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In this paper, water entry process of air launched AUV is investigated by employing fully coupled finite element method and arbitrary Lagrange–Euler formulation (FEM-ALE) and using penalty coupling technique. Numerical model is established to describe the hydrodynamic characteristics and flow patterns of a high-speed water entry AUV. The effectiveness and accuracy of the numerical simulation are verified quantitatively by the experiments of the earlier study. Selection of suitable advection method and mesh convergence study is carried out during experimental validation process. It is found that appropriate mesh size of impact domain is crucial for numerical simulations and second-order Van Leer advection method is more appropriate for high speed water entry problems. Subsequently, the arbitrary Lagrange–Euler (ALE) algorithm is used to describe the variation laws of the impact load characteristics with water entry velocities, water entry angles and different AUV masses. Dimensionless impact coefficient of AUV at different velocities calculated using ALE method is compared with SPH results. This reveals that ALE method can also simulate the water entry process accurately with less computational cost. This research work can provide beneficial reference information for structure design of AUV and for selection of the water entry parameters.

In many contexts, there is a need to construct C¹ maps from a given reference domain to a family of deformed domains. In our case, the motivation comes from the application of the Arbitrary Lagrangian Eulerian (ALE) method and also the reduced basis element method. In these methods, the maps are used to construct the grid-points needed on the deformed domains, and the corresponding Jacobian of the map is used to map vector fields from one domain to another. In order to keep the continuity of the mapped vector fields, the Jacobian must be continuous, and thus the maps need to be C¹. In addition, the constructed grids on the deformed domains should be quality grids in the sense that, for a given partial differential equation defined on any of the deformed domains, the solution should be accurate. Since we are interested in a family of deformed domains, we consider the solutions of the partial differential equation to be a family of solutions governed by the geometry of the domains. Different mapping strategies are discussed and compared: the transfinite interpolation proposed by Gordon and Hall,¹² the pseudo-harmonic extension proposed by Gordon and Wixom,¹³ a new generalization of the Gordon–Hall method (e.g., to general polygons in two dimensions), the harmonic extension, and the mean-valued extension proposed by Floater.⁸

This paper presents a new method of random noise cancellation for removing artefacts from biomedical signals using an adaptive line enhancer (ALE). The ALE is implemented using proposed time domain variable step size Griffith least mean square (VSGLMS) algorithm. The technique is based on the adaptation of the gradient of the error surface. The method makes both the step size and the gradient free from observation noise and reduces the gradient mis-adjustment error. Here, both the gradient and the scale factor for the step size are free from the input noise effects, which makes the algorithm robust to both stationary and non-stationary observation noise. Further the additional computational load involved for this is marginal. The VSGLMS adaptive filter technique for ALE is tested on noise cancellation of two types of bio-medical signals — separation of electro cardiogram (ECG) signal from a background of electro myogram (EMG) and heart sound signal (HSS) from lung sound signal (LSS). Application of VSGLAM–ALE for the separation of HSS from LSS and ECG from EMG has been demonstrated using synthetic White Gaussian noise (WGN). It is found that VSGLMS–ALE can separate the desired signals like ECG or HSS at an input SNR of -5 dB to 27 dB. The performance of VSGLMS is compared with state-of-the-art least mean square LMS–ALE and normalised LMS–ALE. The results of PSDs, time domain waveforms, and mean square error (MSE) have proven that VSGLMS performs better than advanced techniques.

This paper presents a new random noise cancellation technique for cancelling muscle artifact effects from ECG using ALE in the transformed domain. For this a transform domain variable step size griffith least mean square (TVGLMS) algorithm is proposed. The technique is based on the adaptation of the gradient of the error surface. The method frees both the step size and the gradient from observation noise and reduces the gradient mis-adjustment error. The sluggishness introduced due to the averaging of the gradient in the time domain is overcome by the transformed domain approach. The proposed algorithm uses a discrete cosine transform (DCT)-based signal decomposition due to its improved frequency resolution compared to a discrete Fourier transform (DFT). Furthermore, as the data used symmetrical, DCT usage results in low leakage (bias and variance). The performance of the proposed method has been tested on ECG signals combined with WGN, extracted from MIT database, and compared with several existing techniques like LMS, NLMS, and VGLMS.

An efficient implicit unstructured grid algorithm for solving unsteady inviscid compressible flows over moving body employing an Arbitrary Lagrangian Eulerian formulation is presented. In the present formulation, the time discretization is performed using a second-order accurate 3-point time integration scheme and the upwind-biased space discretization using second-order accurate finite volume formulation with Venkatakrishnan limiter. The face-velocities of the control volumes are computed using Geometric Conservation Laws. The nonlinear system arising from the implicit formulation is solved using an ILU preconditioned Newton–Krylov iteration at every time step. The computed results for two test cases involving harmonically oscillating NACA0012 airfoil are presented in order to demonstrate the efficacy of the present solver.

The aim of the paper is to use Arbitrary Lagrangian Eulerian (ALE) formulation for fluid–structure interaction for modeling blood flow in artery. Predicting blood flow and its effects on arteries requires simulation of fluid–structure coupling with deformable mesh. For fluid simulation velocity–pressure formulation is used, we present the algorithm which allows to compute fluid velocity and pressure using explicit time integration. This method has been applied successfully for several applications including sloshing tank analysis. For the structure shell type elements with five points integration through the thickness to accurately represent bending effects, are modeled. Since the structure is deformable, to prevent high mesh distortion an elasticity material model for the mesh is used for mesh deformation. For fluid–structure coupling, explicit contact algorithm based on penalty method. Such a model can be used to study the profile of the flow and pressure waves as they propagate along the arteries. In the paper, the onset of a pressure pulse was simulated at the entrance of a three dimension straight artery blood vessel and the resulting dynamic response in the form of a propagating pulse wave through the wall was analyzed and compared. Good agreement was found between the numerical results and the theoretical description of an idealized artery. Work has also been done on implementing the material constitutive models specific for vascular applications.

Performance analysis of a reversible micro-pump system is obtained by numerical simulations. The unsteady incompressible Navier–Stokes equations are solved in a moving micro-pump system using a spectral h/p element algorithm, employing an arbitrary Lagrangian Eulerian (ALE) formulation on structured/unstructured meshes. The performance of the micro-pump is evaluated as a function of the Reynolds number and the geometric parameters. The volumetric flowrate is shown to increase as a function of the Reynolds number. The unsteady traction forces on the pump membrane and the vorticity dynamics within the pump cavity are presented.

The mechanical properties of Ogden material under biaxial deformation are obtained by using the bubble inflation technique. First, pressure inside the bubble and height at the hemispheric pole are recorded during bubble inflation experiment. Thereafter, Ogden's theory of hyperelasticity is employed to define the constitutive model of flat circular thermoplastic membranes (CTPMs) and nonlinear equilibrium equations of the inflation process are solved using finite difference method with deferred corrections. As a last step, a neuronal algorithm artificial neural network (ANN) model is employed to minimize the difference between calculated and measured parameters to determine material constants for Ogden model. This technique was successfully implemented for acrylonitrile-butadiene-styrene (ABS), at typical thermoforming temperatures, 145°C. When solving for the bubble inflation, the recorded pressure is applied uniformly on the structure. During the process inflation, the pressure is not uniform inside the bubble, thus full gas dynamic equations need to be solved to get the appropriate nonuniform pressure to be applied on the structure. In order to simulate the inflation process accurately, computational fluid dynamics in a moving fluid domain as well as fluid structure interaction (FSI) algorithms need to be performed for accurate pressure prediction and fluid structure interface coupling. Fluid structure interaction solver is then required to couple the dynamic of the inflated gas to structure motion. Recent development has been performed for the simulation of gas dynamic in a moving domain using arbitrary Lagrangian Eulerian (ALE) techniques.

In multi-physical investigations, modeling moving objects at the micro-scale often requires the inclusion of mesh movement and viscous losses due to boundary layers. State-of-the-art approaches use, for example, the full set of flow equations. However, these equations are more computationally expensive due to their non-linearity. Here, we present a formulation for efficiently modeling visco-acoustic propagation problems on moving domains combined with fluid-solid-acoustic interaction. Therefore, we apply the Arbitrary-Lagrangian-Eulerian (ALE) framework to the fully linearized flow equations for a Newtonian fluid. Neglecting the non-linearity means that no sub-iterations during the solving process are necessary compared to the full set of flow equations. For the mesh deformation, we utilize a quasi-static mechanical field which is iteratively coupled to the flow equations in a strong sense. Furthermore, we use non-conforming interfaces to couple the acoustic and flow fields directly. The formulation presented is verified through convergence studies, proving second-order convergence using Taylor-Hood elements. Finally, the formulation is applied to model a Micro-Electro-Mechanical-System (MEMS) loudspeaker unit cell useable for ultrasound-based pumping principles like Advanced Digital Sound Reconstruction (ADSR). In summary, this formulation can efficiently model acoustic propagation problems of moving objects at the micro-scale.

Numerical techniques for solving the problem of fluid-structure interaction with an elastic material in a laminar incompressible viscous flow are described. An Arbitrary Lagrangian–Eulerian (ALE) formulation is employed in a fully coupled monolithic way, considering the problem as one continuum. The mathematical description and the numerical schemes are designed in such a way that more complicated constitutive relations (and more realistic for biomechanics applications) for the fluid as well as the structural part can be easily incorporated. We utilize the well-known Q₂P₁ finite element pair for discretization in space to gain high accuracy and perform as time-stepping the second-order Crank–Nicholson, respectively, Fractional-Step-θ-scheme for both solid and fluid parts. The resulting nonlinear discretized algebraic system is solved by a Newton method which approximates the Jacobian matrices by a divided differences approach, and the resulting linear systems are solved by iterative solvers, preferably of Krylovmultigrid type.

For validation and evaluation of the accuracy of the proposed methodology, we present corresponding results for a newset of FSI benchmarking configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in laminar channel flow, allowing stationary as well as periodically oscillating deformations. Then, as an example for fluid-structure interaction (FSI) in biomedical problems, the influence of endovascular stent implantation onto cerebral aneurysm hemodynamics is numerically investigated. The aim is to study the interaction of the elastic walls of the aneurysm with the geometrical shape of the implanted stent structure for prototypical 2D configurations. This study can be seen as a basic step towards the understanding of the resulting complex flow phenomena so that in future aneurysm rupture shall be suppressed by an optimal setting for the implanted stent geometry.