• Coupled systems mechanics
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• v.8 no.1
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• pp.71-93
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• 2019

Finite element simulations of solid mechanics problems often involve the use of Non-Confirming Meshes (NCM) to increase accuracy in capturing nonlinear behavior, including damage and plasticity, in part of a solid domain without an undue increase in computational costs. In the presence of material nonlinearity and plasticity, higher-order variables are often needed to capture nonlinear behavior and material history on non-conforming interfaces. The most popular formulations for coupling non-conforming meshes are dual methods that involve the interpolation of a traction field on the interface. These methods are subject to the Ladyzhenskaya-Babuska-Brezzi (LBB) stability condition, and are therefore limited in their implementation with the higher-order elements needed to capture nonlinear material behavior. Alternatively, the enriched discontinuous Galerkin approach (EDGA) (Haikal and Hjelmstad 2010) is a primal method that provides higher order kinematic fields on the interface, and in which interface tractions are computed from local finite element estimates, therefore facilitating its implementation with nonlinear material models. The inclusion of higher-order interface variables, however, presents the issue of preserving material history at integration points when a increase in integration order is needed. In this study, the enriched discontinuous Galerkin approach (EDGA) is extended to the case of small-deformation plasticity. An interface-driven Gauss-Kronrod integration rule is proposed to enable adaptive enrichment on the interface while preserving history-dependent material data at existing integration points. The method is implemented using classical J2 plasticity theory as well as the pressure-dependent Drucker-Prager material model. We show that an efficient treatment of interface variables can improve algorithmic performance and provide a consistent approach for coupling non-conforming meshes in inelasticity.

• Wind and Structures
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• v.34 no.1
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• pp.59-72
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• 2022

In this work the numerical results of the flow around a 5:1 rectangular cylinder at Reynolds numbers 3 000 and 40 000, zero angle of attack and smooth incoming flow condition are presented. Implicit Large Eddy Simulations (ILES) have been performed with a high-order accurate spatial scheme and an implicit high-order accurate time integration method. The spatial approximation is based on a discontinuous Galerkin (dG) method, while the time integration exploits a linearly-implicit Rosenbrock-type Runge-Kutta scheme. The aim of this work is to show the feasibility of high-fidelity flow simulations with a moderate number of DOFs and large time step sizes. Moreover, the effect of different parameters, i.e., dimension of the computational domain, mesh type, grid resolution, boundary conditions, time step size and polynomial approximation, on the results accuracy is investigated. Our best dG result at Re=3 000 perfectly agrees with a reference DNS obtained using Nek5000 and about 40 times more degrees of freedom. The Re=40 000 computations, which are strongly under-resolved, show a reasonable correspondence with the experimental data of Mannini et al. (2017) and the LES of Zhang and Xu (2020).

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2008.10a
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• pp.263-266
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• 2008

This paper is concerned with the analysis of elasto-plastic stress waves in a mode I semi-infinite cracked solid subjected to Heaviside pulse load. This study adopts a time-discontinuous variational integrator based on Hamiltonian in order to reduce the numerical dispersive and dissipative errors. This also utilizes an integration scheme of the constitutive model with 2nd-order accuracy which is formulated on the strain space for a rate and temperature dependent material model. Finite element analyses of elasto-plastic stress waves are carried out in order to compare the accuracy between a conventional Galerkin method and the time- discontinuous variational integrator.

• Journal of computational fluids engineering
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• v.19 no.3
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• pp.52-61
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• 2014

The present paper deals with the efficient computation of higher-order CFD methods for compressible flow using graphics processing units (GPU). The higher-order CFD methods, such as discontinuous Galerkin (DG) methods and correction procedure via reconstruction (CPR) methods, can realize arbitrary higher-order accuracy with compact stencil on unstructured mesh. However, they require much more computational costs compared to the widely used finite volume methods (FVM). Graphics processing unit, consisting of hundreds or thousands small cores, is apt to massive parallel computations of compressible flow based on the higher-order CFD methods and can reduce computational time greatly. Higher-order multi-dimensional limiting process (MLP) is applied for the robust control of numerical oscillations around shock discontinuity and implemented efficiently on GPU. The program is written and optimized in CUDA library offered from NVIDIA. The whole algorithms are implemented to guarantee accurate and efficient computations for parallel programming on shared-memory model of GPU. The extensive numerical experiments validates that the GPU successfully accelerates computing compressible flow using higher-order method.

• Advances in aircraft and spacecraft science
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• v.3 no.2
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• pp.149-170
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• 2016

Multi-Disciplinary Optimization (MDO) is widely used to handle the advanced design in several engineering applications. Such applications are commonly simulation-based, in order to capture the physics of the phenomena under study. This framework demands fast optimization algorithms as well as trustworthy numerical analyses, and a synergic integration between the two is required to obtain an efficient design process. In order to meet these needs, an adaptive Computational Fluid Dynamics (CFD) solver and a fast optimization algorithm have been developed and combined by the authors. The CFD solver is based on a high-order discontinuous Galerkin discretization while the optimization algorithm is a high-performance version of the Artificial Bee Colony method. In this work, they are used to address a typical aero-mechanical problem encountered in turbomachinery design. Interesting achievements in the considered test case are illustrated, highlighting the potential applicability of the proposed approach to other engineering problems.

• Structural Engineering and Mechanics
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• v.3 no.1
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• pp.61-74
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• 1995

A linearly tapered, doubly symmetric thin-walled closed member, such as power-transmission towers and tourist towers, are often characterized by local variation in mass and/or rigidity, due to additional mass and rigidity. On the preliminary stage of design the closed-form solution is more effective than the finite element method. In order to propose approximate solutions, the discontinuous and local variation in mass and/or rigidity is treated continuously by means of a usable function proposed by Takabatake(1988, 1991, 1993). Thus, a simplified analytical method and approximate solutions for the free and forced transverse vibrations in linear elasticity are demonstrated in general by means of the Galerkin method. The solutions proposed here are examined from the results obtained using the Galerkin method and Wilson-${\theta}$ method and from the results obtained using NASTRAN.

• Proceedings of the Korea Water Resources Association Conference
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• 2021.06a
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• pp.253-253
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• 2021

천수방정식에 대한 불연속 갤러킨 기법 (DG) 모형은 주로 양해법 기반으로 개발되어 적용되어 왔으나, 바닥마찰항의 처리, 과도한 CFL 조건 등의 불리한 점이 지적되어 왔으며, 이로 인하여 실제 적용에서 FDM, FEM 등 다른 고전적인 수치기법과 비교하여 경쟁력을 갖기 어려웠다. 이에 대한 대안으로써, 최근, 불연속 갤러킨 기법에 대한 음해법 기반의 모형이 연구되고 있으며, 다소 복잡한 알고리즘에도 불구하고 적용이 확대되고 있다. 또한, 널리 알려진 바와 같이, 천수방정식의 실제 하도에 대한 적용에 있어 문제점 중 하나는 나비에-스토크스 방정식으로부터 유도할 때 사용된 정수압 가정으로 인하여, 하도의 계단과 같은 불연속 지형에 적용이 용이하지 않다는 것이다. 본 연구에서는 기존에 개발된 불연속 갤러킨 음해법에 불연속 지형의 해석을 위한 표면경사법(surface gradient method)을 결합하여 이러한 문제에 효과적으로 대응할 수 있는 기법을 제시하였다. 개발된 모형의 검증을 위하여, 제방 등 하도 구조물 위의 장주기 조석흐름, 홍수파, 계단 등을 포함하는 댐 붕괴류 모의에 적용하고 실용적인 기능성을 검증하였다. 향후 구조물이 많은 국내 하천에 적용이 가능할 것으로 사료된다.

• Journal of the Korean GEO-environmental Society
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• v.15 no.3
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• pp.41-48
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• 2014

Experimental study of sedimentation and self-weight consolidation has been primary research area in dredged soil. However, good quality of the dredged soil and minimum water pollution caused by the pumping of reclaimed soil require intensive study of the flow characteristics of dredged material due to dumping. In this study, continuity and the equilibrium equations for mass flow assuming single phase was derived to simulate mass flow in dredged containment area. To optimize computation and modeling time for three dimensional geometry and boundary conditions, depth integration is applied to governing equations to consider three dimensional topography of the site. Petrov-Galerkin formulation is applied in spatial discretization of governing equations. Generalized trapezoidal rule is used for time integration, and Newton iteration process approximated the solution. DG and CDG technique were used for weighting matrix in discontinuous test function in dredged flow analysis, and numerical stability was evaluated by performed a square slump simulation. A comparative analysis for numerical methods showed that DG method applied to SU / PG formulation gives minimal pseudo oscillation and reliable numerical results.

• Nuclear Engineering and Technology
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• v.24 no.3
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• pp.319-328
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• 1992

The Galerkin formulation of the finite element method is applied to the integral law of the first-order form of the one-group neutron transport equation in one-dimensional spherical geometry. Piecewise linear or quadratic Lagrange polynomials are utilized in the integral law for the angular flux to establish a set of linear algebraic equations. Numerical analyses are performed for the scalar flux distribution in a heterogeneous sphere as well as for the criticality problem in a uniform sphere. For the criticality problems in the uniform sphere, the results of the finite element method, with the use of continuous finite elements in space and angle, are compared with the exact solutions. In the heterogeneous problem, the scalar flux distribution obtained by using discontinuous angular and spatical finite elements is in good agreement with that from the ANISN code calculation.

• Journal of the Korean Geotechnical Society
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• v.30 no.10
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• pp.55-65
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• 2014

Recent researches on debris flow is focused on understanding its movement mechanism and building a numerical simulator to predict its behavior. However, previous simulators emulating fluid-like debris flow have limitations in numerical stability, geometric modeling and application of various boundary conditions. In this study, depth integration is applied to continuity equation and force equilibrium for debris flow. Thickness of sediment, and average velocities in x and y flow direction are chosen for main variables in the analysis, which improve numerical stability in the area with zero thickness. Petrov-Galerkin formulation uses a discontinuous test function of the weighted matrix from DG scheme. Presented mechanical constitutive model combines fluid and granular behaviors for debris flow. Effects on slope angle, inducing debris height, and bottom friction resistance are investigated for a simple slope. Numerical results also show the effect of embankment at the bottom of the slope. Developed numerical simulator can assess various risk factors for the expected area of debris flow, and facilitate embankment design in order to minimize damage.