• Journal of computational fluids engineering
• /
• v.17 no.3
• /
• pp.25-32
• /
• 2012

This work was devoted to compare two different cavitation models to study the dependency of model constants. The cavitation model of Merkle et al.(2006) and Kunz et al.(2000) were used for the present computational study. The cavitation models were coupled with the incompressible unsteady Reynolds-Averaged Navier-Stokes solver to indicate the vaporization and condensation processes. For this purpose, a preconditioning method was added as the pseudo-time term to solve the unsteady stiffness problems. For the validation of the numerical simulation, the computation was performed for the cavitating flow in a converging-diverging channel. The present results show that Merkle's cavitation model is independent to the model constants, and the higher numerical accuracy over Kunz's cavitation model.

• Honam Mathematical Journal
• /
• v.43 no.2
• /
• pp.183-197
• /
• 2021

Recently several authors have extended the Beta function by using its integral representation. However, in many cases no expression of these extended functions in terms of classic special functions is known. In the present paper, we introduce a further extension by defining a family of functions G_r,s : ℝ^*₊ → ℂ, with r, s ∈ ℂ and ℜ(r) > 0. For given r, s, we prove that this function satisfies a second-order linear differential equation with rational coefficients. Solving this ODE, we express G_r,s as a combination of confluent hypergeometric functions. From this we deduce a new integral relation satisfied by Tricomi's function. We then investigate additional specific properties of G_r,1 which take the form of new non trivial integral relations involving exponential and error functions. We discuss the connection between G_r,1 and Stokes' first problem (or Rayleigh problem) in fluid mechanics which consists in determining the flow created by the movement of an infinitely long plate. For $r{\in}{\frac{1}{2}}{\mathbb{N}}^*$, we find additional relations between G_r,1 and Hermite polynomials. In view of these results, we believe the family of extended beta functions G_r,s will find further applications in two directions: (i) for improving our knowledge of confluent hypergeometric functions and Tricomi's function, (ii) and for engineering and physics problems.

• Journal of computational fluids engineering
• /
• v.16 no.2
• /
• pp.1-10
• /
• 2011

A new computational program, which is based on the CIP/CCUP(Constraint Interpolation Profile/CIP Combined Unified Procedure) method, has been developed to numerically analyse sloshing phenomena dealt as multiphase-flow problems. For the convection terms of Navier-Stokes equations, the RCIP(Rational function CIP) method was adopted and the THINC-WLIC(Tangent of Hyperbola for Interface Capturing-Weighted Line Interface Calculation) method was used to capture the air/water interface. To validate the present numerical method, two-dimensional dam-breaking and sloshing problems in a rectangular tank were solved by the developed method in a stationary Cartesian grid system. In the case of sloshing problems, simulations by using a improved MPS(Moving Particle Simulation) method, which is named as PNU-MPS(Pusan National University-MPS), were also carried out. The computational results are compared with those of experiments and most of the comparisons are reasonably good.

• Journal of Advanced Research in Ocean Engineering
• /
• v.1 no.3
• /
• pp.157-167
• /
• 2015

In order to provide simple and accurate wave theory in design of offshore structure, an analytical approximation is introduced in this paper. The solution is limited to flat bottom having a constant water depth. Water is considered as inviscid, incompressible and irrotational. The solution satisfies the continuity equation, bottom boundary condition and non-linear kinematic free surface boundary condition exactly. Error for dynamic condition is quite small. The solution is suitable in description of breaking waves. The solution is presented with closed form and dispersion relation is also presented with closed form. In the last century, there have been two main approaches to the nonlinear problems. One of these is perturbation method. Stokes wave and Cnoidal wave are based on the method. The other is numerical method. Dean's stream function theory is based on the method. In this paper, power series method was considered. The power series method can be applied to certain nonlinear differential equations (initial value problems). The series coefficients are specified by a nonlinear recurrence inherited from the differential equation. Because the non-linear wave problem is a boundary value problem, the power series method cannot be applied to the problem in general. But finite number of coefficients is necessary to describe the wave profile, truncated power series is enough. Therefore the power series method can be applied to the problem. In this case, the series coefficients are specified by a set of equations instead of recurrence. By using the set of equations, the nonlinear wave problem has been solved in this paper.

• Journal of the Society of Naval Architects of Korea
• /
• v.30 no.2
• /
• pp.98-111
• /
• 1993

Two-dimensional nonlinear free-surface wave problems are analyzed with consideration of viscosity. Navier-Stokes equation and continuity equation are solved by the application of Finite Analytic Method, and MAC scheme is used far the treatment of free surface. Surface tension effect is also considered and laminar flow is assumed. The free-surface waves in shallow water, the flows around a vortex-pair with free surface and the wave ahead of a rectangular body are simulated to test the present numerical scheme. In the shallow water problem, viscous effect due to the friction on the bottom is observed. In the second problem, the approach of a vortex-pair to the free surface is simulated to examine the interaction of vortex-pair with the free surface. In the third problem, the wave ahead of a semi-infinite floating body is simulated.

• 한국전산유체공학회:학술대회논문집
• /
• 2005.10a
• /
• pp.1-10
• /
• 2005

A new approach, Multi-Objective Design Exploration (MODE), is presented to address Multidisciplinary Design Optimization (MDO) problems by CFD-CSD coupling. MODE reveals the structure of the design space from the trade-off information and visualizes it as a panorama for Decision Maker. The present form of MODE consists of Kriging Model, Adaptive Range Multi Objective Genetic Algorithms, Analysis of Variance and Self-Organizing Map. The main emphasis of this approach is visual data mining. An MDO system using high fidelity simulation codes, Navier-Stokes solver and NASTRAN, has been developed and applied to a regional-jet wing design. Because the optimization system becomes very computationally expensive, only brief exploration of the design space has been performed. However, data mining result demonstrates that design knowledge can produce a good design even from the brief design exploration.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.33 no.4
• /
• pp.242-247
• /
• 2009

AILU type preconditioners for a two-dimensional combined P2P1 finite element formulation of the interaction of rigid cylinder with incompressible fluid flow have been devised and tested by solving fluid-structure interaction (FSI) problems. The FSI code simulating the interaction of a rigid cylinder with an unsteady flow is based on P2P1 mixed finite element formulation coupled with combined formulation. Four different preconditioners were devised for the two-dimensional combined P2P1 finite element formulation extending the idea of Nam et al., which was proposed for the preconditioning of a P2P1 mixed finite element formulation of the incompressible Navier-Stokes equations. It was found that PC-III or PC-IV among them perform well with respect to computational memory and convergence rate for some bench-mark problems.

• 한국전산유체공학회:학술대회논문집
• /
• 2004.10a
• /
• pp.121-125
• /
• 2004

The preprocessor - solver - postprocessor software for 2D/Axisymmetric CSCM Upwind Flux Difference Splitting Navier-Stokes code has been developed for undergraduate educational purpose. This computational fluid dynamics (CFD) software allows students to setup, solve, visualize and control dynamically server for their own fluid problems via Internet. The preprocessor Is capable of generating geometry and grid, initial solution data and required solver control parameters. The postprocessor shows vector plot and contour plot with different options while residual plot shows root-mean-square (RMS) error history graphically and retrieves the data from solver interactively. Special feature of the preprocessor is grid generation part which is based on MFC/Visual C++ application and FORTRAN single block grid generator process. Many users can access solver via Internet from client computers and solve desired problems using locally installed pre- and postprocessor and remote powerful solver part.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.19 no.10
• /
• pp.2667-2677
• /
• 1995

A new numerical algorithm using equal order linear finite element and fractional step method has been developed which is capable of analyzing unsteady fluid flow and heat transfer problems. Streamline Upwind Petrov-Galerkin (SUPG) method is used for the weighted residual formulation of the Navier-Stokes equations. It is shown that fractional step method, in which pressure term is splitted from the momentum equation, reduces computer memory and computing time. In addition, since pressure equation is derived without any approximation procedure unlike in the previously developed SIMPLE algorithm based FEM codes, the present numerical algorithm gives more accurate results than them. The present algorithm has been applied preferentially to the well known bench mark problems associated with steady flow and heat transfer, and proves to be more efficient and accurate.

• Journal of Korean Society for Atmospheric Environment
• /
• v.9 no.E
• /
• pp.347-357
• /
• 1993

The Lagrangian grid-free numerical method, the discrete vortex method, was applied to solve the Navier-Stokes euqations. This method avoids the introduction of numerical viscosity swamping the real physical viscosity at high Reynolds number, unlike Eulerian method, e.g. finite difference and element methods. The boundary integral equation method for the potential flow solution was included to make the discrete vortex method more feasible for complex geometries. The fast adaptive multipole expansion method was incorporated to reduce the computational time from $O(N^2)$ to O(N) for the computations of vortex-vortex interactions. The test problems were air flow around one circular cylinder and two circular cylinders in tandem with various gaps. The numerical results were in excellent gareement with the experimental and other computational results. The applicabilty of the method was discussed with the indoor and the outdoor air pollution problems, especially the contaminant transport in the recirculation regions.