• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.717-737
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• 2014

We study the effect of numerical quadrature in space on semidiscrete and fully discrete piecewise linear finite element methods for parabolic interface problems. Optimal $L^2(L^2)$ and $L^2(H^1)$ error estimates are shown to hold for semidiscrete problem under suitable regularity of the true solution in whole domain. Further, fully discrete scheme based on backward Euler method has also analyzed and optimal $L^2(L^2)$ norm error estimate is established. The error estimates are obtained for fitted finite element discretization based on straight interface triangles.

• Wind and Structures
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• v.18 no.3
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• pp.215-233
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• 2014

This paper presents a method to extract flutter derivatives of bridge decks based on a combination of the computational fluid dynamics (CFD), system simulations and system identifications. The incompressible solver adopts an Arbitrary Lagrangian-Eulerian (ALE) formulation with the finite volume discretization in space. The imposed sectional motion in heaving or pitching relies on exponential time series as input, with aerodynamic forces time histories acting on the section evaluated as output. System identifications are carried out to fit coefficients of the inputs and outputs of ARMA models, as to establish discrete-time aerodynamic models. System simulations of the established models are then performed as to obtain the lift and moment exerting on the sections to a sinusoidal displacement. It follows that flutter derivatives are identified. The present approaches are applied to a hexagon thin plate and a real bridge deck. The results are compared to the Theodorsen closed-form solution and those from wind tunnel tests. Satisfactory agreements are observed.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.813-829
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• 2011

In this article, we present a numerical scheme for solving singularly perturbed (i.e. highest -order derivative term multiplied by small parameter) Burgers-Huxley equation with appropriate initial and boundary conditions. Most of the traditional methods fail to capture the effect of layer behavior when small parameter tends to zero. The presence of perturbation parameter and nonlinearity in the problem leads to severe difficulties in the solution approximation. To overcome such difficulties the present numerical scheme is constructed. In construction of the numerical scheme, the first step is the dicretization of the time variable using forward difference formula with constant step length. Then, the resulting non linear singularly perturbed semidiscrete problem is linearized using quasi-linearization process. Finally, differential quadrature method is used for space discretization. The error estimate and convergence of the numerical scheme is discussed. A set of numerical experiment is carried out in support of the developed scheme.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2008.03a
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• pp.666-670
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• 2008

The low-speed preconditioning technique is applied to solve the compressible Reynolds averaged Navier-Stokes equations for low-speed flows. The space discretization is based on Roe's flux-difference splitting with third-order-accurate MUSCL extrapolation. Time integration is performed employing a diagonal approximate factorization algorithm. The dual-time stepping has been incorporated to solve the unsteady flows. Full multigrid method is implemented to accelerate the convergence rate. To verify the algorithms several cases have been tested. Demonstrated the improvement on convergence and quality of the solution.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.8
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• pp.37-45
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• 2002

A two-dimensional unsteady, inviscid flow solver has been developed for the simulation of airfoil-vortex interactions on unstructured dynamically adapted meshes. The Euler solver is based on a second-order accurate implicit time integration using a point Gauss-Seidel relaxation scheme and a dual time-step subiteration. A vertex-centered, finite-volume discretization is used in conjunction with the Roe's flux-difference splitting. An unsteady solution-adaptive dynamic mesh scheme is used by adding and deleting mesh points to take account of both spatial and temporal variations of the flow field. The effect of vortex interaction on the aeroelastic displacement of an airfoil attached to the idealized two degree-of-freedom spring system is investigated.

• Advances in nano research
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• v.16 no.3
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• pp.231-249
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• 2024

When the amplitude of the vibrations is equivalent to that clearance, the vibrations for small amplitudes will really be significantly nonlinear. Nonlinearities will not be significant for amplitudes that are rather modest. Finally, nonlinearities will become crucial once again for big amplitudes. Therefore, the concrete panel system may experience a big amplitude in this work as a result of the high temperature. Based on the 3D modeling of the shell theory, the current work shows the influences of the von Kármán strain-displacement kinematic nonlinearity on the constitutive laws of the structure. The system's governing Equations in the nonlinear form are solved using Kronecker and Hadamard products, the discretization of Equations on the space domain, and Duffing-type Equations. Thermo-elasticity Equations. are used to represent the system's temperature. The harmonic solution technique for the displacement domain and the multiple-scale approach for the time domain are both covered in the section on solution procedures for solving nonlinear Equations. An effective data-driven solution is often utilized to predict how different systems would behave. The number of hidden layers and the learning rate are two hyperparameters for the network that are often chosen manually when required. Additionally, the data-driven method is offered for addressing the nonlinear vibration issue in order to reduce the computing cost of the current study. The conclusions of the present study may be validated by contrasting them with those of data-driven solutions and other published articles. The findings show that certain physical and geometrical characteristics have a significant effect on the existing concrete panel structure's susceptibility to temperature change and GPL weight fraction. For building construction industries, several useful recommendations for improving the thermo-mechanics' behavior of structural concrete panels are presented.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.41 no.6
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• pp.507-515
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• 2017

Flexible multibody simulations are widely used in the industry to design mechanical systems. In flexible multibody dynamics, deformation coordinates are described either relatively in the body reference frame that is floating in the space or in the inertial reference frame. Moreover, these deformation coordinates are generated based on the discretization of the body according to the finite element approach. Therefore, the formulation of the flexible multibody system always deals with a huge number of degrees of freedom and the numerical solution methods require a substantial amount of computational time. Parallel computational methods are a solution for efficient computation. However, most of the parallel computational methods are focused on the efficient solution of large-sized linear equations. For multibody analysis, we need to develop an efficient formulation that could be suitable for parallel computation. In this paper, we developed a subsystem synthesis method for a flexible multibody system and proposed efficient parallel computational schemes based on the OpenMP API in order to achieve efficient computation. Simulations of a rotating blade system, which consists of three identical blades, were carried out with two different parallel computational schemes. Actual CPU times were measured to investigate the efficiency of the proposed parallel schemes.

• Nuclear Engineering and Technology
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• v.55 no.2
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• pp.769-779
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• 2023

This paper describes an hp-angular adaptivity algorithm in the discrete ordinates method for Boltzmann transport applications with strong angular effects. This adaptivity uses discontinuous finite element quadrature sets with different degrees, which updates both angular mesh and the degree of the underlying discontinuous finite element basis functions, allowing different angular local refinement to be applied in space. The regular and goal-based error metrics are considered in this algorithm to locate some regions to be refined. A mapping algorithm derived by moment conservation is developed to pass the angular solution between spatial regions with different quadrature sets. The proposed method is applied to some test problems that demonstrate the ability of this hp-angular adaptivity to resolve complex fluxes with relatively few angular unknowns. Results illustrate that a reduction to approximately 1/50 in quadrature ordinates for a given accuracy compared with uniform angular discretization. This method therefore offers a highly efficient angular adaptivity for investigating difficult particle transport problems.

• Advances in aircraft and spacecraft science
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• v.11 no.2
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• pp.177-194
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• 2024

The objective of this paper is to compute entire flow field over Apollo-II, Aerospace Reentry Demonstrator (ARD), Orbital Experiment (OREX) with sharp shoulder and rounded shape shoulder and Space Recovery Experiment (SRE) at different flare-cone half-angle of 20° and 35°. This paper addresses numerical solutions of the compressible three-dimensional Euler equations on hexahedral meshes for a freestream Mach 6 and at an angle of incidence 5°. Furthermore, spatial discretization is accomplished by a cell centred finite volume formulation solution and advanced in time by an explicit multi-stage Runge-Kutta method. The flow field characteristics, distribution of surface pressure coefficient and Mach number on fore-body and aft-body are presented as a function of the geometrical parameters of many reentry capsules. The surface pressure variation is numerically integrated to obtain the aerodynamic drag and compared well with impact theory. The present numerical study has observed the significant dependence of the blunt body and the aft-body geometry of the vehicle and can be used to study atmospheric conditions during re-entry trajectory. The numerical analysis reveals the significant influence of capsule geometry on the flow characteristics of the mechanism of upstream and structure of the flow near the wake region and aerodynamic drag coefficient.

• The Journal of Engineering Geology
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• v.18 no.4
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• pp.381-391
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• 2008

The eigenvalue technique is introduced to overcome the problem of truncation errors caused by temporal discretization of numerical analysis. The eigenvalue technique is different from simulation in that only the space is discretized. The spatially discretized equation is diagonized and the linear dynamic system is then decoupled. The time integration can be done independently and continuously for any nodal point at any time. The results of eigenvalue technique are compared with the exact solution and FEM numerical solution. The eigenvalue technique is more efficient than the FEM to the computation time and the computer storage in the same conditions. This technique is applied to the solute transport analysis in nonuniform flow fields around underground storage caverns. This method can be very useful for time consuming simulations. So, a sensitivity analysis is carried out by using this method to analyze the safety of caverns from nearly located contaminant sources. According to the simulations, the reaching time from source to the nearest cavern may takes 50 years with longitudinal dispersivity of 50 m and transversal dispersivity of 5 m, respectively.