Results for "Spectral Element Method" : Scipedia

14th WCCM-ECCOMAS Congress 2020

Geomechanical Modeling Using Variable Order Spectral Element Method at Non-Conformal Meshes

Abstract

The paper considers an overview of the problems of mathematical modeling of geomechanical processes occurring in rocks during the geological exploration and development of reservoirs and well boring process. The mathematical formulation is based on the theory of repeated superposition of large deformations. A numerical discretization of the posed boundary problems of interacting solids is performed using a discontinuous spectral element method and multi-point constraints at non-matching mesh interfaces between interacting solid rock structures. Several industrial applications of the developed approach are considered. Seismic wave propagation in the heterogeneous media with initial geomechanical stresses is considered. A modelling of an induced anisotropy is performed by the superposition of dynamic deformations onto initial generally finite strains. Use of variable order spectral elements at non-conformal meshes allows one to simplify the process of unstructured mesh generation for the discretization of complex geological models and to set the local spatial order of the SEM discretization depending on the speed of seismic waves in geological structures, which significantly reduces the computational costs when conducting numerical modeling and lowers the requirements to the model preprocessing and mesh quality. The considered approach allows predicting in more detail the behavior of the rock during reservoir development, taking into account different stages of the field deformations. In particular, the redistribution of accumulated deformations during multistep loading and / or changes in the structure (topology) of the loaded body, as well as contact conditions of adhesion / sliding at the interlayer boundaries and bonded contacts are taken into account. These problems were solved using CAE Fidesys software, which allows solving static and dynamic problems of geomechanics and geophysics using finite (FEM) and spectral (SEM) element methods of a variable approximation order in space at non-conformal unstructured meshes.

Abstract

The paper considers an overview of the problems of mathematical modeling of geomechanical processes occurring in rocks during the geological exploration and development [...]

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14th WCCM-ECCOMAS Congress 2020

Vibration Control Using Piezoelectric Connected with Shunts Circuits

Abstract

The study analyzes the dynamic behaviour and vibration attenuation of an Euler Bernoulli beam coupled with a piezoelectric layer. The vibration attenuation is given by the shunt circuit connected to the piezoelectric. This paper shows different shunt circuit impedances and how they [...]

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ECCOMAS Congress 2022 - 8th European Congress on Computational Methods in Applied Sciences and Engineering

Data-driven enhanced model reduction for bifurcating models in computational fluid dynamics

Abstract

We investigate various data-driven methods to enhance projection-based model reduction techniques with the aim of capturing bifurcating solutions. To show the effectiveness of the data-driven enhancements, we focus on the incompressible Navier-Stokes equations and different types [...]

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WCCM-APCOM 2022

Simulation of wave propagation in remote bonded FBG sensors using the spectral element method

Abstract

Ultrasonic guided waves (GW) due to their ability to monitor large areas with few sensors, are commonly employed for structural health monitoring (SHM) in aerospace, civil, and mechanical industries. The FBG sensors in the edge filtering setup are re-emerging as a favored technique for GW sensing. The FBG sensors offer embeddability, ability to be multiplexed, small size, and immunity to electric and magnetic fields. To enhance the sensitivity of these sensors, these sensors are deployed in the so-called remote bonding configuration where the optical fiber is bonded to the structure while the FBG sensor is free. This configuration not only enhances the sensitivity but also opens up possibility of self-referencing. In this setup the GW in the structure is coupled to the fiber and converted into fiber modes. These modes propagate along the fiber and then are sensed at the FBG. The conversion of the plate modes to fiber modes is a phenomenon which is still being studied. The effect of the adhesive layer and the material properties of the adhesive on the coupling are still not known. Furthermore the directional nature of this coupling and its marked difference from the directly bonded configuration needs to be studied in detail. For this detailed study a computationally efficient model which captures the physics of the coupling is necessary. Hence, in this research we develop a numerical model based on the spectral element method (SEM) for the modeling of the remote bonded configuration of the FBG. The model comprises four meters long optical fiber bonded to the center of the plate by the adhesive layer and the piezoelectric disc (PZT) used for wave excitation. The ability of the SEM model to capture the effect of the adhesive and the remote bonding as well as the directional nature of the coupling has been studied in this paper. The model is validated with analytical and experimental results. It has been shown that the SEM model captures the physics of the coupling and is computationally more efficient than other methods using conventional finite element software.

Abstract

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ECCOMAS Congress 2022 - 8th European Congress on Computational Methods in Applied Sciences and Engineering

Implicit LES of the Transonic Flow Over A High-Pressure Turbine Cascade using DG Subcell Shock Capturing

Abstract

Implicit large-eddy simulations of the high-pressure turbine cascade VKI-LS89 under transonic operating conditions using a high-order accurate discontinuous Galerkin spectral element method are presented. The subcell shock capturing method by Hennemann et al. [1] is investigated [...]

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