• Bulletin of the Society of Naval Architects of Korea
• /
• v.24 no.3
• /
• pp.9-16
• /
• 1987

In this paper, the fluid flow in the two-dimensional tank is analyzed by the Finite Difference Method. The Navier-Stokes equation is modified for the tank fixed coordinate system. For the treatment of the free surface, the Volume of Fluid Method by Hirt and Nichols is adopted. The continuity equation and the Poisson equation which is derived from the Navier-Stokes equation to find the pressure are solved by the Successive-Line-Overrelaxation Method. The comparison of the calculated results with experimental data show a favorable agreement. The fluid flow in the two-dimensional tank can be predicted reasonably before the free surface reaches breaking by this numerical method.

• 유체기계공업학회:학술대회논문집
• /
• 2006.08a
• /
• pp.349-352
• /
• 2006

The conventional segregated finite element formulation produces a small and simple matrix at each step than in an integrated formulation. And the memory and cost requirements of computations are significantly reduced because the pressure equation for the mass conservation of the Navier-Stokes equations is constructed only once if the mesh is fixed. However, segregated finite element formulation solves Poisson equation of elliptic type so that it always needs a pressure boundary condition along a boundary even when physical information on pressure is not provided. On the other hand, the conventional integrated finite element formulation in which the governing equations are simultaneously treated has an advantage over a segregated formulation in the sense that it can give a more robust convergence behavior because all variables are implicitly combined. Further it needs a very small number of iterations to achieve convergence. However, the saddle-paint-type matrix (SPTM) in the integrated formulation is assembled and preconditioned every time step, so that it needs a large memory and computing time. Therefore, we newly proposed the P2PI semi-segregation formulation. In order to utilize the fact that the pressure equation is assembled and preconditioned only once in the segregated finite element formulation, a fixed symmetric SPTM has been obtained for the continuity constraint of the present semi-segregation finite element formulation. The momentum equation in the semi-segregation finite element formulation will be separated from the continuity equation so that the saddle-point-type matrix is assembled and preconditioned only once during the whole computation as long as the mesh does not change. For a comparison of the CPU time, accuracy and condition number between the two methods, they have been applied to the well-known benchmark problem. It is shown that the newly proposed semi-segregation finite element formulation performs better than the conventional integrated finite element formulation in terms of the computation time.

• International Journal of Naval Architecture and Ocean Engineering
• /
• v.10 no.3
• /
• pp.329-347
• /
• 2018

The Smoothed Particle Hydrodynamics (SPH) method has proved to have great potentials in dealing with the wave-structure interactions. Compared with the Weakly Compressible SPH (WCSPH) method, the ISPH approach solves the pressure by using the pressure Poisson equation rather than the equation of state. This could provide a more stable and accurate pressure field that is important in the study of wave-structure interactions. This paper improves the solid boundary treatment of ISPH by using a high accuracy Simplified Finite Difference Interpolation (SFDI) scheme for the 2D wave-structure coupling problems, especially for free-moving structure. The proposed method is referred as the ISPH_BS. The model improvement is demonstrated by the documented benchmark tests and laboratory experiment covering various wave-structure interaction applications.

• Advances in Computational Design
• /
• v.9 no.1
• /
• pp.39-52
• /
• 2024

If the governing differential equation arising from engineering problems is treated as an analytic, continuous and derivable function, it can be expanded by one point as a series of finite numbers. For the function to be zero for each value of its domain, the coefficients of each term of the same power must be zero. This results in a recursive relationship which, after applying the natural conditions or the boundary conditions, makes it possible to obtain the values of the derivatives of the function with acceptable accuracy. The elastoplastic analysis of an inhomogeneous thick sphere of metallic materials with linear variation of the modulus of elasticity, yield stress and Poisson's ratio as a function of radius subjected to internal pressure is presented. The Beltrami-Michell equation is established by combining equilibrium, compatibility and constitutive equations. Assuming axisymmetric conditions, the spherical coordinate parameters can be used as principal stress axes. Since there is no analytical solution, the natural boundary conditions are applied and the governing equations are solved using a proposed new method. The maximum effective stress of the von Mises yield criterion occurs at the inner surface; therefore, the negative sign of the linear yield stress gradation parameter should be considered to calculate the optimal yield pressure. The numerical examples are performed and the plots of the numerical results are presented. The validation of the numerical results is observed by modeling the elastoplastic heterogeneous thick sphere as a pressurized multilayer composite reservoir in Abaqus software. The subroutine USDFLD was additionally written to model the continuous gradation of the material.

• 한국전산유체공학회:학술대회논문집
• /
• 1998.11a
• /
• pp.160-166
• /
• 1998

In this paper, incompressible two-dimensional Navier-Stokes equations are numerically solved for the study of steady laminar flow around a body with the wall effect. A second-order finite difference method is used for the spatial discretization on the nonstaggered grid system and the 4-stage Runge-Kutta scheme for the numerical integration in time. The pressure field is obtained by solving the pressure-Poisson equation with the Neumann boundary condition. To investigate the wall effect, numerical computations are carried out for the NACA 0012 section at the various blockage ratios. The pressure and skin friction on the foil surface, velocity pronto in its wake and drag coefficient are investigated as functions of the blockage ratio.

• Journal of the Society of Naval Architects of Korea
• /
• v.33 no.2
• /
• pp.13-29
• /
• 1996

This paper presents calculated results of the free-surface flow around a Series 60($C_B=0.6$) model. Three-dimensional Navier-Sotkes equations are solved and Baldwin-Lomax algebraic turbulence model is adopted to simulate the high Reynolds-number flow. To reduce computational efforts, velocity components near the wall are extrapolated with a the solved by using the Implicit Approximate Factorization method[2]. The successive-over-relaxation method is used for solving pressure-Poisson equation when obtaining the pressure field projecting the divergence-free velocity field. To simulate the free-surface flows more precisely, the numerical scheme solving the equation for the kinematic boundary condition is very important. In this paper, there numerical schemes are employed and the results are compared with the available experimental data.

• Journal of the Society of Naval Architects of Korea
• /
• v.51 no.4
• /
• pp.328-333
• /
• 2014

A hybrid particle-mesh method based on the vorticity-velocity formulation for solving the incompressible Navier-Stokes equations is a combination of the Vortex-In-Cell(VIC) method for convection and the penalization method for diffusion. The key feature of the numerical methods is to determine velocity and vorticity fields around a solid body on a temporary grid, and then the time evolution of the flow is computed by tracing the convection of each vortex element using the Lagrangian approach. Assuming that the vorticity and velocity fields are to be computed in time domain analysis, pressure fields are estimated through a complete set of solutions at present time step. It is possible to obtain vorticity and velocity fields prior to any pressure calculation since the pressure term is eliminated in the vorticity-velocity formulation. Therefore, pressure field is explicitly treated by solving a suitable Poisson equation. In this paper, we propose a simple way to numerically implement the vorticity-velocity-pressure formulation including a penalty term. For validation of the proposed numerical scheme, we illustrate the early development of viscous flows around an impulsive started circular cylinder for Reynolds number of 9500.

• Journal of the Korean Society of Visualization
• /
• v.21 no.2
• /
• pp.14-23
• /
• 2023

The pressure difference across stenotic blood vessels is a commonly used clinical metric for diagnosing many cardiovascular diseases. At present, most clinical pressure measurements rely solely on invasive catheterization. In this study, we propose a novel method for non-invasive pressure estimation using the incompressible Navier-Stokes equations and a 3D multi-path integration approach. We verify spatio-temporal convergence on an in-silico dataset of a cylindrical straight pipe phantom with steady and pulsatile flow fields. We then evaluate the proposed method on an in vitro dataset of reconstructed control, pre-operative, and post-operative carotid artery cases acquired from 4D flow MRI. The performance of our method is compared to existing approaches based on the pressure Poisson equation and work-energy relative pressure. The results demonstrate the proposed method's high accuracy, robustness to spatio-temporal subsampling, and reduced sensitivity to noise, highlighting its great potential for non-invasive pressure estimation.

• Journal of the Society of Naval Architects of Korea
• /
• v.35 no.4
• /
• pp.1-10
• /
• 1998

This paper presents a vorticity-based numerical method for analyzing an incompressible Newtonian viscous flow around an impulsively started cylinder. The Navier-Stockes equations have a natural Helmholtz decomposition. The vorticity transport equation and the pressure equation are derived from this decoupled form. The associated boundary conditions are dynamic for the vorticity and pressure variables representing the coupling relation between them and the force balance on the wall. The various numerical treatments for solving the governing equations are introduced. According to Wu et al.(1994), the boundary conditions are decoupled, keeping the dynamic relation between vorticity and pressure. The vorticity transport equation is formulated by FVM and TVD(Total Variation Diminishing) scheme is used for the convection term. An integral approach similar to the panel method is used to obtain the velocity field for a given vorticity field and the pressure field, instead of the conventional differential approaches. In the numerical process, the structured grid is generated. The results are compared to existing numerical and analytic results for the validity of the present method.

• Proceedings of the KIEE Conference
• /
• 2003.10a
• /
• pp.220-222
• /
• 2003

In this paper, we analyze on the discharge characteristics through 1-D simulations in an at plasma display panel discharge cell. The model is based on a Poisson' equation, continuity and drift-diffusion equation. Results are presented in a 95% neon, 5% xenon gas mixture, for a gap length of 100us and a gas pressure of 400Torr at ambient temperature. Results for other gap length are also discussed. As a result, an increase of the gap cause increase of luminous efficiency but with larger sustaining voltage.