A time discontinuous Galerkin isogeometric analysis method for non-Fourier thermal wave propagation problem

Modeling concept and numerical simulation of ultrasonic wave propagation in a moving fluid-structure domain based on a monolithic approach

Numerical modeling of wave propagation into a harbor using improved characteristic scheme

A particle-based continuum model is presented for the simulation of seismic wave propagation. Accurate simulation of seismic ground motion for the model with arbitrary free surface of the ground is a key issue for not only scientific interest but also in practical fields to estimate seismic signals traveled through subsurface structure. In the present study, a Hamiltonian particle method (HPM) is proposed to seismological numerical modeling. HPM has some advantages comparing to traditional continuous and discontinuous methods in terms of; (i) the introduction of the traction-free boundary conditions is easier than that in finite difference methods (FDM), (ii) data structure in HPM is simpler than that in finite element methods (FEM) because of no need to consider the connectivity between nodes and elements when discretizing object of analysis, and (iii) no need to calibrate material parameters that is a cumbersome process in distinct element method (DEM) with a hexagonal arrangement. In this paper, we first calculate the seismic wave propagation in a homogeneous media and compare the results with that from FDM to demonstrate the performance of the method. Next, we simulate surface wave propagation in a model with arbitrary surface topology. These results indicate that HPM can calculate elastic and surface wave propagation with sufficient accuracy for models with a free surface of arbitrary shape.

Elastic wave propagation in a segmented X-ray computed tomography model of a concrete specimen

A modification of the wave-propagation algorithm is used as a tool for determining contact quantities in a finite-volume scheme for the numerical simulation of two-dimensional thermoelastic wave propagation in inhomogeneous media. The modification is needed to provide the satisfaction of the thermodynamic consistency conditions between adjacent elements. It appears that the algorithm is thermodynamically consistent except for the limiter functions. Therefore, a composite scheme is used where the Godunov step is applied after each three second-order Lax–Wendroff steps. Elimination of source terms is made following the method of balancing source terms after independent solution of the heat conduction equation.

Iterative solution of Helmholtz problem with high-order isogeometric analysis and finite element method at mid-range frequencies

Exact geometry based quasi-conforming analysis for Euler-Bernoulli beam

An isogeometric analysis (IGA) framework is presented to construct and solve dispersion relations for generating the band structure of periodic materials with complicated geometries representing phononic crystals and elastic metamaterials. As the dispersive properties depend on the microstructural geometry, an accurate representation of microstructural geometrical features is paramount. To this end, the ability of isogeometric analysis to exactly model complex curved geometries is exploited, and wave propagation in infinitely periodic solids is combined with isogeometric analysis. The benefits of IGA are demonstrated by comparing the results to those obtained using standard finite element analysis (FEA). It is shown that the IGA solutions can reach the same level of accuracy as FEA while using significantly fewer degrees of freedom. IGA is applied to phononic crystals and elastic metamaterials and the band structure for a variety of unit cells with complex microstructural geometries is investigated to illustrate the desirable dispersive effects in these metamaterials.

Simulations of wave propagation in porous media are important to the understanding of various phenomena, such as seismic effects and non-destructive testing. The derivation and implementation of finite element analysis for a fully dynamic three-field deformable porous media model based on the de la Cruz and Spanos (dCS) theory [1] is presented. The dCS theory accounts for the fluid viscous dissipation mechanism and nonreciprocal solid-fluid interactions, which are neglected in Biot theory [2]. While the Biot theory is based on experimental data, the dCS theory is derived from mixture theories associated with the volume fraction concept and representing the connection between micro and macro pore scales. dCS results presented build upon recent FE model for quasi-static analysis [3]. Here, for the fully dynamic case incorporating both fluid and solid inertia, the accuracy and robustness of the FEA model is verified by wave propagation examples in one and two dimensions. Time integration scheme utilized and the changes in convergence rates according to how strongly coupled is the system will be discussed. The required element approximation order for all variables to ensure numerical stability will be demonstrated. The presented model is compared with the results from Biot theory, allowing one to observe the differences between the two theories and their relevance. The solutions in the time and frequency domain are also discussed, where the analysis of the correspondent eigenproblem leads to important information regarding wave velocity and attenuation.

In this paper a discontinuous, hanging-node, isogeometric analysis (IGA) method is developed and applied to the first-order form of the neutron transport equation with a discrete ordinate (SN) angular discretisation in two-dimensional space. The complexities involved in upwinding across curved element boundaries that contain hanging-nodes have been addressed to ensure that the scheme remains conservative. A robust algorithm for cycle-breaking has also been introduced in order to develop a unique sweep ordering of the elements for each discrete ordinates direction. The convergence rate of the scheme has been verified using the method of manufactured solutions (MMS) with a smooth solution. Heuristic error indicators have been used to drive an adaptive mesh refinement (AMR) algorithm to take advantage of the hanging-node discretisation. The effectiveness of this method is demonstrated for three test cases. The first is a homogeneous square in a vacuum with varying mean free path and a prescribed extraneous unit source. The second test case is a radiation shielding problem and the third is a 3×3 “supercell” featuring a burnable absorber. In the final test case, comparisons are made to the discontinuous Galerkin finite element method (DGFEM) using both straight-sided and curved quadratic finite elements.

The ultrasonic nondestructive testing of components with inhomogeneous, anisotropic crystalline structure may encounter considerable difficulties. Due to the curved propagation paths of ultrasonic waves in these materials, inspection results may be hard to interpret. We present a numerical method for the simulation of elastic wave propagation in inhomogeneous, general elastically anisotropic media which is based on the general finite integration (FI) approach. The numerical examples given, deal with the ultrasonic impulse-echo inspection of a typical austenitic V-shaped butt weld with a spatially varying grain structure. Discussion of the results is done in comparison with those obtained from a ray tracing algorithm.

Anisotropy is widely-used nowadays in seismic processing as it may characterize fractured reservoirs, pre-stressed state of formations etc. However, numerical simulation of seismic wave propagation in anisotropic media requires the use of advanced, computationally-intense algorithms. Meanwhile anisotropic formations take relatively small part, several percents, of the model. In this situation it is reasonable to develop a finite-difference algorithm coupling the anisotropy-oriented scheme with efficient standard staggered grid, or Virieux, scheme. So, that the computationally-intense algorithm is used only inside the anisotropic formations, while the Virieux scheme is used in the major isotropic part of the model. The coupled scheme may be almost as efficient as Virieux scheme but providing full detailed knowledge about wave propagation in anisotropic formations.

Dynamic analysis of two-dimensional elasticity problems using the Isogeometric analysis method and its comparison with the finite element method is the subject of this research. For this purpose, formulation of the governing differential equation is obtained by using the B-spline basis functions. Some numerical examples employing consistent and lumped mass matrices are presented in order to compare the results of Isogeometric analysis and finite elements. The effect of increasing the number of control points and the degree of B-spline basis functions on the accuracy of the solution are also investigated. Furthermore, since the Newmark method is employed for transient dynamic analysis, the effects of parameters α and β on the solution accuracy are investigated. The obtained results demonstrate higher accuracy of the isogeometric analysis method in comparison with the FEM, despite employing fewer numbers of degrees of freedom and consequently reduction in the dimensions of system of equations and computational effort.

Parallel isogeometric boundary element analysis with T-splines on CUDA

In order to perform large scale numerical simulation of wave propagation in 3D heterogeneous multiscale viscoelastic media, Finite Difference technique and its parallel implementation based on domain decomposition is used. A couple of typical statements of borehole geophysics are dealt with—sonic log and cross well measurements. Both of them are essentially multiscales, which claims to take into account heterogeneities of very different sizes in order to provide reliable results of simulations. Locally refined spatial grids help us to avoid the use of redundantly tiny grid cells in a target area, but cause some troubles with uniform load of Processor Units involved in computations. We present results of scalability tests together with results of numerical simulations for both statements performed for some realistic models.