• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
• /
• 2003.09a
• /
• pp.6-6
• /
• 2003

In this work we consider the mathematical formulation and numerical resolution of the linear feedback control problem for Boussinesq equations. The controlled Boussinesq equations is given by $$\frac{{\partial}u}{{\partial}t}-{\nu}{\Delta}u+(u{\cdot}{\nabla}u+{\nabla}p={\beta}{\theta}g+f+F\;\;in\;(0,\;T){\times}\;{\Omega}$$, $${\nabla}{\cdot}u=0\;\;in\;(0,\;T){\times}{\Omega}$$, $$u|_{{\partial}{\Omega}=0,\;u(0,x)=\;u_0(x)$$ $$\frac{{\partial}{\theta}}{{\partial}t}-k{\Delta}{\theta}+(u{\cdot}){\theta}={\tau}+T,\;\;in(0,\;T){\times}{\Omega}$$ $${\theta}|_{{\partial}{\Omega}=0,\;\;{\theta}(0,X)={\theta}_0(X)$$, where $\Omega$ is a bounded open set in $R^{n}$, n=2 or 3 with a $C^{\infty}$ boundary ${\partial}{\Omega}$. The control is achieved by means of a linear feedback law relating the body forces to the velocity and temperature field, i.e., $$f=-{\gamma}_1(u-U),\;\;{\tau}=-{\gamma}_2({\theta}-{\Theta}}$$ where (U,$\Theta$) are target velocity and temperature. We show that the unsteady solutions to Boussinesq equations are stabilizable by internal controllers with exponential decaying property. In order to compute (approximations to) solution, semi discrete-in-time and full space-time discrete approximations are also studied. We prove that the difference between the solution of the discrete problem and the target solution decay to zero exponentially for sufficiently small time step.

• Nuclear Engineering and Technology
• /
• v.55 no.6
• /
• pp.2112-2124
• /
• 2023

With the rise of economic and safety standards for nuclear reactors, new concepts of Gen-IV reactors and modular reactors showed more complex designs that challenge current tools for reactor physics analysis. A Monte Carlo (MC) two-step method was proposed in this work. This calculation scheme uses the continuous-energy MC method to generate multi-group cross-sections from heterogeneous models. The multi-group MC method, which can adapt locally-heterogeneous models, is used in the core calculation step. This calculation scheme is verified using a Gen-IV modular lead-based fast reactor (LFR) benchmark case. The influence of homogenized patterns, scatter approximations, flux separable approximation, and local heterogeneity in core calculation on simulation results are investigated. Results showed that the cross-sections generated using the 3D assembly model with a locally heterogeneous representation of control rods lead to an accurate estimation with less than 270 pcm bias in core reactivity, 0.5% bias in control rod worth, and 1.5% bias on power distribution. The study verified the applicability of multi-group cross-sections generated with the MC method for LFR analysis. The study also proved the feasibility of multi-group MC in core calculation with local heterogeneity, which saves 85% time compared to the continuous-energy MC.

• Geomechanics and Engineering
• /
• v.31 no.1
• /
• pp.113-127
• /
• 2022

The undrained shear strength of soil is considered one of the engineering parameters of utmost significance in geotechnical design methods. In-situ experiments like cone penetration tests (CPT) have been used in the last several years to estimate the undrained shear strength depending on the characteristics of the soil. Nevertheless, the majority of these techniques rely on correlation presumptions, which may lead to uneven accuracy. This research's general aim is to extend a new united soft computing model, which is a combination of random forest (RF) with grasshopper optimization algorithm (GOA) to the pile set-up parameters' better approximation from CPT, based on two different types of data as inputs. Data type 1 contains pile parameters, and data type 2 consists of soil properties. The contribution of this article is that hybrid GOA - RF for the first time, was suggested to forecast the pile set-up parameter from CPT. In order to do this, CPT data and related bore log data were gathered from 70 various locations across Louisiana. With an R² greater than 0.9098, which denotes the permissible relationship between measured and anticipated values, the results demonstrated that both models perform well in forecasting the set-up parameter. It is comprehensible that, in the training and testing step, the model with data type 2 has finer capability than the model using data type 1, with R² and RMSE are 0.9272 and 0.0305 for the training step and 0.9182 and 0.0415 for the testing step. All in all, the models' results depict that the A parameter could be forecasted with adequate precision from the CPT data with the usage of hybrid GOA - RF models. However, the RF model with soil features as input parameters results in a finer commentary of pile set-up parameters.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.19 no.1
• /
• pp.1-21
• /
• 2015

This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r > d, $r{\leq}d$, long-time or short-time maturity T.

• Korea-Australia Rheology Journal
• /
• v.14 no.1
• /
• pp.33-45
• /
• 2002

Recent results obtained for the port-pom model and the constitutive equations with time-strain separability are examined. The time-strain separability in viscoelastic systems Is not a rule derived from fundamental principles but merely a hypothesis based on experimental phenomena, stress relaxation at long times. The violation of separability in the short-time response just after a step strain is also well understood (Archer, 1999). In constitutive modeling, time-strain separability has been extensively employed because of its theoretical simplicity and practical convenience. Here we present a simple analysis that verifies this hypothesis inevitably incurs mathematical inconsistency in the viewpoint of stability. Employing an asymptotic analysis, we show that both differential and integral constitutive equations based on time-strain separability are either Hadamard-type unstable or dissipative unstable. The conclusion drawn in this study is shown to be applicable to the Doi-Edwards model (with independent alignment approximation). Hence, the Hadamardtype instability of the Doi-Edwards model results from the time-strain separability in its formulation, and its remedy may lie in the transition mechanism from Rouse to reptational relaxation supposed by Doi and Edwards. Recently in order to describe the complex rheological behavior of polymer melts with long side branches like low density polyethylene, new constitutive equations called the port-pom equations have been derived in the integral/differential form and also in the simplifled differential type by McLeish and carson on the basis of the reptation dynamics with simplifled branch structure taken into account. In this study mathematical stability analysis under short and high frequency wave disturbances has been performed for these constitutive equations. It is proved that the differential model is globally Hadamard stable, and the integral model seems stable, as long as the orientation tensor remains positive definite or the smooth strain history in the flow is previously given. However cautious attention has to be paid when one employs the simplified version of the constitutive equations without arm withdrawal, since neglecting the arm withdrawal immediately yields Hadamard instability. In the flow regime of creep shear flow where the applied constant shear stress exceeds the maximum achievable value in the steady flow curves, the constitutive equations exhibit severe instability that the solution possesses strong discontinuity at the moment of change of chain dynamics mechanisms.

• Tunnel and Underground Space
• /
• v.25 no.1
• /
• pp.56-67
• /
• 2015

In this study, a source locating technique applicable to transversely isotropic media was developed. Wave velocity anisotropy was considered based on the partition approximation method, which simply enabled AE source locating. Sets of P wave arrival time were decided by the two-step AIC algorithm and they were later used to locate the AE sources when having the least error compared with the partitioned elements. In order to validate the technique, pencil lead break test on artificial transversely isotropic mortar specimen was carried out. Defining the absolute error as the distance between the pencil lead break point and the located point, 1.60 mm ~ 14.46 mm of range and 8.57 mm of average were estimated therefore it was regarded as thought to be 'acceptable' considering the size of the specimen and the AE sensors. Comparing each absolute error under different threshold levels, results showed small discrepancies therefore this technique was hardly affected by background noise. Absolute error could be decomposed into each coordinate axis error and through it, effect of AE sensor position could be understood so if optimum sensor position was able to be decided, one could get more precise outcome.

• Journal of KIISE:Computer Systems and Theory
• /
• v.27 no.1
• /
• pp.61-67
• /
• 2000

Digital controllers found in many industrial real-time systems consist of a number of interacting periodic tasks. To sustain the required control quality, these tasks possess the maximum activation periods as performance constraints. An essential step in developing a real-time system is thus to assign each of these tasks a constant period such that the maximum activation requirements are met while the system utilization is minimized [1]. Given a task graph design allowing producer/consumer relationships among tasks [2], resource demands of tasks, and range constraints on periods, the period assignment problem falls into a class of nonlinear optimization problems. This paper proposes a ploynomial time approximation algorithm which produces a solution whose utilization does not exceed twice the optimal utilization. Our experimental analysis shows that the proposed algorithm finds solutions which are very close to the optimal ones in most cases of practical interest.

• 한국전산유체공학회:학술대회논문집
• /
• 1998.05a
• /
• pp.145-155
• /
• 1998

A computer code has been developed for the computation of the viscous flow around a ship model with the free surface. In this code, the incompressible Reynolds-averaged Navier-Stokes equations are solved numerically by a finite difference method which employes second-order finite differences for the spatial discretization and a four-stage Runge-Kutta scheme for the temporal integration of the governing equations. For the turbulence closure, a modified version of the Baldwin-Lomax model is exploited. The location of the free surface is determined by solving the equation of the kinematic free-surface condition using the Lax-Wendroff scheme and the boundary-fitted grid is generated at each time step so that one of the grid surfaces always coincides with the free surface. An inviscid approximation of the dynamic free-surface boundary condition is applied as the boundary conditions for the velocity and pressure on the free surface. To validate the computational method and the computer code developed in the present study, the numerical computations are carried out for both Wigley parabolic hull and Series 60 $C_B=0.6$ ship model and the computational results are compared with the experimental data.

• Journal of the Society of Naval Architects of Korea
• /
• v.42 no.3
• /
• pp.205-211
• /
• 2005

In this study, a new numerical procedure for the generation of a nonlinear tailored group of waves is presented. The procedure is based on the transient wave group technique. In order to integrate the nonlinearity during the wave propagation in the computational method, the Navier-Stokes equations are applied as governing equations. The governing equations are discretized by finite volume approximation. The deformation of the free water surface in each time step is pursued with a moving grid. A two-dimensional, numerical wave tank for the simulation of the wave propagation is developed and tested in detail. The numeric results are compared first with analytical wave theories and with measurements, in order to examine the correctness of the numerical wave tank. Wave surface elevation and associated fields of velocity and pressure are numerically computed and compared with measurements. Very good agreements show up.

• Journal of Korean Port Research
• /
• v.14 no.4
• /
• pp.451-461
• /
• 2000

The design and maintenance of navigation channel and water facilities of an harbor which is located at the mouth of river or at the estuary area are difficult due to the complexity of estuarial water and sediment circulation. Effects of deepening navigable waterways, of changing coastline configurations, or of discharging dredged material to the open sea are necessary to be investigated and predicted in terms of water quality and possible physical changes to the coastal environment. A borad analysis of the transport mechanism in the estuary area was made in terms of sediment property, falling velocity, concentration and flow characteristics. In order to simulate the transport processes, a two-dimensional finite element model is developed, which includes erosion, transport and deposition mechanism of suspended sediments. Galerkin’s weighted residual method is used to solve the transient convection-diffusion equation. The fluid domain is subdivided into a series of triangular elements in which a quadratic approximation is made for suspended sediment concentration. Model could deal with a continuous aggregation by stipulating the settling velocity of the flocs in each element. The model provides suspended sediment concentration, bed shear stress, erosion versus deposition rate and bed profile at the given time step.