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In this paper, a combined numerical and experimental method, called Extended Load Confluence Algorithm, is presented to accurately predict the dynamic response of non-periodic structures when little or no information about the applied loads is available. This approach, which falls into the category of Shape Sensing methods, inputs limited experimental information acquired from sensors to a mapping algorithm that predicts the response at unmeasured locations. The proposed algorithm consists of three major cores: an experimental core for data acquisition, a numerical core based on Finite Element Method for modeling the structure, and a mapping algorithm that improves the numerical model based on a modal approach in the frequency domain. The robustness and precision of the proposed algorithm are verified through numerical and experimental examples. The results of this paper demonstrate that without a precise knowledge of the loads acting on the structure, the dynamic behavior of the system can be predicted in an effective and precise manner after just a few iterations. [ABSTRACT FROM AUTHOR]

In this paper, a segregated algorithm is proposed to suppress high-frequency oscillations in the velocity field for incompressible flows. In this context, a new velocity formula based on a reconstruction of face fluxes is defined eliminating high-frequency errors. In analogy to the Rhie–Chow interpolation, this approach is equivalent to including a flux-based pressure gradient with a velocity diffusion in the momentum equation. In order to guarantee second-order accuracy of the numerical solver, a set of conditions are defined for the reconstruction operator. To arrive at the final formulation, an outlook over the state of the art regarding velocity reconstruction procedures is presented comparing them through an error analysis. A new operator is then obtained by means of a flux difference minimization satisfying the required spatial accuracy. The accuracy of the new algorithm is analyzed by performing mesh convergence studies for unsteady Navier–Stokes problems with analytical solutions. The stabilization properties of the solver are then tested in a problem where spurious numerical oscillations arise for the velocity field. The results show a remarkable performance of the proposed technique eliminating high-frequency errors without losing accuracy. [ABSTRACT FROM AUTHOR]

This paper presents a stable numerical algorithm for the Brinkman equations by using weak Galerkin (WG) finite element methods. The Brinkman equations can be viewed mathematically as a combination of the Stokes and Darcy equations which model fluid flow in a multi-physics environment, such as flow in complex porous media with a permeability coefficient highly varying in the simulation domain. In such applications, the flow is dominated by Darcy in some regions and by Stokes in others. It is well known that the usual Stokes stable elements do not work well for Darcy flow and vice versa. The challenge of this study is on the design of numerical schemes which are stable for both the Stokes and the Darcy equations. This paper shows that the WG finite element method is capable of meeting this challenge by providing a numerical scheme that is stable and accurate for both Darcy and the Stokes dominated flows. Error estimates of optimal order are established for the corresponding WG finite element solutions. The paper also presents some numerical experiments that demonstrate the robustness, reliability, flexibility and accuracy of the WG method for the Brinkman equations. [ABSTRACT FROM AUTHOR]

Abstract: This paper introduces a robust algorithm to determine the interfacial tension (γ) from pendant drop profiles using the Galerkin finite element method (γ-PD-FEM) to solve the axisymmetric form of the Young–Laplace (YL) equation. In this algorithm, the theoretical profiles are generated by solving the spherical coordinate form of the YL equation. γ-PD-FEM also solves for the parameter estimates by minimizing the difference between the theoretical and experimental surface functions, . This technique is compared to the widely used method of converting the YL equation to the three arc length-based (ALB) first-order ODEs developed by Bashforth and Adams (BA) in 1883, or as denoted in this paper, the γ-PD-BA method. The drop apex is the initial condition for the γ-PD-BA algorithm and the integration is terminated at a specified location along the drop profile. In contrast to techniques based on the BA approach, computation of the theoretical drop profile in γ-PD-FEM is obtained from a second-order ordinary differential equation and requires boundary conditions at the drop apex and at the contact line of the drop to the nozzle. By incorporating both boundary conditions into the problem formulation, the algorithm can also determine if the drop shape is at static equilibrium. Results to be presented include an outline of the computer algorithm, and comparison of γ values obtained from the γ-PD-FEM and the traditional γ-PD-BA method using simulated and experimental drop profile data sets. [Copyright &y& Elsevier]

Abstract: This paper deals with a new solid–fluid coupling algorithm between a rigid body and an unsteady compressible fluid flow, using an Embedded Boundary method. The coupling with a rigid body is a first step towards the coupling with a Discrete Element method. The flow is computed using a finite volume approach on a Cartesian grid. The expression of numerical fluxes does not affect the general coupling algorithm and we use a one-step high-order scheme proposed by Daru and Tenaud [V. Daru, C. Tenaud, J. Comput. Phys. (2004)]. The Embedded Boundary method is used to integrate the presence of a solid boundary in the fluid. The coupling algorithm is totally explicit and ensures exact mass conservation and a balance of momentum and energy between the fluid and the solid. It is shown that the scheme preserves uniform movement of both fluid and solid and introduces no numerical boundary roughness. The efficiency of the method is demonstrated on challenging one- and two-dimensional benchmarks. [Copyright &y& Elsevier]

Abstract: The reconstruction of the equilibrium of a plasma in a Tokamak is a free boundary problem described by the Grad–Shafranov equation in axisymmetric configuration. The right-hand side of this equation is a nonlinear source, which represents the toroidal component of the plasma current density. This paper deals with the identification of this nonlinearity source from experimental measurements in real time. The proposed method is based on a fixed point algorithm, a finite element resolution, a reduced basis method and a least-square optimization formulation. This is implemented in a software called Equinox with which several numerical experiments are conducted to explore the identification problem. It is shown that the identification of the profile of the averaged current density and of the safety factor as a function of the poloidal flux is very robust. [Copyright &y& Elsevier]

Abstract: The paper introduces a high-order, adaptive finite-element method for simulation of sonic measurements acquired with borehole-eccentered logging instruments. The resulting frequency-domain based algorithm combines a Fourier series expansion in one spatial dimension with a two-dimensional high-order adaptive finite-element method (FEM), and incorporates a perfectly matched layer (PML) for truncation of the computational domain. The simulation method was verified for various model problems, including a comparison to a semi-analytical solution developed specifically for this purpose. Numerical results indicate that for a wireline sonic tool operating in a fast formation, the main propagation modes are insensitive to the distance from the center of the tool to the center of the borehole (eccentricity distance). However, new flexural modes arise with an increase in eccentricity distance. In soft formations, we identify a new dipole tool mode which arises as a result of tool eccentricity. [Copyright &y& Elsevier]

Abstract: The numerical solution to the Biot equations of 3-D consolidation is still a challenging task because of the ill-conditioning of the resulting algebraic system and the instabilities that may affect the pore pressure solution. Recently new approaches have been advanced based on mixed formulations. In the present paper a fully coupled 3-D mixed finite element model is developed with the aim at alleviating the pore pressure numerical oscillations at the interface between materials with different permeabilities. A solution algorithm is implemented that takes advantage of the block structure of the discretized problem. The proposed model is verified against well-known analytical solutions and successfully experimented with in realistic applications of soil consolidation. [Copyright &y& Elsevier]

In the present work, fluid–structure interaction problems are analysed by means of optimised boundary element–finite element coupling procedures. The boundary element method is here employed to numerically model acoustic fluids and the finite element method is applied to discretise dynamic bodies (nonlinear effects included). Boundary element—finite element coupling is accomplished by an iterative algorithm: each boundary element or finite element sub-domain is analysed independently (as an uncoupled model) and a successive renewal of the variables at the common interfaces is performed, until convergence is achieved. The evaluation of an optimised relaxation parameter is introduced taking into account the minimisation of a square error functional. The algorithm that arises is more efficient and stable, representing an advancement of the iterative procedure. At the end of the paper, numerical examples are presented, illustrating the potentialities of the proposed methodology. [Copyright &y& Elsevier]

Abstract: The pendant and sessile drop profile analysis using the finite element method (PSDA-FEM) is an algorithm which allows simultaneous determination of the interfacial tension (γ) and contact angle () from sessile drop profiles. The PSDA-FEM algorithm solves the nonlinear second-order spherical coordinate form of the Young–Laplace equation. Thus, the boundary conditions at the drop apex and contact position of the drop with the substrate are required to solve for the drop profile coordinates. The boundary condition at the position where the drop contacts the substrate may be specified as a fixed contact line or fixed contact angle. This paper will focus on the fixed contact angle boundary condition for sessile drops on a substrate and how this boundary condition is used in the PSDA-FEM curve-fitting algorithm. The PSDA-FEM algorithm has been tested using simulated drop shapes with and without the addition of random error to the drop profile coordinates. The random error is varied to simulate the effect of camera resolution on the estimates of γ and values obtained from the curve-fitting algorithm. The error in the experimental values for γ from sessile drops of water on acrylic and Mazola corn oil on acrylic falls within the predicted range of errors obtained for γ values from simulated sessile drop profiles with randomized errors that are comparable in magnitude to the resolution of the experimental setup. [Copyright &y& Elsevier]