Constrained Interpolation Profile Method Research Articles

Numerical Simulation of Water Entry of Wedges Based on the CIP Method

The hydrodynamic problems for water entry of wedges are studied by a constrained interpolation profile (CIP) based on Cartesian grid method. The CIP scheme was applied to the Cartesian grid based on flow solver, which was first described. The tangent of hyperbola for interface capturing (THINC) scheme was applied to capture the free surface. The CIP method was extended to capture the dynamics in the water entry approach. The simulations were performed in three aspects. First, pressure distributions for the wedges entering into water with constant speed were predicted, and the results were compared with the similarity solutions by the boundary element method (BEM). Then simulations were conducted for the free-falling wedges entering into water with one degree of freedom. The results were compared with the published experimental data. Finally, the impact of a wedge on the water surface in a free fall motion with an initial heel angle was studied. The motion of the wedge was subjected to three degrees of freedom, and the results were also compared with those of experiments.

Numerical Simulation of Wave Interaction with Coastal Structures using a CIP-based Method

Numerical simulation of nonlinear interactions between water wave and coastal structures is performed using a high-order difference method. In the model, a multiphase flow model based on the Navier-Stokes equations using a constrained interpolation profile (CIP) method for the flow solver is used to estimate wave-structure interactions. A more accurate interface capturing scheme, the VOF/WLIC scheme (WLIC: weighed line interface calculation), is adopted as the interface capturing method. Water wave interacting with submerged breakwater is computed and compared with available experiments. Main attentions are paid to the wave profile and velocity-pressure domain. Comparisons with experimental date show good agreements. It is demonstrated that the proposed model is capable of reproducing the nonlinear flow phenomena and capture the complex free surface flow accurately.

Computation of Lightning Electromagnetic Pulses With the Constrained Interpolation Profile Method in the 2-D Cylindrical Coordinate System

In this paper, a procedure for computing transient electromagnetic fields with the constrained interpolation profile (CIP) method in the two-dimensional (2-D) cylindrical coordinate system has been derived. Then, it has been applied to analyzing electromagnetic pulses produced by a current wave propagating upward along a vertical lightning return-stroke channel. CIP-computed waveforms agree well with corresponding waveforms computed using analytical expression of Uman et al. or the finite-difference time-domain method.

Removal of Contaminant Effectiveness in Cavity Channel Flow with Different Heated Wall Position

Numerical simulation on removal of contaminated cavity in channel was done for various Richardson number and at three different heated wall inside square cavity. Constrained interpolated profile method (CIP) was used to solve advection part of Navier-Stokes equation while non-advection part was solved by using finite central difference. The contaminant has same properties as the fluid and very small so that the particle can be treated without affected the fluid flow. Simulations shows that heated right wall produced the highest removal process and heated left wall will removed the fewest of contaminant from cavity.

A Compact-Type CIP Method for General Korteweg-de Vries Equation

We proposed a hybrid compact-CIP scheme to solve the Korteweg-de Vries equation. The algorithm is based on classical constrained interpolation profile (CIP) method, which is coupled with high-order compact scheme for the third derivatives in Korteweg-de Vries equation. Several numerical examples are presented to confirm the high resolution of the proposed scheme.

Application of Constrained Interpolation Profile Method to Solve the Richards Equation

1 Student member of JSCE, Ph.D. Student, Dept. of Civil and Environmental Engineering, Nagaoka University of Technology (1603-1, Kamitomioka, Nagaoka, Niigata 940-2188, Japan) 2 Member of JSCE, Dr. Eng., Professor, Dept. of Civil and Environmental Engineering, Nagaoka University of Technology (1603-1, Kamitomioka, Nagaoka, Niigata 940-2188, Japan) 3 Member of JSCE, Dr. Eng., Adjunct Professor, Chongqing Jiaotong University, Chongqing, China

A new adaptive Cartesian-grid CIP method for computation of violent free-surface flows

A new adaptive Cartesian-grid for the CIP (constrained interpolation profile) method is proposed and applied to two-dimensional numerical simulations of violent free-surface flows. The CCUP (CIP combined and unified procedure) method is employed and combined with this adaptive Cartesian-grid for robust and efficient computation. This adaptive grid is capable of tracking regions where flows vary violently, and a much finer grid is then concentrated automatically on these regions to adapt to the violent changing of the flow. Unlike the abacus-like Soroban grid which is an adaptive meshless grid with complicated algorithms and inefficiency of evaluation of frequently computed spatial derivatives, the present approach not only simplifies computational algorithm but also enhances efficiency of frequently-computed spatial derivatives. It is also different from most of the remeshing schemes that no additional CPU-time for the value-mapping from the old grid to the new grid is taken in this adaptive grid system provided that the advection velocity is interpolated, since the value-mapping process is accomplished simultaneously within the advection process. To validate the accuracy and efficiency of this newly-proposed CFD model, several two-dimensional benchmark problems are performed, and the results are compared with experimental measurements and other published numerical results. Numerical simulations show that the proposed numerical model is robust, accurate, and efficient for strongly nonlinear free-surface flows.

A new capillary force model implemented in micro-scale CFD–DEM coupling for wet granulation

A DNS (Direct Numerical Simulation) model for solid, liquid, and gas three-phase flow, mainly targeting to simulate the nucleation processes in wet granulation, is presented in this paper. A liquid–gas two-phase flow is solved by using the CIP (Constrained Interpolation Profile) method, which is one of the CFD multi-phase solvers, and a solid particle flow is solved by DEM (Discrete Element Method) separately. The interaction between fluid (liquid and gas) and solid phases is taken into account by coupling CFD and DEM. A new model is developed to account for the capillary force exerted on particles, i.e. the surface tension force which pulls a particle along with the solid–liquid–gas contact line, and the accuracy of the model is examined. Although the main focus in this study is to develop a CFD–DEM coupling and the capillary force models for wet granulation, some simulation results are also presented to see the droplet behaviour often encountered in a wet granulation process, i.e. the droplet penetration into a static particle bed as well as the droplet impingement onto a dynamic particle bed. The simulation results are compared with the experimental results in the literature and it shows a good agreement in terms of tendency.

Application of the Type-C Constrained Interpolation Profile Method to Lightning Electromagnetic Field Analyses

The type-C constrained interpolation profile (CIP) method has been applied to analyzing lightning electromagnetic fields. The CIP method is one of the finite-difference methods. Differently from the finite-difference time-domain (FDTD) method, however, it considers not only electric- and magnetic-field values at each discretized points in a working space but also their spatial-derivative values there. Therefore, in principle, it can compute fields accurately even when a relatively coarse grid and a relatively large time increment are used. In section 2 of this paper, a numerical procedure for computing electromagnetic fields in a three-dimensional space using the CIP method is presented. In section 3, the type-C CIP method is applied to computing electric fields in a uniform grid, which are generated by a lightning return-stroke current wave propagating upward along a vertical straight channel located on flat perfectly conducting ground, and the CIP-computed waveforms are compared with the corresponding waveforms computed theoretically and using the FDTD method. In section 4, the method is applied to computing lightning electric fields in a nonuniform grid, and a similar comparison is made.

Formulation and examination of the perfectly matched layer for sound field analyses using the constrained interpolation profile method

Formulation and examination of the perfectly matched layer for sound field analyses using the constrained interpolation profile method

Numerical Solution of 3-D Water Entry Problems With a Constrained Interpolation Profile Method

This paper presents the numerical solutions of slamming problems for 3D bodies entering calm water with vertical and oblique velocities. The highly nonlinear water entry problems are governed by the Navier-Stokes equations and were solved by a constrained interpolation profile (CIP)-based finite difference method on a fixed Cartesian grid. In the computation, the 3D CIP method was employed for the advection calculations and a pressure-based algorithm was applied for the nonadvection calculations. The solid body and the free surface interfaces were captured by density functions. For the pressure computation, a Poisson-type equation was solved at each time step by using the conjugate gradient iterative method. Validation studies were carried out for a 3D wedge, a cusped body vertically entering calm water, and the oblique entry of a sphere into calm water. The predicted hydrodynamic forces on the wedge, the cusped body, and the sphere were compared with experimental data.

Performance Comparison of Subgrid Techniques in Acoustic Simulation Using the Type-M and Type-C Constrained Interpolation Profile Methods

The constrained interpolation profile (CIP) method, a type of method of characteristics (MOC), is a novel low-dispersive numerical scheme. In an earlier study, we applied the CIP method to quantitative analyses of sound wave propagation. However, a new grid system is important for the CIP simulation of complicated heterogeneous media or large-scale simulations of wave propagation. In this study, we examined a subgrid technique for use with acoustic wave simulation using the type-M and type-C CIP methods. The results indicate that this technique for the CIP methods has advantages of small memory requirements and faster calculation.

Performance Comparison of Subgrid Techniques in Acoustic Simulation Using the Type-M and Type-C Constrained Interpolation Profile Methods

The constrained interpolation profile (CIP) method, a type of method of characteristics (MOC), is a novel low-dispersive numerical scheme. In an earlier study, we applied the CIP method to quantitative analyses of sound wave propagation. However, a new grid system is important for the CIP simulation of complicated heterogeneous media or large-scale simulations of wave propagation. In this study, we examined a subgrid technique for use with acoustic wave simulation using the type-M and type-C CIP methods. The results indicate that this technique for the CIP methods has advantages of small memory requirements and faster calculation.

Build-up processes of an optical cavity enclosing an absorbent thin film: computational study by the CIP method

Propagation of monochromatic light is analyzed by numerical calculations for an optical cavity enclosing a thin absorbent film. The computational study is performed by the CIP (constrained interpolation profile) method, which is shown to be able to solve temporal evolution of Maxwell’s equations even in a strongly absorbing medium. Simulations on build-up processes reveal that such a cavity exhibits transmittance even higher than the intrinsic transmissivity of the absorbent, i.e., the absorbent is virtually transparent, when the following requirements are satisfied: the film is much thinner than the wavelength, it is located at a node of a standing wave, and the cavity consists of a pair of mirrors with optimal reflectivity depending on the film thickness. Optimal conditions are discussed as well for maximizing absorption in the film.

Application of the constrained interpolation profile method to room acoustic problems: Examination of boundary modeling and spatial/time discretization

The constrained interpolation profile (CIP) method is proposed in the field of computational fluid dynamics, because this method is less influenced by numerical dispersions and is stable with an arbitrary time step. In this paper, the CIP method is applied to room acoustic problems, in which boundary modeling and spatial/time discretization are specifically examined. First, frequency-independent and frequency-dependent boundary conditions are introduced and validated with an acoustic tube problem. Second, in one-dimensional and three-dimensional closed sound fields, this paper shows that errors in waveforms and reverberation times using the CIP method are smaller than those using the finite difference time domain method even if the steps for time and space are larger. Third, to deal with complicated shapes, the cubic interpolation with volume/area coordinates (CIVA) method using arbitrary triangular elements is introduced; in two-dimensional sound fields, calculation of the CIVA method is stable even if the quality of triangular elements is low.

Variable-grid technique for sound field analysis using the constrained interpolation profile method

Variable-grid technique for sound field analysis using the constrained interpolation profile method

ダイレイタンシーを考慮したCIP法による砂層における断層関連撓曲の発生シミュレーション

An active fault that develops in a plain is often covered with a weak sand layer. The large-scale fault slip in a bedrock may spread to the surface and will frequently generate a fault rupture. Depending on the case, the fault slip occasionally appears on the surface as a fault flexure. This study identifies the reason for the formation of a fault flexure on the sand layer using numerical simulation. The simulation technique employs the constrained interpolation profile (CIP) method a new technique that overcomes the flaws such as numerical diffusion in the finite difference method. Furthermore, we study the influence of fault parameters on the configuration of the fault-related flexure. The experimental results indicate that the fault-related flexure is generated when a shear-zone migration occurs in the sand. We ascertain that the velocity of the shear-zone migration is proportional to the velocity of the fault slip. As a result, we conclude that this migration is probably one of causes of fault-related flexure generation at faulting. Therefore, we conclude that the velocity and acceleration of the fault slip affect the configuration of the fault-related flexure.

A conservative local interface sharpening scheme for the constrained interpolation profile method

SUMMARYA conservative local interface sharpening scheme has been developed for the constrained interpolation profile method with the conservative semi‐Lagrangian scheme, because the conservative semi‐Lagrangian scheme does not feature a mechanism to control the interface thickness, thus causing an increase of numerical error with the advance of the time step. The proposed sharpening scheme is based on the conservative level set method proposed by Olsson and Kreiss. However, because their method can cause excessive deformation of the free‐surface in certain circumstances, we propose an improvement of the method by developing a local sharpening technique. Several advection tests are presented to assess the correctness of the advection and the improved interface sharpening scheme. This is followed by the validations of dam‐breaking flow and the rising bubble flows. The mass of the fluid is exactly conserved and the computed terminal velocity of the rising bubble agrees well with the experiments compared with other numerical methods such as the volume of fluid method (VOF), the front tracking method, and the level set method. Copyright © 2011 John Wiley & Sons, Ltd.

Examination of Sub-Grid Technique for Simulation of Sound Wave Propagation Using Constrained Interpolation Profile Method with Method of Characteristics

Examination of Sub-Grid Technique for Simulation of Sound Wave Propagation Using Constrained Interpolation Profile Method with Method of Characteristics

Examination of Sub-Grid Technique for Simulation of Sound Wave Propagation Using Constrained Interpolation Profile Method with Method of Characteristics

The constrained interpolation profile (CIP) method is a novel low-dispersive numerical scheme. It is a kind of method of characteristics (MOC). In our past study, we applied the CIP method to numerical analyses of sound wave propagation. For simulations of complicated heterogeneous media or large-scale simulations of wave propagation, a new grid system is indispensable. In this study, we examined a sub-grid technique for the CIP acoustic wave simulation. It is clarified that this technique has the advantages of its small memory requirements and less calculation time.