Then, a standard element can be embedded within the element-independent framework. An accurate two-node curved element and the Kelvin-Voigt model are introduced in this framework to consider the axial deformation, bending deformation, shear deformation, rotary inertia, and viscoelasticity of the beam. Three examples are given to verify the validity, computational efficiency, and versatility of the presented formulation. The effect of internal damping, external damping, the inertia force of a moving mass, and the moment of inertia of the mass on the dynamic response of the beam are investigated. Moreover, the driving force for a prescribed motion of a mass along the beam is investigated.

Dynamic fracture analysis in quasi-brittle materials via a finite element approach based on the combination of the ALE formulation and M−integral method

This work proposes an efficient FE-based approach for reproducing dynamic crack propagation phenomena in quasi-brittle materials. The proposed model uses a Moving Mesh technique based on the Arbitrary Lagrangian-Eulerian formulation (ALE) to adapt the computational mesh consistently to the geometry variations caused by dynamically growing cracks. Specifically, the motion of mesh nodes occurs according to Fracture Mechanics criteria, which provide suitable conditions regarding the direction and velocity of a growing crack tip. These conditions usually depend on the Dynamic Stress Intensity Factors (DSIFs) at the crack front. For extracting the DIFSs at a moving crack tip, this work introduces the ALE formulation of the dynamic M−integral as a key novelty. This strategy offers the key advantage of performing numerical integration procedures on deforming finite elements without losing accuracy. The validity of the proposed method has been assessed through comparisons with experimental and numerical data reported in the literature.

An Arbitrary Lagrangian Eulerian formulation for tire production simulation

Tire production is a complex process due to large deformations, highly non-linear uncured rubber material and large temperature. It can be observed, that the production conditions have a strong influence on the cured tire behaviour and should be studied to minimize possible defects in the final product. In this contribution, an Arbitrary Lagrangian Eulerian (ALE) formulation is presented to overcome convergence issues stemming from large distortion of elements in a pure Lagrangian description. In an ALE formulation, the computational mesh is not fixed in space and can move relatively to the material motion, which allows to control the distortion of the mesh by a smoothing algorithm. Coupling the material motion with the newly obtained mesh is done by an advection algorithm to project the internal variables of a thermo-mechanically consistent material model. Based on the assumption that the internal variables are projected directly from the integration points, an additional mesh is generated with the integration points of the old mesh as grid. To show the capabilities of the presented algorithm, several numerical examples are shown ranging from a simple forging example to a complex tire production process. • A new algorithm for the projection of history variables in an Arbitrary Lagrangian Eulerian framework. • A finite strain thermo-mechanically consistent material model for rubber curing. • Applied ALE framework to the tire production process.

Design and execution of a verification, validation, and uncertainty quantification plan for a numerical model of left ventricular flow after LVAD implantation.

Left ventricular assist devices (LVADs) are implantable pumps that act as a life support therapy for patients with severe heart failure. Despite improving the survival rate, LVAD therapy can carry major complications. Particularly, the flow distortion introduced by the LVAD in the left ventricle (LV) may induce thrombus formation. While previous works have used numerical models to study the impact of multiple variables in the intra-LV stagnation regions, a comprehensive validation analysis has never been executed. The main goal of this work is to present a model of the LV-LVAD system and to design and follow a verification, validation and uncertainty quantification (VVUQ) plan based on the ASME V&V40 and V&V20 standards to ensure credible predictions. The experiment used to validate the simulation is the SDSU cardiac simulator, a bench mock-up of the cardiovascular system that allows mimicking multiple operation conditions for the heart-LVAD system. The numerical model is based on Alya, the BSC's in-house platform for numerical modelling. Alya solves the Navier-Stokes equation with an Arbitrary Lagrangian-Eulerian (ALE) formulation in a deformable ventricle and includes pressure-driven valves, a 0D Windkessel model for the arterial output and a LVAD boundary condition modeled through a dynamic pressure-flow performance curve. The designed VVUQ plan involves: (a) a risk analysis and the associated credibility goals; (b) a verification stage to ensure correctness in the numerical solution procedure; (c) a sensitivity analysis to quantify the impact of the inputs on the four quantities of interest (QoIs) (average aortic root flow [Formula: see text], maximum aortic root flow [Formula: see text], average LVAD flow [Formula: see text], and maximum LVAD flow [Formula: see text]); (d) an uncertainty quantification using six validation experiments that include extreme operating conditions. Numerical code verification tests ensured correctness of the solution procedure and numerical calculation verification showed a grid convergence index (GCI)95% <3.3%. The total Sobol indices obtained during the sensitivity analysis demonstrated that the ejection fraction, the heart rate, and the pump performance curve coefficients are the most impactful inputs for the analysed QoIs. The Minkowski norm is used as validation metric for the uncertainty quantification. It shows that the midpoint cases have more accurate results when compared to the extreme cases. The total computational cost of the simulations was above 100 [core-years] executed in around three weeks time span in Marenostrum IV supercomputer. This work details a novel numerical model for the LV-LVAD system, that is supported by the design and execution of a VVUQ plan created following recognised international standards. We present a methodology demonstrating that stringent VVUQ according to ASME standards is feasible but computationally expensive.

A data-driven model for pressure distribution measurements by a four-electrode polymer sensor

Machine learning techniques have significantly enhanced signal handling and prediction accuracy in electronic skins by facilitating the extraction of useful information hidden in the sensory outputs. We present a polymer sensor with four irregularly shaped electrodes enabling energy-efficient sensing and improved data interpretation. We first compute the resistance change for the sensing element under pressure. The finite element method is used to solve the three-dimensional nonlinear elasticity. The electric potential distribution is simulated using an arbitrary Lagrangian-Eulerian formulation. We then build reduced-order models for detecting pressure distribution for different pressure cases. The inverse models built using deep neural networks showed good prediction accuracy and resolution. The irregular arrangement of the electrodes resulted in low correlation coefficients between the input resistances, and therefore, efficient predictions of the four-electrode sensor. It is demonstrated that the present four-electrode sensor could replace at least four sensors in an array. For arbitrary pressure distributions over a 2 × 2 surface resolution, a model is trained with a mean accuracy of 22 Pa in the range of 1–20 kPa. Additionally, for a single square-shaped pressure with arbitrary magnitude and surface area, position prediction accuracies of 99% and 96% are obtained at 4 × 4 and 8 × 8 resolutions, respectively. Moreover, the models showed low sensitivity to the uncertainty in the measured signals.

Two dimensional computational model coupling myoarchitecture-based lingual tissue mechanics with liquid bolus flow during oropharyngeal swallowing

Biomechanical relationships involving lingual myoanatomy, contractility, and bolus movement are fundamental properties of human swallowing. To portray the relationship between lingual deformation and bolus flow during swallowing, a weakly one-way solid-fluid finite element model (FEM) was derived employing an elemental mesh aligned to magnetic resonance diffusional tractography (Q-space MRI, QSI) of the human tongue, an arbitrary Lagrangian-Eulerian (ALE) formulation with remeshing to account for the effects of lingual surface (boundary) deformation, an implementation of patterned fiber shortening, and a computational visualization of liquid bolus flow. Representing lingual tissue deformation in terms of its 2D principal Lagrangian strain in the mid-sagittal plane, we demonstrated that the swallow sequence was characterized by initial superior-anterior expansion directed towards the hard palate, followed by sequential, radially directed, contractions of the genioglossus and verticalis to promote lingual rotation (lateral perspective) and propulsive displacement. We specifically assessed local bolus velocity as a function of viscosity (perfect slip conditions) and observed that a low viscosity bolus (5 cP) exhibited maximal displacement, surface spreading and local velocity compared to medium (110 cP, 300 cP) and high (525 cP) viscosity boluses. Analysis of local nodal velocity revealed that all bolus viscosities exhibited a bi-phasic progression, with the low viscosity bolus being the most heterogeneous and fragmented and the high viscosity bolus being the most homogenous and cohesive. Intraoral bolus cohesion was depicted in terms of the distributed velocity gradient, with higher gradients being associated with increased shear rate and bolus fragmentation. Lastly, we made a sensitivity analysis on tongue stiffness and contractility by varying the degree of extracellular matrix (ECM) stiffness through effects on the Mooney-Rivlin derived passive matrix and by varying maximum tetanized isometric stress, and observed that a graded increase of ECM stiffness was associated with reduced bolus spreading, posterior displacement, and surface velocity gradients, whereas a reduction of global contractility resulted in a graded reduction of obtainable accommodation volume, absent bolus spreading, and loss of posterior displacement. We portray a unidirectionally coupled solid-liquid FEM which associates myoarchitecture-based lingual deformation with intra-oral bolus flow, and deduce that local elevation of the velocity gradient correlates with bolus fragmentation, a precondition believed to be associated with aspiration vulnerability during oropharyngeal swallowing.

An Arbitrary Lagrangian–Eulerian Formulation of Two-Dimensional Viscoelastic Beams Based on the Consistent Corotational Method

Abstract In this paper, an arbitrary Lagrangian–Eulerian (ALE) formulation based on the consistent corotational method is presented for the geometric nonlinear dynamic analysis of two-dimensional (2D) viscoelastic beams. In the ALE description, mesh nodes can be moved in some arbitrarily specified way, which is convenient for investigating problems with moving boundaries and loads. By introducing a corotational frame, the rigid-body motion of an element can be removed. Then, the pure deformation and the deformation rate of the element can be measured in the local frame. This method can avoid rigid-body motion damping. In addition, the elastic force vector, the inertia force vector, and the internal damping force vector are derived with the same shape functions to ensure the consistency and independence of the element. Therefore, different assumptions can be made to describe the local deformation of the element. In this paper, the interdependent interpolation element (IIE) and the Kelvin–Voigt model are introduced in the local frame to consider the shear deformation, rotary inertia, and viscoelasticity. Moreover, the presented method is capable of considering the arbitrary curved initial geometry of a beam. Numerical examples show that internal damping dampens only the pure elastic deformation of the beam but does not dampen the rigid-body motion. Three dynamic problems of a beam with a moving boundary or subjected to a moving load are investigated numerically by the presented formulation and the commercial software ansys to verify the validity, versatility, and computational efficiency of the presented formulation.

A Hybrid Arbitrary Lagrangian Eulerian Formulation for the Investigation of the Stability of Pipes Conveying Fluid and Axially Moving Beams

Abstract This work addresses pipes conveying fluid and axially moving beams undergoing large deformations. A novel two-dimensional beam finite element is presented, based on the absolute nodal coordinate formulation (ANCF) with an extra Eulerian coordinate to describe axial motion. The resulting formulation is well known as the arbitrary Lagrangian Eulerian (ALE) method, which is often used to model axially moving beams and pipes conveying fluid. The proposed approach, which is derived from an extended version of Lagrange's equations of motion, allows for the investigation of the stability of pipes conveying fluid and axially moving beams for a certain axial velocity and stationary state of large deformation. Additionally, a multibody modeling approach allows us to extend the beam formulation for comoving discrete masses, which represent concentrated masses attached to the beam, e.g., gondolas in ropeway systems, or transported masses in conveyor belts. Within numerical investigations, we show that axially moving beams and a larger number of discrete masses behave similarly as in the case of beams with evenly distributed mass.

Finite element hybrid and direct computational aeroacoustics at low Mach numbers in slow time-dependent domains

In this work, we address the finite element computation of flow noise in the presence of arbitrarily slowly moving rigid bodies at low Mach numbers, by means of hybrid and direct computational aeroacoustics (CAA) strategies. As regards the former, the problem could be dealt with by means of the Ffowcs Williams–Hawkings acoustic analogy. That reduces to Curle’s analogy for a static body, which is analogous to a problem of diffraction of sound waves generated by flow eddies in the vicinity of the body. Acoustic analogies in CAA first demand computing the flow motion to extract an acoustic source term from it and then use the latter to calculate the acoustic pressure field. However, in the case of low Mach number flows, the Ffowcs Williams–Hawkings and Curle analogies present a problem as they require knowing the total pressure distribution on the body’s boundary (i.e. the aerodynamic pressure plus the acoustic one). As incompressible computational fluid dynamics (CFD) simulations are usually performed to determine the flow motion, the acoustic pressure distribution on the body surface is unavoidably missing, which can yield acoustic analogies inaccurate. In a recent work, it was proposed to tackle that problem for static and rigid surfaces, by keeping the incompressible CFD and then splitting the acoustic pressure into direct and diffracted components. Two separate wave equations were solved for them, in the framework of the finite element method (FEM). In this article, we extend that work to compute the aerodynamic sound generated by a flow interacting with a slowly moving rigid body. The incompressible Navier–Stokes equations are first solved in an arbitrary Lagrangian–Eulerian (ALE) frame of reference to obtain the acoustic source term. Advantage is then taken from the same computational run to separately solve two acoustic ALE wave equations in mixed form for the incident and diffracted acoustic pressure components. For validation of the total acoustic pressure field, an ALE formulation of a direct CAA approach consisting of a unified solver for a compressible isentropic flow in primitive variables is considered. The performance of the exposed methods is illustrated for the aeroacoustics of flow past a slowly oscillating two-dimensional NACA airfoil and for flow exiting a duct with a moving teeth-shaped obstacle at its termination.

Fluid–structure interaction with ALE formulation and skeleton-based structural models

This paper presents a fluid–structure interaction (FSI) framework that combines an Arbitrary Lagrangian–Eulerian (ALE) formulation with skeleton-based structural models consisting of force-based frame elements. For the first time in literature, a methodology is proposed to enable coupling between fluid and force-based frame elements through an ALE formulation. In the proposed methodology, communication between the fluid and skeleton-based domains is performed through a geometric model of the physical fluid–structure interface. With the use of force-based frame elements, the intent is to perform accurate FSI calculations in cases where axial, flexure, and shear motions dominate the structural responses. The proposed framework is evaluated against FSI problems involving steady and unsteady incompressible laminar flows and different structural models representing horizontal (beam) and vertical (column) solid members.

On the combination of Moving Mesh technique and M-integral method for predicting crack propagation mechanisms in Functionally Graded Materials

This work presents an efficient FE modeling approach for predicting crack propagation mechanisms in Functionally Graded Materials (FGMs). The proposed strategy combines the Moving Mesh (MM) technique and the Interaction Integral method (M-integral). The MM is used to reproduce the geometry evolution induced by the crack advance. Specifically, the mesh nodes around the crack tip are moved in such a way to follow crack path evolutions, thus reducing the need for continuous remeshing events that affect negatively the computational efficiency of standard FE modeling strategies. In particular, the proposed scheme employs a moving mesh strategy consistent with the Arbitrary Lagrangian-Eulerian (ALE) formulation, which is suitable for handling the motion of mesh nodes with great flexibility. In addition, the use of proper regularization procedures ensures the consistency of the mesh motion, reducing elevated elements distortions. The motion of the mesh nodes requires a proper definition of crack onset conditions and propagation direction. Hence, a correct evaluation of fracture variables at the crack front (i.e., Stress Intensity Factors and T-stress) is necessary. For this purpose, the proposed method adopts the M-integral approach, which is a widely used method due to its simplicity and accuracy. Since the crack front moves during the crack advance, the M-integral is implemented by using the ALE formulation, thus extracting fracture variables on distorting elements. The validity of the proposed strategy has been validated through comparisons with experimental and numerical data reported in the literature.

Simulation of dynamic fracture in quasi-brittle materials using a finite element modeling approach enhanced by moving mesh technique and interaction integral method

This work presents an efficient modeling approach for predicting dynamic crack propagation mechanisms in quasi-brittle materials. The proposed method consists of a standard Finite Element code enhanced by Moving Mesh (MM) technique consistent with the Arbitrary Lagrangian-Eulerian (ALE) formulation. The MM is used to reproduce the geometry evolution caused by dynamically growing cracks. More precisely, the nodes of the computational mesh around the crack tip change position during the simulation consistently with the growth of the crack front. In such a context, the ALE formulation ensures an effective re-location of mesh nodes inside the computational domain, reducing the overall amount of remeshing events. The motion of the computational mesh takes place according to previsions dictated by classic fracture criteria, which define crack initiation conditions, the direction of propagation, and the velocity of the advancing crack front. Such conditions depend on Dynamic Stress Intensity Factors at the crack front. Hence, accurately predicting these fracture variables is mandatory to ensure consistent mesh motions. To this end, the proposed approach implements the ALE formulation of the M-integral, which enables computing fracture variables on moving elements without losing accuracy. The validity of the proposed modeling strategy has been assessed through comparisons with numerical data and analytical formulations reported in the literature.

Numerical investigation on VIV energy harvesting enhancement with adding eccentricity to a circular cylinder

In recent years, energy harvesting from vortex-induced vibration (VIV) of a cylinder as a renewable source of energy has been increased. The main goal is to enhance the harnessed hydrokinetic energy of the VIV converters. In this work, the effect of adding a rotational degree of freedom by giving eccentricity to the circular cylinder is investigated on vibration and rotational response as well as hydrokinetic energy conversion. Simulations are done at the Reynolds number ranging from 2×10^3 to 13×10^3. Twodimensional unsteady Reynolds-averaged Navier–Stokes equations (URANS), supplemented with SST turbulence models, are solved on moving mesh, and arbitrary Lagrangian-Eulerian formulation is employed to accommodate the deforming boundaries. For the freely rotating and vibrating cylinder, results demonstrate that increasing the inlet velocity increases the vibration amplitude, and the cylinder experiences complete rotation in some of the flow times. Moreover, adding a rotational degree of freedom causes hydrodynamic instability, in which the location of separation points changes and makes a wide wake pattern with unstable vortexes behind the cylinder. As a result, the harnessed power and energy conversion efficiency of the system is increased. The freely vibrating-rotating system generates a maximum power of 0.024 (W), and the energy conversion efficiency increases and fluctuates around 11.2%.

A geometric multiscale model for the numerical simulation of blood flow in the human left heart

&lt;p style='text-indent:20px;'&gt;We present a new computational model for the numerical simulation of blood flow in the human left heart. To this aim, we use the Navier-Stokes equations in an Arbitrary Lagrangian Eulerian formulation to account for the endocardium motion and we model the cardiac valves by means of the Resistive Immersed Implicit Surface method. To impose a physiological displacement of the domain boundary, we use a 3D cardiac electromechanical model of the left ventricle coupled to a lumped-parameter (0D) closed-loop model of the remaining circulation. We thus obtain a one-way coupled electromechanics-fluid dynamics model in the left ventricle. To extend the left ventricle motion to the endocardium of the left atrium and to that of the ascending aorta, we introduce a preprocessing procedure according to which an harmonic extension of the left ventricle displacement is combined with the motion of the left atrium based on the 0D model. To better match the 3D cardiac fluid flow with the external blood circulation, we couple the 3D Navier-Stokes equations to the 0D circulation model, obtaining a multiscale coupled 3D-0D fluid dynamics model that we solve via a segregated numerical scheme. We carry out numerical simulations for a healthy left heart and we validate our model by showing that meaningful hemodynamic indicators are correctly reproduced.&lt;/p&gt;

Impact of the Thruster Jet Flow of Ultra-large Container Ships on the Stability of Quay Walls

As the size of ships increases, the size and output power of their thrusters also increase. When a large ship berths or unberths, the jet flow produced from its thruster has an adverse effect on the stability of quay walls. In this study, we conducted a numerical analysis to examine the impact of the thruster jet flow of a 30,000 TEU container ship, which is expected to be built in the near future, on the stability of a quay wall. In the numerical simulation, we used the fluid–structure interaction analysis technique of LS-DYNA, which is calculated by the overlapping capability using an arbitrary Lagrangian Eulerian formulation and Euler–Lagrange coupling algorithm with an explicit finite element method. As the ship approached the quay wall and the vertical position of the thruster approached the mound of the quay wall, the jet flow directly affected the foot-protection blocks and armor stones. The movement and separation of the foot-protection blocks and armor stones were confirmed in the area affected directly by the thruster jet flow of the container ship. Therefore, the thruster jet flows of ultra-large ships must be considered when planning and designing ports. In addition, the stability of existing port structures must be evaluated.

A mass conserving arbitrary Lagrangian–Eulerian formulation for three‐dimensional multiphase fluid flows

AbstractThe arbitrary Lagrangian–Eulerian (ALE) framework presented in [Sahin and Guventurk, An arbitrary Lagrangian–Eulerian framework with exact mass conservation for the numerical simulation of 2D rising bubble problem.Int J Numer Methods Eng. 2017;112:2110–2134] has been extended to simulate three‐dimensional immiscible incompressible multiphase fluid flows. The div‐stable side centered unstructured finite volume formulation is used for the discretization of the incompressible Navier–Stokes equations. A novel kinematic boundary condition that satisfies the local discrete geometric conservation law (DGCL) is implemented to ensure the mass conservation of each species at the machine precision. The pressure field is treated to be discontinuous across the interface with the discontinuous treatment of density and viscosity. Surface tension force is treated as a tangent force and discretized in a semi‐implicit form. Two different approaches for the computation of unit normal vector have been implemented: the least squares biquadratic surface fitting (LSBSF) and the mean weighted by sine and edge length reciprocals (MWSELR). The resulting large system of algebraic equations is solved in a fully coupled manner in order to improve the time step restrictions. As a preconditioner, an approximate matrix factorization similar to that of the projection method is employed and the parallel algebraic multigrid solver BoomerAMG provided by the HYPRE library, which is accessed through the PETSc library, has been utilized for the scaled discrete Laplacian of pressure and the diagonal blocks of mesh deformation equations. The accuracy of the proposed method is initially validated on the static bubble problem, since the surface tension force is highly sensitive to the accurate evaluation of the unit normal vector and the inaccuracies significantly contribute to unphysical velocities, called parasitic currents. The calculations indicate that the parasitic currents can be reduced to machine precision for the MWSELR method. Then, the proposed approach is applied to the single bubble rising in a viscous quiescent liquid for both low and high density ratios. The calculations produce accurate predictions of the bubble shape, center of mass, rise velocity, and so forth. Furthermore, the mass of each species is conserved at machine precision and discontinuous pressure field is obtained in order to avoid errors due to the incompressibility restriction in the vicinity of liquid‐liquid interfaces at large density and viscosity ratios.

Upwind finite element-PML approximation of a novel linear potential model for free surface flows produced by a floating rigid body

A novel linear potential model is presented to compute free surface flows of incompressible fluids produced by the motion of a floating rigid body in the presence of an underlying non-uniform flow. In particular, the proposed model enables the accurate numerical simulation of the Kelvin wake pattern in a computational domain of reduced size. The governing equations are obtained by using an Arbitrary Lagrangian Eulerian (ALE) formulation which involves the underlying velocity of the fluid around the floating body assuming flat free surface, and a non-dimensional analysis to derive the novel linear system of equations for free surface flows. The discretization of the proposed model is made by a standard Galerkin finite element method, where a SUPG-inspired upwinding strategy has been used in combination with a Perfectly Matched Layer technique which allows truncating the original unbounded fluid domain without introducing spurious reflections in the Kelvin wake pattern. The numerical simulations computed with the proposed approach are compared with the results obtained by the classical linear potential model with uniform underlying flow and also with those from the full incompressible Navier–Stokes equations equipped with the k−ω SST turbulent model. This numerical comparison is discussed in terms of a classical hydrodynamic floating body benchmark involving the Wigley hull.

Performance of an auxetic honeycomb-core sandwich panel under close-in and far-field detonations of high explosive

This paper aims to scrutinise the effectiveness of a re-entrant auxetic honeycomb-core sandwich panel (AHSP) to protect reinforced concrete (RC) slab under close-in and far-field detonations of high explosive. A series of quarter symmetric 3D comprehensive numerical models were developed by using Arbitrary Lagrangian Eulerian (ALE) formulation in LS-DYNA hydrocode. Strain rate effects of the rate sensitive materials were employed in the model to consider dynamic behaviour of the materials during blast loading. The developed numerical model was validated with the documented experimental results. Deformation patterns, energy absorption, overpressure damping, blast pressure deflection, and stress-transmission to the protected structure were investigated with the computational models. Furthermore, the performance of AHSP sacrificial protective structure was compared with an equivalent areal density conventional honeycomb-core sandwich panel (CHSP) structure. The results showed that AHSP not only absorbed higher blast energy but also acted as a pressure deflector by forming a densified concave depression under close-in blast load. AHSP damped higher magnitude of blast overpressure in both close-in and far-field blasts. Moreover, a uniform redistribution of the stress on the protected structure was observed with AHSP protection. The overall response of AHSP was found to be better than CHSP to protect the RC slab.

UnDiFi-2D: An unstructured discontinuity fitting code for 2D grids

UnDiFi-2D, an open source (free software) Unstructured-grid, Discontinuity Fitting code, is presented. The aim of UnDiFi-2D is to model gas-dynamic discontinuities in two-dimensional (2D) flows as if they were true discontinuities of null thickness that bound regions of the flow-field where a smooth solution to the governing PDEs exists. UnDiFi-2D therefore needs to be coupled with an unstructured CFD solver that is used to discretize the governing PDEs within the smooth regions of the flow-field. Two different, in-house developed, CFD solvers are also included in the current distribution.The main features of the UnDiFi-2D software can be summarized as follows:Programming languageUnDiFi-2D is written in standard Fortran 77/95; its design is highly modular in order to enhance simplicity of use, maintenance and allow coupling with virtually any existing CFD solver;Usability, maintenance and enhancement In order to improve the usability, maintenance and enhancement of the code also the documentation has been carefully taken into account. The git distributed versioning system has been adopted to facilitate collaborative maintenance and code development;CopyrightsUnDiFi-2D is a free software that anyone can use, copy, distribute, change and improve under the GNU Public License version 3.The present paper is a manifesto of the first public release of the UnDiFi-2D code. It describes the currently implemented features, which are the result of more than a decade of still ongoing CFD developments. This work is focused on the computational techniques adopted and a detailed description of the main characteristics is reported. UnDiFi-2D capabilities are demonstrated by means of examples test cases. The design of the code allows to easily include existing CFD codes and is aimed at ease code reuse and readability. Program summaryProgram title: UnDiFi-2DCPC Library link to program files:https://doi.org/10.17632/5hwssmc2mx.1Licensing provisions: GNU General Public License, version 3Programming language: Fortran; developed and tested with Intel Fortran Compiler v. 18.0.3 and GNU gfortran.External routines: The code depends on several libraries and third-party packages which are detailed in the corpus of the text.Nature of problem: Numerical computation of flows with discontinuities.Solution method: Shock-fitting technique.Additional comments including restrictions and unusual features:•At present, UnDiFi-2D is validated for inviscid steady and unsteady two-dimensional flows without changes in the number of discontinuity lines and interaction points.•UnDiFi-2D implements a shock-fitting algorithm and can be coupled with unstructured cell-vertex solvers, with an Arbitrary Lagrangian-Eulerian (ALE) formulation.•UnDiFi-2D project adopts git [1], a free and open source distributed version control system. A public repository dedicated to UnDiFi-2D project [2] has been created on github [3], a web-based hosting service for software development projects using git versioning system. Finally, a comprehensive documentation is provided in the form of user manual developed in Pandoc [4].

Assessment of two wind gust injection methods: Field velocity vs. split velocity method

The objective of the present paper is to revisit two well-known wind gust injection methods in a consistent manner and to assess their performance based on different application cases. These are the field velocity method (FVM) and the split velocity method (SVM). For this purpose, both methods are consistently derived pointing out the link to the Arbitrary Lagrangian Eulerian formulation and the geometric conservation law. Furthermore, the differences between FVM and SVM are worked out and the advantages and disadvantages are compared. Based on a well-known test case considering a vertical gust hitting a plate and a newly developed case taking additionally a horizontal gust into account, the methods are evaluated and the deviations resulting from the disregard of the feedback effect in FVM are assessed. The results show that the deviations between the predictions by FVM and SVM are more pronounced for the horizontal gust justifying the introduction of this new test case. The main reason is that the additional source term in SVM responsible for the feedback effect of the surrounding flow on the gust itself nearly vanishes for the vertical gust, whereas it has a significant impact on the flow field and the resulting drag and lift coefficients for the horizontal gust. Furthermore, the correct formulation of the viscous stress tensor relying on the total velocity as done in case of SVM plays an important role, but is found to be negligible for the chosen Reynolds number of the present test cases. The study reveals that SVM is capable of delivering physical results in contradiction to FVM. It paves the way for investigating further complex gust configurations (e.g., inclined gusts) and practical applications towards coupled fluid–structure interaction simulations of engineering structures impacted by wind gusts.