• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.25 no.3
• /
• pp.66-81
• /
• 2021

In this paper, we review the lowest order staggered discontinuous Galerkin methods on polygonal meshes in 2D. The proposed method offers many desirable features including easy implementation, geometrical flexibility, robustness with respect to mesh distortion and low degrees of freedom. Discrete function spaces for locally H¹ and H(div) spaces are considered. We introduce special properties of a sub-mesh from a given star-shaped polygonal mesh which can be utilized in the construction of discrete spaces and implementation of the staggered discontinuous Galerkin method. For demonstration purposes, we consider the lowest case for the Poisson equation. We emphasize its efficient computational implementation using only geometrical properties of the underlying mesh.

• Journal of Mechanical Science and Technology
• /
• v.14 no.9
• /
• pp.985-996
• /
• 2000

The issue of quench is related to safety operation of large-scale superconducting magnet system fabricated by cable-in-conduit conductor. A numerical method is presented to simulate the thermal hydraulic quench characteristics in the superconducting Tokamak magnet system, One-dimensional fluid dynamic equations for supercritical helium and the equation of heat conduction for the conduit are used to describe the thermal hydraulic characteristics in the cable-in-conduit conductor. The high heat transfer approximation between supercritical helium and superconducting strands is taken into account due to strong heating induced flow of supercritical helium. The fully implicit time integration of upwind scheme for finite volume method is utilized to discretize the equations on the staggered mesh. The scheme of a new adaptive mesh is proposed for the moving boundary problem and the time term is discretized by the-implicit scheme. It remarkably reduces the CPU time by local linearization of coefficient and the compressible storage of the large sparse matrix of discretized equations. The discretized equations are solved by the IMSL. The numerical implement is discussed in detail. The validation of this method is demonstrated by comparison of the numerical results with those of the SARUMAN and the QUENCHER and experimental measurements.

• Interaction and multiscale mechanics
• /
• v.5 no.3
• /
• pp.287-318
• /
• 2012

We apply a partitioned-solution (iterative-staggered) coupling method based on a fixed Eulerian mesh with the level set function to a large-deformation fluid-structure interaction (FSI) problem where a large-deformable thin structure moves in a high-speed flow field, as an airbag does during deployment. This method combines advanced fluid and structure solvers-specifically, the constrained interpolation profile finite element method (CIP-FEM) for fluid Eulerian mesh and large-deformable structural elements for Lagrangian structural mesh. We express the large-deformable interface as a zero isosurface by the level set function, and introduce virtual nodes with level sets and structural normal velocities to generate the level set function according to the large-deformable interfacial geometry and enforce the kinematic condition at the interface. The virtual nodes are located in the direction normal to the structural mesh. It is confirmed that application of the method to unfolded airbag deployment simulation shows the adequacy of the method.

• Nuclear Engineering and Technology
• /
• v.16 no.2
• /
• pp.47-57
• /
• 1984

Mathematically-rigorous time-volume averaged conservation equations were simplified to established the differential equations of THERMIT-6S, which is a two-fluid 3-D code. The difference equations of THERMIT-6S were obtained by discretizing the proceeding set of differential equations. The spatial discretization is characterized by a first-order spatial scheme, donor cell method, and staggered mesh layout. For time discretization, a first order semi-implicit scheme treats implictly sonic terms and terms relating to local transport phenomena and explicitly convective terms. The results were linearized by the Newton-Raphson method. In order to construct the reduced pressure equation, the linearized equations were manipulated so that all variables are coupled between mesh cells through only the pressure variable. By simulating numerically the OPERA-15 experiment, it was found that THERMIT-6S is a very powerful code in predicting reactor behavior after sodium boiling including flow coastdown, reversal flow and flow oscillation.

• 한국전산유체공학회:학술대회논문집
• /
• 2011.05a
• /
• pp.68-74
• /
• 2011

Recently, thanks to the advanced computational power and numerical methods, it is made possible to analyze the flow around moving bodies using computational fluid dynamics techniques. In those simulations, moving mesh techniques should be able to represent both the body motion and boundary deformation, which are frequently encountered in fluid-structure interaction and/or six degree-of-freedom problems. In the present study, the staggered loosely coupling algorithm was used for fluid-structure interaction and the Laplacian operator based technique was used for moving mesh. For the verification of the developed computational method, the flow around a two-dimensional cylinder was simulated and analyzed.

• Journal of Advanced Marine Engineering and Technology
• /
• v.32 no.1
• /
• pp.82-93
• /
• 2008

The flowfield behind two cylinders and flow-induced noise generated from the cylinders in various arrangement are numerically investigated based on the finite difference lattice Boltzmann model with 21 velocity bits. which is introduced a flexible specific heat ${\gamma}$ to simulate diatomic gases like air. In an isolated cylinder with two type of mesh. some flow parameters such as Strouhal number $S_t$ and acoustic pressure ${\Delta}p$ simulated from the solution are given and quantitatively compared with those provided the previous works. The effects of the center-to-center pitch ratio $L_{cc}/d=2.0$ in staggered circular cylinders as shown in Fig. 1 and angles of incidence ${\alpha}=30^{\circ}(T_{cc}/d=0.5)$, $45^{\circ}(T_{cc}/d =0.707)$ and $60^{\circ}\;(T_{cc}/d=0.866)$, respectively, are studied. Our analysis focuses on the small-scale instabilities of vortex shedding, which occurs in staggered arrangement. With the results of drag $C_d$ and lift $C_l$ coefficients and vorticity contours. the mechanisms of the interference phenomenon and its interaction with the two-dimensional vortical structures are present in the flowfields under $Re\;{\le}\;200$. The results show that we successively capture very small pressure fluctuations, with the same frequency of vortex shedding, much smaller than the whole pressure fluctuation around pairs of circular cylinders. The upstream cylinder behaves like an isolated single cylinder, while the downstream one experiences wake-induced flutter. It is expected that, therefore, the relative position of the downstream cylinder has significant effects on the flow-induce noise, hydrodynamic force and vortex shedding characteristics of the cylinders.

• Journal of computational fluids engineering
• /
• v.16 no.1
• /
• pp.73-82
• /
• 2011

In this paper, the vortex-induced vibration of circular cylinders is studied using the immersed boundary method on the Cartesian mesh. The Reynolds numbers considered is from 100 to 200. Using the configuration of tendemly arranged multiple circular cylinders, the vortex shedding behind of the cylinders and their flow-induced motion are investigated. The staggered MAC grid arrangement, which is the typical grid system for the incompressible flow on the Cartesian meshes, is utilized. Pressure correction method is applied for solving the divergence-free incompressible velocity field. The body motion is described by immersed boundary technique that has advantages for moving object on the fixed computational domain. It is also discussed for the computational noise in hydrodynamic forces when body motion is represented by the immersed boundary method. The Predictor/Corrector method is used for simulating the nonlinear response of the elastically mounted cylinder excited by vortex-shedding.

• 한국전산유체공학회:학술대회논문집
• /
• 2007.10a
• /
• pp.243-248
• /
• 2007

A three-dimensional (3D) unstructured hydrodynamic solver for transient two-phase flows has been developed. A two-fluid three-field model was adopted for the two-phase flows. The three fields represent a continuous liquid, an entrained liquid, and a vapour field. The hydrodynamic solver is for the 3D component of a nuclear system code and the component-scale analysis tools for transient two-phase flows. The finite volume method and unstructured grid are adopted, which are useful for the flows in a complicated geometry. The semi-implicit ICE (Implicit Continuous-fluid Eulerian) numerical scheme has been adapted to the unstructured non-staggered grid. This paper presents the numerical method and the preliminary results of the calculations. The results show that the numerical scheme is robust and predicts the phase change and the flow transitions due to boiling and flashing problems well.

• 한국전산유체공학회:학술대회논문집
• /
• 2010.05a
• /
• pp.326-334
• /
• 2010

In this study, we provide a comprehensive review of the CIP(Constrained Interpolation Pro file/Cubic Interpolated Propagation) method with a pressure-based algorithm that is known as a general numerical solver for soled liquid, gas and plasmas. And also we introduce a body-fitted grid system(Soroban grid) for computation of strongly nonlinear marine hydrodynamic problems such as slamming water on deck, wave impact by green water. This grid system can keep the third-order accuracy in time and space with the help of the CIP method. The grid system consists of the straight lines and grid points. In the 2-dimensional grid case, each grid points moving in these lines like abacus - Soroban in Japanese. The length of each line can be different and the number of grid points in each line can be different. Mesh generation and searching of upstream departure point are very simple and possible to mesh-free treatment. To optimize computation of free-surface and multi-fluid flows, We adopt the C-CUP method. In most of the earlier computations, the C-CUP method was used with a staggered-grid approach. Here, because of the mesh free nature of the Soroban grid, we use the C-CUP method with a collocated-grid approach.

• Journal of Energy Engineering
• /
• v.17 no.4
• /
• pp.218-226
• /
• 2008

A component-scale two-phase analysis code has been developed for a realistic simulation of two-phase flow transients in a light water nuclear reactor component. In the code, a two-fluid three-field model is adopted and the governing equations are solved on an unstructured mesh. For the numerical solution scheme, the semi-implicit method used in the RELAP5 code was selected, which has been proved to be very stable and accurate for most of practical applications. However, some modifications were needed for its application to an unstructured non-staggered grid. This paper presents the modified semi-implicit numerical method for unstructured grid and the preliminary results of the calculations.