• 한국소성가공학회:학술대회논문집
• /
• 한국소성가공학회 2006년도 춘계학술대회 논문집
• /
• pp.99-104
• /
• 2006

A semi-Lagrangian finite element scheme with objective time stepping algorithm for solving viscoelastic flow problem is presented. The convection terms in the momentum and constitutive equations are treated using a quasi-monotone semi-Lagrangian scheme, in which characteristic feet on a regular grid are traced backwards over a single time-step. Concerned with the generalized midpoint rule type of algorithms formulated to exactly preserve objectivity, we use the geometric transformation such as pull-back, push-forward operation. The method is applied to the 4:1 planar contraction problem for an Oldroyd B fluid for both creeping and inertial flow conditions.

• 한국전산유체공학회지
• /
• 제9권3호
• /
• pp.8-17
• /
• 2004

A Semi-Lagrangian method based on CIP(Cubic Interpolated Pseudoparticle)method is proposed and it is applied to solve the two dimensional advection equation. Especially the attentions are given to settle the pole problem and to enhance the accuracy in solving the advection equation on the spherical coordinate system. Tn this algorithm, the CU method is employed as the Semi-Lagrangian method and extended to the spherical coordinate system. To enhance the accuracy of the solution, the spatial discretization is made by CIP method. The mathematical formulation and numerical results are also described. To verify the efficiency, accuracy and capability of proposed algorithm, two dimensional rotating cosine bell problem and the frontogenesis problem are simulated by the present scheme. As results, it is confirmed that the present scheme gives an accurate solution and settles the pole problem in the advection equation on the sphere.

• 충청수학회지
• /
• 제28권4호
• /
• pp.623-633
• /
• 2015

In this paper, a general Weighted Essentially Non-Oscillatory (WENO) interpolation is proposed and applied to a semi-Lagrangian method. The proposed method is based on the conservation law, and characteristic curves are used to complete the semi-Lagrangian method. Therefore, the proposed method satisfies conservation of mass and is free of the CFL condition which is a necessary condition for convergence. Using a several standard examples, the proposed method is compared with the third order Strong Stability Preserving (SSP) Runge-Kutta method to verify the high-order accuracy.

• Nuclear Engineering and Technology
• /
• 제55권12호
• /
• pp.4395-4407
• /
• 2023

Bubble columns are widely encountered in several industries, especially in the field of nuclear safety. The Eulerian-Eulerian and the Eulerian-Lagrangian methods are commonly used to investigate bubble columns. Eulerian approaches require additional tasks such as strict volume conservation at the interface and a predefined well-structured grid. In contrast, the Lagrangian approach can be easily implemented. Hence, we introduce a fully Lagrangian approach for the simulation of bubble columns using the discrete bubble model (DBM) and moving particle semi-implicit (MPS) methods. Additionally, we propose a rigorous method to estimate the volume fraction accurately, and verified it through experimental data and analytical results. The MPS method was compared with the experimental data of Dambreak. The DBM was verified by analyzing the terminal velocity of a single bubble for each bubble size. It agreed with the analytical results for each of the four drag correlations. Additionally, the improved method for calculating the volume fraction showed agreement with the Ergun equation for the pressure drop in a packed bed. The implemented MPS-DBM was used to simulate the bubble column, and the results were compared with the experimental results. We demonstrated that the MPS-DBM was in quantitative agreement with the experimental data.

• East Asian mathematical journal
• /
• 제35권1호
• /
• pp.59-66
• /
• 2019

In this paper we study implicit-explicit (IMEX) methods combined with a semi-Lagrangian scheme to evaluate the prices of fixed strike arithmetic Asian options under jump-diffusion models. An Asian option is described by a two-dimensional partial integro-differential equation (PIDE) that has no diffusion term in the arithmetic average direction. The IMEX methods with the semi-Lagrangian scheme to solve the PIDE are discretized along characteristic curves and performed without any fixed point iteration techniques at each time step. We implement numerical simulations for the prices of a European fixed strike arithmetic Asian put option under the Merton model to demonstrate the second-order convergence rate.

• 한국해양공학회지
• /
• 제16권5호
• /
• pp.41-48
• /
• 2002

Numerical experiments are conducted using a three-dimensional baroclinic equation model and a Lagrangian method for clarifying the effect of th settling velocity on the suspended solids diffusion caused by the dredging and the reclamination works. Diffusion characteristics of the neutral particles and the weighting particles is experimented by the Lagrangian particles trajectory model, The results show that the diffusion characteristics of the suspended solids is effected by the settling velocity classified by the particles size in the density layered semi-closed bay. To estimate exactly the diffusion characteristics of the suspended solids and the contaminant with weight the three-dimensional baroclinic equation model and the three-dimensional Lagrangian particles trajectory model considering the settling velocity of the particle in the density layered semi-closed bay must be used.

• 정보처리학회논문지A
• /
• 제16A권6호
• /
• pp.419-426
• /
• 2009

일반적으로 사실성 있는 유체를 시뮬레이션하기 위해 Navier-Stokes 방정식을 사용한다. Euler 구조에서 Navier-Stokes 방정식을 풀 때, 이 류항은 비선형이어서 계산이 복잡하기 때문에 근사화한 모델로 Semi-Lagrangian 방법을 사용한다. Semi-Lagrangian 방법에서는 먼저 이류하 는 위치를추적하고, 추적한 위치에서 값을 보간해서 사용한다. Stam이 제안한 방법으로 계산할 경우, 이 과정에서 수치적 소실이 많이 발생하 기 때문에 수치적 소실을 보정하려는 노력들이 있어 왔다. 그러나 대부분의 경우에 보간하는 과정에서의 소실을 줄이려는 노력이거나, 입자를 같이 사용하는 방법이었다. 따라서 본 논문에서는 Euler 구조에서 다른 추가나 변형을 가하지 않고 이류항의 연산에서 추적법을 개선함으로 수 치적 소실을 줄이는 방법을 제안한다. 우리의 방법에서는 현재 격자의 속도로 역추적하는 기존의 방법이 아니라, 현재의 격자로 오게 될 속도 를 가진 격자를 찾아서, 그 격자의 물리량들을 선형 보간하여 사용한다. 이는 직관적으로 생각할 때, 어느 지점의 물리량은 그 지점의 속도로 인해 다음 단계에 다른 지점에 있게 된다는 사실을 그대로 적용한 것이다. 본 논문에서 제안한 방법으로 기체를 시뮬레이션 했을 때 수치적 소 실이 줄었으며, 그로 인해 사실성을 높이면서도 실시간 처리가 가능했다.

• 한국컴퓨터정보학회:학술대회논문집
• /
• 한국컴퓨터정보학회 2023년도 제68차 하계학술대회논문집 31권2호
• /
• pp.581-583
• /
• 2023

기존의 불 영역 검출을 위한 이미지 전처리 기법은 임계값에 영향을 많이 받기 때문에 사진의 색상 분포에 의존하는 결과가 나온다. 이를 보완하고자 본 논문에서는 화염이 가지고 있는 특유의 비선형적이고 불규칙한 움직임을 추출할 수 있는 방법을 제안한다. 유체 시뮬레이션에서 활용되는 준 라그랑지안(Semi-Lagrangian) 활용하여 유동을 분석하고 이를 기반으로 영상에서 화염의 움직임을 추출한다.

• 한국해안해양공학회지
• /
• 제10권2호
• /
• pp.73-82
• /
• 1998

연안에서 표층 방류된 온수의 확산-이송을 모의하고자 배출구 인근의 근역에서는 반능동적 입자추적의 원리가 적용된 부작위행보모형과 원역에서는 Eulerian-Lagrangian 농도가 결합된 2차원 모형이 개발되었다. 근역에서 표층으로 부상되는 온수괴는 부력을 갖는 다수의 입자군으로 변환되어 초기 평면확산의 증가를 나타내고, 이러한 부력확산의 영향이 무작위행보의 기본식에 도입되었다. 개발된 모형의 초기평가는 단순한 지형의 해역과 실제해역에서 수행되었다. 단순해역에서는 부력이 고려되지 않는 중립입자모형의 결과에 비하여 초기 확산이 크게 나타나고, 기존 근역모형CORMIX3과 유사하나 외해측으로 확장된 성향을 보인다. 천수만에서 실제적용 결과도 배출구 근처에서 관측치에 유사한 퍼짐 효과가 나타나며 모형의 적용성이 인정된다.

• Wind and Structures
• /
• 제20권3호
• /
• pp.423-448
• /
• 2015

In this paper the unsteady fluid-structure interaction (FSI) problems with large structural displacement are solved by partitioned solution approaches in the arbitrary Lagrangian-Eulerian finite element framework. The incompressible Navier-Stokes equations are solved by the characteristic-based split (CBS) scheme. Both a rigid body and a geometrically nonlinear solid are considered as the structural models. The latter is solved by Newton-Raphson procedure. The equation governing the structural motion is advanced by Newmark-${\beta}$ method in time. The dynamic mesh is updated by using moving submesh approach that cooperates with the ortho-semi-torsional spring analogy method. A mass source term (MST) is introduced into the CBS scheme to satisfy geometric conservation law. Three partitioned coupling strategies are developed to take FSI into account, involving the explicit, implicit and semi-implicit schemes. The semi-implicit scheme is a mixture of the explicit and implicit coupling schemes due to the fluid projection splitting. In this scheme MST is renewed for interfacial elements. Fixed-point algorithm with Aitken's ${\Delta}^2$ method is carried out to couple different solvers within the implicit and semi-implicit schemes. Flow-induced vibrations of a bridge deck and a flexible cantilever behind an obstacle are analyzed to test the performance of the proposed methods. The overall numerical results agree well with the existing data, demonstrating the validity and applicability of the present approaches.