In this presentation, I talk about various fluid simulation methods that have been developed for computer graphics special effects since 1996. They are all based on CFD but sacrifice physical reality for visual plausability and time. But as the speed of computer increases rapidly and the capability of GPU (graphics processing unit) improves, methods for more physical realism have been tried. In this talk, I will focus on four aspects of fluid simulation methods for computer graphics: (1) particle level-set methods, (2) particle-based simulation, (3) methods for exact satisfaction of incompressibility constraint, and (4) GPU-based simulation. (1) Particle level-set methods evolve the surface of fluid by means of the zero-level set and a band of massless marker particles on both sides of it. The evolution of the zero-level set captures the surface in an approximate manner and the evolution of marker particles captures the fine details of the surface, and the zero-level set is modified based on the particle positions in each step of evolution. (2) Recently the particle-based Lagrangian approach to fluid simulation gains some popularity, because it automatically respects mass conservation and the difficulty of tracking the surface geometry has been somewhat addressed. (3) Until recently fluid simulation algorithm was dominated by approximate fractional step methods. They split the Navier-Stoke equation into two, so that the first one solves the equation without considering the incompressibility constraint and the second finds the pressure which satisfies the constraint. In this approach, the first step introduces error inevitably, producing numerical diffusion in solution. But recently exact fractional step methods without error have been developed by fluid mechanics scholars), and another method was introduced which satisfies the incompressibility constraint by formulating fluid in terms of vorticity field rather than velocity field (by computer graphics scholars). (4) Finally, I want to mention GPU implementation of fluid simulation, which takes advantage of the fact that discrete fluid equations can be solved in parallel.

전통적으로 선박 프로펠러의 설계에 사용되는 수치해석방법을 소개하고, 점성유동장에서 작동하는 프로펠러의 해석을 포텐셜 이론을 적용해서 수행하는 방법을 소개한다. 캐비테이션 해석 등 최근의 프로펠러 주위 유동의 해석에 CFD가 적용되는 예를 보이고, 프로펠러의 성능 검증을 위해 실제 선박에서 수행되는 실험의 예를 보이고자 한다.

In this study, two and three dimensional low Reynolds number flows are compared. For the two dimensional flow, an airfoil was considered and for the three dimensional low wing and full-body aircraft were considered. Because a flight condition of the aircraft is in a low Reynolds number flow, itl requires reflecting flow transition. In the two dimensional analysis, transition is predicted using en method. In the three dimensional flow, the effect of transition is included using k-w SST turbulence models.

In this study the performance of the nozzle of a rocket system is evaluated using a CFD code. The main emphasis of the investigation is placed on the effects of the number (9 and 12) and the depth of fluted edge in the rocket nozzle. It is observed that as the depth increases the rolling moment of the nozzle increases while the thrust of the nozzle decreases.

Flight vehicles such as wheel wells and bomb bays have many cavities. The flow around a cavity is characterized as an unsteady flow because of the formation and dissipation of vortices brought about by the interaction between the free stream shear layer and the internal flow of the cavity. The resonance phenomena can damage the structures around the cavity and negatively affect the aerodynamic performance and stability of the vehicle. In this study, a numerical analysis was performed for the cavity flows using the unsteady compressible three-dimensional Reynolds-Averaged Navier-Stokes (RANS) equation with Wilcox's turbulence model. The Message Passing Interface (MPI) parallelized code was used for the calculations by PC-cluster. The cavity has aspect ratios (L/D) of 2.5 ~ 7.5 with width ratios (W/D) of 2 ~ 4. The Mach and Reynolds numbers are 0.4 ~ 0.6 and $1.6{\times}106$, respectively. The occurrence of oscillation is observed in the "shear layer and transient mode" with a feedback mechanism. Based on the Sound Pressure Level (SPL) analysis of the pressure variation at the cavity trailing edge, the dominant frequencies are analyzed and compared with the results of Rossiter's formula. The dominant frequencies are very similar to the result of Rossiter's formula and other experimental data in the low aspect ratio cavity (L/D = ~ 4.5). In the large aspect ratio cavity, however, there are other low dominant frequencies due to the leading edge shear layer with the dominant frequencies of the feedback mechanism. The characteristics of the acoustic wave propagation are analyzed using the Correlation of Pressure Distribution (CPD).

The objective of this study is to investigate aerodynamic characteristics of a Horizontal-axis wind turbines(HAWT), using CFD method with a commercial code STAR-CCM+ version 3.06. To verify the reliability of the computations, the CFD results are compared with the experimental ones of the National Renewable Energy Laboratory(NREL) Phase Ⅵ HAWT. For the comparison and examination of aerodynamic characteristics, the existent shape with a predesigned twist angle was replaced by the one with one-dimensional linear twist angle. In this study, the pressure contour and stream line around the blade were analyzed as main focus. Through this study the more efficient shape of airfoil is suggested with consideration of manufacturing cost.

In this paper, the flow past a rotary oscillating circular cylinder is simulated. The high-order and high-resolution numerical schemes with the characteristic boundary conditions are used for the compressible Navier-Stokes equation. The frequencies of rotating oscillation are $0.19\;{\leq}\;S_f\;{\leq}\;0.25$ for the maximum angular $\theta_{max}=10^{\circ}$ and $17^{\circ}$. The flow conditions are Mach number of 0.3 and Reynolds number of 1000. At Lock-on and Non-lock-on region which are defined by the relation between the vortex shedding frequency and the oscillating frequency, the drag and lift coefficient are analyzed.

Deforming mesh should be used when bodies are deforming or moving relative to each other due to the presence of aerodynamic forces and moments. Also, the flow solver for such a flow problem should satisfy the geometric conservation law to ensure the accuracy of the solutions. In this paper, a RANS(Reynolds Averaged Navier-Stokes) solver including automatic mesh capability using TFI(Transfinite Interpolation) method and GCL is developed and applied to flows induced by oscillating wings with given frequencies. The computations are performed both on deforming meshes and on rigid meshes. The computational results are compared with experimental data, which shows a good agreement.

The objective of this study is to get a fundamental data for the shape of a robot which operates in blood vessels. The overall analysis was calculated with a CFD code. The flow was idealized as a pulsatile flow, and first the robot was assumed as a simple capsule model. Then a drag of the body in the flow was calculated, and this process was repeated, varying the shape. To validate all the result, the pulastile velocity simulation was compared with the theoretical data, and the drag of a body was compared with the existing data of the other papers first. Then with the next calculation the guideline for the design of robot shape was presented.

In this study, a vortex visualization method based on the vorticity magnitude is developed. One of the simplest models for a vortex is a vortex filament with the maximum vorticity on its center. The proposed method is based on the observation of this ideal distribution of vorticity magnitude. Laplacian and Hessian matrix of vorticity magnitude are tested for detecting the local maximum of vorticity magnitude. These ideas were applied to wake flow past a sphere. It was found that the Laplacian method is not able to distinguish vortices from the underlying shear layer clearly, while the Hessian matrix method does not suffer from this problem.

This paper evaluates performances of a recently developed divergence-free finite element method based on Hermite interpolated stream functions. Velocity bases are derived from Hermite interpolated stream functions to form divergence-free basis functions. These velocity basis functions constitute a solenoidal function space, and the simple gradient of the Hermite functions constitute an irrotational function space. The incompressible Navier-Stokes equation is orthogonally decomposed into a solenoidal and an irrotational parts, and the decoupled Navier-Stokes equations are projected onto their corresponding spaces to form proper variational formulations. To access accuracy and convergence of the present algorithm, three test problems are selected. They are lid-driven cavity flow, flow over a backward-facing step and buoyancy-driven flow within a square enclosure. Hermite interpolation functions from cubic to quintic are chosen to run the test problems. Numerical results are shown. In all cases it has shown that the present method has performed well in accuracies and convergences. Moreover, the present method does not require an upwinding or a stabilized term.

In the present work, LES with new variational multiscale method is conducted on the fully developed channel flow with Reynolds number is 180 based on the friction velocity and the channel half width. Incompressible Navier-Stokes equations are integrated using finite element method with the basis function of NURBS. To solve space-time equations, Newton's method with two stage predictor multicorretor algorithm is employed. The code is parallelized using MPI. The computational domain is a rectangular box of size $2{\pi}{\times}2{\times}4/3{\pi}$ in the streamwise, wall normal and spanwise direction. Mean velocity profiles and velocity fluctuations are compared with the data of DNS. The results agree well with those of DNS and other traditional LES.

Laminar separation bubble and transitional flow over an airfoil are investigated at a moderate range of Reynolds numbers. In this research, a Reynolds-Averaged Navier-Stokes code is coupled with an empirical transition model that can predict transition onset points and the length of transition region. Without solving the boundary layer equations, approximated e-N method is directly applied to the RANS code and iteratively solved together. The computational results are compared with the experimental data for NACA0012 airfoil. Results of transition onset point and length are compared well with experimental and XFOIL prediction. In high angle of attack the present RANS results show better agreement than XFOIL results using the boundary layer equations.

In this paper a hybrid grid generation program for general 2-D region is introduced. The program is developed by using JAVA programming language, and it can be used either as an application program on a local computer or as an applet in the network environment. The hybrid grid system for a 2-D problem means a combination of triangular cells and quadrilateral cells, and it can offer both of the high flexibility of triangular cells and the high accuracy and efficiency of structured-type quadrilateral cells. To accommodate a quadrilateral-cell region and a triangular-cell region into one computational domain, it is importance to take good care of the interface between two different regions so that overall good grid quality can be maintained. In this research advancing layer method(ALM) augmented by elliptic smoothing method is used for the quadrilateral-cell region and advancing front method(AFM) is used for the triangular-cell region. A special treatment technique for the interface between those two regions is also developed. The interface treatment technique is basically to prevent the propagation of small cell size due to ALM method into the triangular region and maintain the smooth transition of cell-size scale between two different regions. By applying current technique high-quality hybrid grids for general 2-D regions can be easily generated, and typical grid generation results and flow solutions are demonstrated.

The research to predict the resistance performance of the ship using the CFD analysis is increasing. For the CFD numerical analysis the computational mesh, which is proper to computational model, has to be made before the analysis is begun. In the parametric study, even though the deformation of each case is not very sharp, the whole computational mesh should be regenerated according to the conventional way. Hence, lots of effort is needed to repeated mesh generation work. To solve these problems, the automatic mesh generation method using the macro function of commercial CAD program and mesh generation program is introduced in this study. First, in the CAD program, by using the macro function and putting the deformation rate of bow and stern in lengthwise, the repeated modeling work is performed automatically. Next, the generated geometries are read by the mesh generation program and the proper mesh for the geometry is created automatically also using the macro function. The hybrid mesh which has unstructured grid near the bow and stern and structured grid in the remaining part of domain is used. The verification of the developed method is done by applying the method to predict the resistance performance of the podded propulsion cruise ship of the Daewoo Shipbuilding & Marine Engineering (DSME) in the cases of different length of bow and stern and pod set in different position. The author believes that the introduced method can help to make the database to optimize the resistance performance of the ship in various cases can be constructed without difficulty.

In this study, we conducted resistance and propulsion performance test of ship composed of the Resistance Test, Propeller Open Water Test and Self Propulsion Test using the CFD(Computational Fluid Dynamics). We used commercial RANS(Reynolds Averaged Navier Stokes equation) solver, as a calculating tool. The unstructured grids were used in a bow and stern of ship, having complex shape, for a convenience of generating grids, and the structured grids were adopted in a central hull and rest of hull having a relatively simple shape which is called hybrid grid method. In addition, The sliding mesh method was adopted to rotate a propeller directly in the Propeller Open Water and Self Propulsion Test. The Resistance Test and Self Propulsion Test were calculated using Volume of Fluid (VOF) model and considering a free surface. And all The three cases were applied realizable k-epsilon model as the turbulence model. The results of calculations were verified for the suitability of calculations by comparing MOERI's EFD results.

Electrowetting is a versatile tool to handle tiny droplets and forms a backbone of digital microfluidics. Numerical analysis is necessary to fully understand the dynamics of electrowetting, especially in designing electrowetting-based devices, such as liquid lenses and reflective displays. We developed a numerical method to analyze the general contact-line problems, incorporating dynamic contact angle models. The method is based on the conservative level set method to capture the interface of two fluids without loss of mass. We applied the method to the analysis of spreading process of a sessile droplet for step input voltages and oscillation of the droplet for alternating input voltages in electrowetting. The result was compared with experimental data. It is shown that contact line friction significantly affects the contact line motion and the oscillation amplitude. The pinning process of contact line was well represented by including the hysteresis effect in the contact angle models.

When exposed to uniform magnetic fields externally applied, paramagnetic particles acquire dipole moments and the induced moments interacting with each other lead to the formation of chainlike structures or clusters of particles aligned with the field direction. A direct simulation method, based on the Maxwell stress tensor and a fictitious domain method, is applied to solve flows with magnetic chains in simple shear flow. We assumed that the particles constituting the chains are paramagnetic, and inertia of both flow and magnetic particles is negligible. The numerical scheme enables us to take into account both hydrodynamic and magnetic interactions between particles in a fully coupled manner, enabling us to numerically visualize breakup and reformation of the chains by the combined effect of the external field and the shear flow. Simple shear flow with suspended magnetic chains is solved in a periodic domain for a given magnetic field. Dynamics of interacting magnetic chains is found to be significantly affected by a dimensionless parameter called the Mason number, the ratio of the viscous force to the magnetic force in the shear flow. The effect of particle area fraction on the chain dynamics is investigated as well.

In the cathode channel of a PEM fuel cell, the local concentration of oxygen near the gas diffusion layer (GDL) decreases in streamwise direction due to chemical reactions, which degrades the efficiency of the oxygen consumption and overall fuel cell efficiency. We numerically studied the influence of the swirling flow generated by a slanted groove mixer (SGM) on the concentration distribution of oxygen. We found that the swirling flow can increase the concentration of oxygen near the GDL, and subsequently improves the oxygen consumption rate.

Translocation of biopolymers such as DNA and RNA through a nano-pore is an important process in biotechnology applications. The translocation process of a biopolymer through an artificial nano-pore in the presence of a fluid solvent is simulated. The polymer motion is simulated by Langevin molecular dynamics (MD) techniques while the solvent dynamics are taken into account by lattice-Boltzmann method (LBM). The hydrodynamic interactions are considered explicitly by coupling the polymer and solvent through the frictional and the random forces. From simulation results we found that the hydrodynamic interactions between polymer and solvent speed-up the translocation process. The translocation time ${\tao}_T$ scales with the chain length N as ${{\tau}_T}^{\propto}N^{\alpha}$. The value of scaling exponents($\alpha$) obtained from our simulations are $1.29{\pm}0.03$ and $1.41{\pm}0.03$, with and without hydrodynamic interactions, respectively. Our simulation results are in good agreement with the experimentally observed value of $\alpha$, which is equal to $1.27{\pm}0.03$, particularly when hydrodynamic interaction effects are taken into account.

The droplet impact and merging process on a flat substrate with contact angle hysteresis is numerically studied. The droplet deformation is determined by an improved level-set method employing a sharp-interface technique for the stress condition at the liquid-gas interface and the contact angle condition at the liquid-gas-solid interline. Based on the computations, the droplet impact and merging pattern is investigated to find the optimal condition in manufacturing a micro-line. The effects of dynamic contact angles and droplet spacing on droplet motion are quantified.

As one of the promising model on the multiphase fluid mixtures, the Lattice-Boltzmann Method(LBM) is being developed to simulate flows containing two immisible components which are different mass values. The equilibrium function in the LBM can have a nonideal gas model for the equation of state and use the interfacial energy for the phase separation effect. An example on the phase separation has been carried out through the time evolution. The LBM based on the statistic mechanics is appropriate to solve very complicated flow problems and this model gives comparative merits rather than the continuum mechanics model.

We numerically investigated propagation of various waves in the two-phase flows such as sound wave, shock wave, rarefaction wave, and contact discontinuity in terms of pressure, void fraction, velocity and density of the two phases. The waves have been generated by a hydrodynamic shock tube, a pair of symmetric impulsive expansion, impulsive pressure and impulsive void waves. The six compressible two-fluid two-phase conservation laws with interfacial friction terms have been solved in two fractional steps. The first PDE Operator is solved by the HLL scheme and the second Source Operator by the semi-implicit stiff ODE solver. In the HLL scheme, the fastest wave speeds were estimated by the analytic eigenvalues of an approximate Jacobian matrix. We have discussed how the interfacial friction terms affect the wave structures in the numerical solution.

During a hypothetical high-pressure accident in a nuclear power plant (NPP), molten corium can be ejected through a breach of a reactor pressure vessel (RPV) and dispersed by a following jet of a high-pressure steam in the RPV. The dispersed corium is fragmented into smaller droplets in a reactor cavity of the NPP by the steam jet and released into other compartments of the NPP by a overpressure in the cavity. The fragments of the corium transfer thermal energy to the ambient air in the containment or interact chemically with steam and generate hydrogen which may be burnt in the containment. The thermal loads from the ejected molten corium on the containment which is called direct containment heating (DCH) can threaten the integrity of the containment. DCH in a NPP containment is related to many physical phenomena such as multi-phase hydrodynamics, thermodynamics and chemical process. In the evaluation of the DCH load, the melt dispersion rates depending on the RPV pressure are the most important parameter. Mostly, DCH was evaluated by using lumped-analysis codes with some correlations obtained from experiments for the dispersion rates. In this study, MC3D code was used to evaluate the dispersion rates in the APR1400 NPP during the high-pressure accidents. MC3D is a two-phase analysis code based on Eulerian four-fields for melt jet, melt droplets, gas and water. The dispersion rates of the corium melt depending on the RPV pressure were obtained from the MC3D analyses and the values specific to the APR1400 cavity geometry were compared to a currently available correlation.

In the present study, the characteristic of flow distribution in the channel of a plate heat exchanger is investigated numerically. In order to accomplish the efficient and fast analyses of the flow characteristics in the channel, a semi-microscopic analysis has been performed using a porous media model. For semi-microscopic analysis using porous media, the flow resistance coefficients are obtained through the result of pressure drop in the experimental data. The results showed that the variation of mass flow rate, geometry and chevron angle strongly depend on the flow distribution in the channel. Particularly, the chevron angle is most important factor for uniform flow distribution.

In this study, the heat transfer and fluid flow characteristics of a condenser for a refrigerator are analyzed with the numerical method. The main objective of the study is to obtain basic data in order to develop a new type of condenser focused on an influence of thermal resistance of air side and thermal contact resistance on the heat transfer performance. The CFD technique was used for whole study, and experiments were performed in order to verify the reliability of the numerical analysis and predict the thermal contact resistance. In this study, a heat exchanger sample was made of a part of condenser to make the experimental and numerical analysis simple and efficient. Water was used for the inner working fluid of the heat exchanger, and an experimental apparatus was composed concisely. A heat exchanger sample of tube type was used to verify the reliability of numerical analysis, and a heat exchanger of fin and tube type was used to predict the ratio of thermal contact resistance to the overall thermal resistance.

In this study, characteristics of microwave and convective drying are studied by using a multiphase porous media model. Temperature and moisture profiles for hot-air convective heating and microwave heating of 1-D porous media with varying time and space are numerically investigated. This result shows the microwave drying method is more effective than the convective drying method. Comparing to convective drying, microwave drying can increase temperature and evaporation rate significantly since microwave generates internal heat and increases internal pressure, which results in moisture movement toward the surface on which moisture is vaporized.

To implement the insects' flapping flight for developing flapping MAVs(micro air vehicles), the unsteady flow characteristics of the insects' forward flight is investigated. In this paper, two-dimensional FSI(Fluid-Structure Interaction) simulations are conducted to examine realistic flow features of insects' flapping flight and to examine the flexibility effects of the insect's wing. The unsteady incompressible Navier-Stokes equations with an artificial compressibility method are implemented as the fluid module while the dynamic finite element equations using a direct integration method are employed as the solid module. In order to exchange physical information to each module, the common refinement method is employed as the data transfer method. Also, a simple and efficient dynamic grid deformation technique based on Delaunay graph mapping is used to deform computational grids. Compared to the earlier researches of two-dimensional rigid wing simulations, key physical phenomena and flow patterns such as vortex pairing and vortex staying can still be observed. For example, lift is mainly generated during downstroke motion by high effective angle of attack caused by translation and lagging motion. A large amount of thrust is generated abruptly at the end of upstroke motion. However, the quantitative aspect of flow field is somewhat different. A flexible wing generates more thrust but less lift than a rigid wing. This is because the net force acting on wing surface is split into two directions due to structural flexibility. As a consequence, thrust and propulsive efficiency was enhanced considerably compared to a rigid wing. From these numerical simulations, it is seen that the wing flexibility yields a significant impact on aerodynamic characteristics.

In this paper, the fluid dynamic forces and performances of a moving airfoil in the low Reynolds number flow is addressed. In order to calculate the necessary propulsive force for the moving airfoil in a low Reynolds number flow, a lattice-Boltzmann method is used. The critical Reynolds and Strouhal numbers for the thrust generation are investigated for the four propulsion types. It was found that the Normal P&D type produces the largest thrust with highest efficiency among the investigated types. The leading edge of the airfoil has an effect of deciding the force production types, whereas the trailing edge of the airfoil plays an important role in augmenting or reducing the instability produced by the leading edge oscillation. It is believed that present results can be used to decide the optimal propulsion devices for the given Reynolds number flow.

Study on swimming of microorganisms like, sperm motility, cilia beating, bacterial flagellar propulsion has found immense significance in the field of biological fluiddynamics. Because of the complexity involved, it is challenging for the researchers to model such problems. Immersed boundary method has proved its efficacy in the field of biological fluiddynamics, The present work aims at performing a numerical study on the microorganism locomotion using the immersed boundary method proposed by Peskin[1]. A two-dimensional model of the microorganism is modeled as thin elastic filament described as a sine wave. The neutrally buoyant organism undergoing deformations is immersed in a viscous and incompressible fluid. The fluid quantities are described using Eulerian coordinates and the immersed body is represented by Lagrangian coordinates. The Eulerian and Lagrangian variables are connected by the Dirac delta function. The Navier-Stokes equations governing the fluid flow are solved using the fractional step method on a staggered Cartesian grid system. The developed numerical code in FORTRAN will be validated by comparing the numerical results with the available results.

Flow control butterfly valve(FCBV) is known to have difficulty in controlling flow rate along valve opening due to its high flow rate. In low opening condition, the butterfly valve also has some shortcomings such as noise, vibration and erosion which are mostly caused by cavitation effects. Therefore, the FCBV requires proper remedies to reduce cavitation effects and to improve flow control performance. Numerical analysis is applied to FCBV flow to find effects of design factors such as seat diameter and valve opening rate. Cases with 3 different sizes of seat diameter and various valve opening rate are selected for the numerical analysis. From the analysis results, it is found that the FCBV with small seat diameter shows better pressure loss performance and reduced cavitation effects.

Cavitating flow simulation is of practical importance for many engineering systems, such as marine propellers, pump impellers, nozzles, injectors, torpedoes, etc. The present work has focused on the simulation of cavitating flow past cylinders with strong side flows. The governing equation is the Navier-Stokes equation based on the homogeneous mixture model. The momentum and energy equation is in the mixture phase while the continuity equation is solved liquid and vapor phase, separately. An implicit dual time and preconditioning method are employed for computational analysis. For the code validation, the results from the present solver have been compared with experiments and other numerical results. A fairly good agreement with the experimental data and other numerical results have been obtained. After the code validation, the strong side flow was applied to include the wake flow effects of the submarine or ocean tide.

A density based method with homogeneous cavitation model to investigate cavitation-bubble collapsing behavior is proposed and applied to bubble-shock interaction problems. By applying this method, cylindrical bubbles located in the liquid and incident liquid shock wave are computed. Bubble collapsing behavior, shock-bubble interaction and shock transmission/reflection pattern are investigated.

A massive cavity is generated behind the underwater vehicles, such as marine propellers, pump impellers, nozzles, injectors, torpedoes, etc. when a underwater vehicle moves at very high speed in the underwater. At this point it makes supercavitating flow and the nose, ie., the cavitator is very important fator at the vehicle since it should be surrounded by the cavity. The present work has focused on the simulation of cavitation flow using the new cavitator. The governing equation is the Navier-Stokes equation based on homogeneous mixture model. For the code validation, the results from the present solver have been compared with experiments and other numerical results. A fairly good agreement with the experimental data and other numerical results have been obtained.

Recently, there have been efforts to construct hybrids among the existing methodologies for multiphase flow such as VOF, Level Set, and Front Tracking with the intention of facilitating simulations of general three-dimensional problems. As one of the hybrid method, we have developed the Level Contour Reconstruction Method (LCRM) for general three-dimensional multiphase flows including phase change. The main idea was focused on simplicity and a robust algorithm especially for the three-dimensional case. It combines characteristics of both Front Tracking and Level Set methods. While retaining an explicitly tracked interface using interfacial elements, the calculation of a vector distance function plays a crucial role in the periodic reconstruction of the interface elements in the LCRM method to maintain excellent mass conservation and interface fidelity. In addition, compact curvature formulation is incorporated for the calculation of the surface tension force thereby reducing parasitic currents to a negligible level.

A volume capturing method using unstructured grid system for numerical analysis of multiphase flows is introduced in the present paper. This method uses an interface capturing method (CICSAM) in a volume of fluid(VOF) scheme for phase interface capturing. The novelty of CICSAM lies in the adaptive combination of high resolution discretization scheme which ensures the preservation of the sharpness and shape of the interface while retaining boundedness of the field, and no explicit interface reconstruction which is perceived to be difficult to implement on unstructured grid system. Several typical test cases for multiphase flows are presented, which are simulated by an in-house solution code(PowerCFD). This code employs an unstructured cell-centered method based on a conservative pressure-based finite-volume method with CICSAM. It is found that the present method simulates efficiently and accurately complex free surface flows such as multiphase flows.

The numerical program has been developed for the purpose of the complicate geometries application using CIP method. The non-staggered, non-orthogonal, and unstructured grid system can be also used for the various geometries in the program. For validating CIP solver, the lid-driven cavity flow and solitary wave propagation flow are carried out. Test results show a good agreement with the verified results. The dynamic solver was used for the behavior of moving body. Interface process between the two solvers is introduced. The research was performed on the flow problem around torpedo and log and the flow problem in a tank in order to analyze the three phase flow problem Although the comparison to the verified results was not quantitatively performed, the trend of the results was reasonable.

A level-set (LS) method is presented for computation of boiling phenomena which involve liquid-vapor interfaces that evolve, merge and break up in time, the flow and temperature fields influenced by the interfacial motion, and the microlayer that forms between the solid and the vapor phase near the wall. The LS formulation for tracking the phase interfaces is modified to include the effects of phase change on the liquid-vapor interface and contact angle on the liquid-vapor-solid interline. The LS method can calculate an interface curvature accurately by using a smooth distance function. Also, it is straightforward to implement for two-phase flows in complex geometries. The numerical method is applied for analysis of nucleate boiling on a horizontal surface and film boiling on a horizontal cylinder.

In the present study, a least square weighted residual method and Taylor-Galerkin method were formulated and tested for the discretization of the two hyperbolic type equations of level set method; advection and reinitialization equations. The two approaches were compared by solving a time reversed vortex flow and three-dimensional broken dam flow by employing a four-step splitting finite element method for the solution of the incompressible Navier-Stokes equations. From the numerical experiments, it was shown that the least square method is more accurate and conservative than Taylor-Galerkin method and both methods are approximately first order accurate when both advection and reinitialization phase are involved in the evolution of free surface.

The moment-of-fluid (MOF) method is a new volume-tracking method that accurately treats evolving material interfaces. Based on the moment data (volume and centroid) for each material, the material interfaces are reconstructed with second-order spatial accuracy in a strictly conservative manner. The MOF method is coupled with a stabilized finite element incompressible Navier-Stokes solver for two fluids, namely water and air. The effectiveness of the MOF method is demonstrated with a free-surface dam-break problem.