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This contribution benchmarks the aeroacoustic workflow of the perturbed convective wave equation and the Ffowcs Williams and Hawkings analogy in Farassat’s 1A version for a low-pressure axial fan. Thereby, we focus on the turbulence modeling of the flow simulation and mesh convergence concerning the complete aeroacoustic workflow. During the validation, good agreement has been found with the efficiency, the wall pressure sensor signals, and the mean velocity profiles in the duct. The analysis of the source term structures shows a strong correlation to the sound pressure spectrum. Finally, both acoustic sound propagation models are compared to the measured sound field data.

We present a family of high-order trapezoidal rule-based quadratures for a class of singular integrals, where the integrand has a point singularity. The singular part of the integrand is expanded in a Taylor series involving terms of increasing smoothness. The quadratures are based on the trapezoidal rule, with the quadrature weights for Cartesian nodes close to the singularity judiciously corrected based on the expansion. High-order accuracy can be achieved by utilizing a sufficient number of correction nodes around the singularity to approximate the terms in the series expansion. The derived quadratures are applied to the implicit boundary integral formulation of surface integrals involving the Laplace layer kernels.

This paper illustrates the development of a recursive QR technique for the analysis of transient events, such as disruptions or scenario evolution, in fusion devices with three-dimensional conducting structures using an integral eddy current formulation. An integral formulation involves the solution, at each time step, of a large full linear system. For this reason, a direct solution is impractical in terms of time and memory consumption. Moreover, typical fusion devices show a symmetric/periodic structure. This can be properly exploited when the plasma and other sources possess the same symmetry/periodicity of the structure. Indeed, in this case, the computation can be reduced to only a single sector of the overall structure. In this work the periodicity and the symmetries are merged in the recursive QR technique, exhibiting a huge decrease in the computational cost. Finally, the proposed technique is applied to a realistic large-scale problem related to the International Thermonuclear Experimental Reactor (ITER).

We study the two-phase Stokes flow driven by surface tension with two fluids of equal viscosity, separated by an asymptotically flat interface with graph geometry. The flow is assumed to be two-dimensional with the fluids filling the entire space. We prove well-posedness and parabolic smoothing in Sobolev spaces up to critical regularity. The main technical tools are an analysis of nonlinear singular integral operators arising from the hydrodynamic single-layer potential and abstract results on nonlinear parabolic evolution equations.

Purpose The purpose of this study is to apply the Meshless Local Petrov–Galerkin (MLPG) method to solve the bending problems of linear viscoelastic plates, considering Reissner’s theory.Design/methodology/approachThe weak formulation for the set of equations that govern Reissner’s plate theory is implemented in conjunction with the integral formulation applied to viscoelastic constitutive expressions. A meshless method based on the Moving Least Squares (MLS) approximation is considered in the numerical implementation. The final equation system is assembled by adopting simple and efficient schemes for numerical integration, considering a simplified formulation through centralization of the local interpolation domains and Gaussian quadrature at the same field point. The results obtained are compared with available solutions to demonstrate the efficiency of the proposed formulation.FindingsThe hereditary integral approach proved to be the most general way to analyze the viscoelastic problem, especially when applied together with the modified scheme for numerical integration. In addition, the variable changing technique is demonstrated to be an efficient formulation for solving shear-locking effects in thin plate problems.Originality/valueThe differential of the present study is related to the manner in which the properties of linear viscoelastic materials are considered in the formulation. Although most authors consider this point through the application of the correspondence principle, the present study works with a hereditary integral formulation. In addition, the variable changing technique is applied to solve the shear-locking effects, and an alternative approximation technique is considered to speed up the numerical integration process.

The reproducing kernel particle method (RKPM) is a widely used meshless method that has been extensively applied in numerical analysis. The drawback of RKPM is that when different kernel functions are chosen during the computation process, there are different calculation accuracy, and significant discreteness. To address this issue, the radial basis function is introduced to RKPM, and the radial basis reproducing kernel particle method (RB-RKPM) is proposed. The negative impacts of different kernel functions on calculation accuracy can be eliminated by RB-RKPM, which possesses some advantages, such as good convergence, high computational accuracy and efficiency. Furthermore, the RB-RKPM is applied to the damped elastic dynamics problems (DEDPs), the governing equations for the DEDPs are derived based on the weak integral formulation, and the time is integrated by using the Newmark-linear acceleration method. Finally, the correctness of the proposed method in analyzing the DEDPs is verified through numerical examples.

In this paper, we describe and analyze fast procedures for numerical resolution of Dirichlet and mixed boundary value problems in linear elasticity, in the particular case of two-dimensional circular domain. The direct boundary integral formulation of the Dirichlet problem is approximated by using the B-splines on the boundary curve. This yields an algebraic linear system involving two dense matrices with block structure, the single layer and the double layer matrices. The associated matrix entries are computed explicitly and efficiently. Additionally, the circulant block structure of the single layer matrix and the discrete Fourier transform (DFT) matrix enable us to easily compute the inverse of the single layer matrix as a product of sparse matrices and the discrete Fourier transform matrix which speed up the matrix-vector multiplication. Moreover, the discrete Fourier transform permits us to construct some optimal preconditioners for the conjugate gradient methods. Some numerical examples for the Dirichlet and the mixed problems which show a remarkable efficiency and accuracy of algorithms for the problems are presented.

Multiphysics problems represent an open issue in numerical modeling. Electromagnetic launchers represent typical examples that require a strongly coupled magnetoquasistatic and mechanical approach. This is mainly due to the high velocities which make comparable the electrical and the mechanical response times. The analysis of interacting devices (e.g., a rail launcher and its feeding generator) adds further complexity, since in this context the substitution of one device with an electric circuit does not guarantee the accuracy of the analysis. A simultaneous full 3D electromechanical analysis of the interacting devices is often required. In this paper a numerical 3D analysis of a full launch system, composed by an air-core compulsator which feeds an electromagnetic rail launcher, is presented. The analysis has been performed by using a dedicated, in-house developed research code, named “EN4EM” (Equivalent Network for Electromagnetic Modeling). This code is able to take into account all the relevant electromechanical quantities and phenomena (i.e., eddy currents, velocity skin effect, sliding contacts) in both the devices. A weakly coupled analysis, based on the use of a zero-dimensional model of the launcher (i.e., a single loop electrical equivalent circuit), has been also performed. Its results, compared with those by the simultaneous 3D analysis of interacting devices, show an over-estimate of about 10–15% of the muzzle speed of the armature.

The paper deals with the numerical solution of 2D wave propagation exterior problems including viscous and material damping coefficients and equipped by Neumann boundary condition, hence modeling the hard scattering of damped waves. The differential problem, which includes, besides diffusion, advection and reaction terms, is written as a space–time boundary integral equation (BIE) whose kernel is given by the hypersingular fundamental solution of the 2D damped waves operator. The resulting BIE is solved by a modified Energetic Boundary Element Method, where a suitable kernel treatment is introduced for the evaluation of the discretization linear system matrix entries represented by space–time quadruple integrals with hypersingular kernel in space variables. A wide variety of numerical results, obtained varying both damping coefficients and discretization parameters, is presented and shows accuracy and stability of the proposed technique, confirming what was theoretically proved for the simpler undamped case. Post-processing phase is also taken into account, giving the approximate solution of the exterior differential problem involving damped waves propagation around disconnected obstacles and bounded domains.