Constrained Interpolation Profile Method Research Articles

Consideration of Treatment of the Boundary Between Different Media in Electromagnetic Field Analysis Using the Constrained Interpolation Profile Method

The treatment of a boundary between different media to simulate an electromagnetic (EM) field is examined using the constrained interpolation profile (CIP) method. Consideration of the way of handling spatial derivatives of fields is very important for CIP-EM field analysis. We demonstrate a method of handling this boundary and report results of CIP-EM field analysis using the present approach

Analysis of an Electromagnetic Field Created by Line Current Using Constrained Interpolation Profile Method

Development of accurate schemes is a technical issue related to calculation of electromagnetic fields. This study uses constrained interpolation profile (CIP) method to analyze electromagnetic fields created by line current. This is a novel method proposed by Yabe. Comparison of results obtained using finite difference time domain (FDTD) analysis and CIP analysis indicates that CIP analysis provides higher accuracy using identical discretization. In addition, given the same level of accuracy, CIP analysis requires less memory and less calculation time

Numerical study on the improvement of resistance performance for fast-ferry with transom appendage

In recent, stern wedges and stern flaps are installed for the improvement of propulsion and resistance performance of fast-ferry. For example, U.S. Navy has achieved the development of stern wedges and stern flaps for destroyer to enhance powering performance. It is generally known that stern wave systems as well as bow wave systems play an important role in the wave making resistance performance for fast-ferry. The bow diverging wave system has been usually simulated by an interface tracking method (ITM). However, it is difficult to apply the ITM to the numerical simulation of the stern wave and spray phenomenon because of over-turning wave and wave-breaking. Therefore, to solve this problem an interface capturing method (ICM) is introduced. In the present study, a numerical method with the ICM is developed to evaluate the resistance performance of fast-ferry. Incompressible Navier-Stokes and continuity equations are employed in the present study and the equations are discretized by Finite Difference Method in the general curvilinear coordinate system. CIP (Constrained Interpolated Profile) method is used for the discretization of convection terms, respectively. The free surface location is determined by level set method. In order to validate the numerical method, numerical simulations for Wigley hull are performed and their results are compared with experimental results. Several numerical simulations of ship waves for fast-ferry are performed to find advantages of appendage installation. Through those simulations, the computed results, such as wave profile and resistance coefficient, are compared with the measured results which are achieved from Samsung Ship Model Basin (SSMB). The effects of transom appendage on the resistance performance are discussed with the computed results in this study.

Visualization of electromagnetic waves emitted from partial discharge using the constrained interpolation profile (CIP) method

AbstractThe constrained interpolation profile method (CIP) is used in order to visualize the electromagnetic (EM) waves emitted from partial discharge (PD) for understanding the physical mechanisms. In this paper, the PD current is numerically obtained by the total amount of charge and the rise time. Numerical results show that the CIP is useful for visualizing the generation and the propagation of the EM waves emitted form the PD current. Copyright © 2007 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.

Water Entry and Exit of a Horizontal Circular Cylinder

In this paper we describe the fully nonlinear free-surface deformations of initially calm water caused by the water entry and water exit of a horizontal circular cylinder with both forced and free vertical motions. Two-dimensional flow conditions are assumed in the study. This has relevance for marine operations as well as for the ability to predict large amplitude motions of floating sea structures. A new numerical method called the CIP (Constrained Interpolation Profile) method is used to solve the problem. In this paper, the circular cylinder and free surface interaction is treated as a multiphase problem, which has liquid (water), gas (air), and solid (circular cylinder) phases. The flow is represented by one set of governing equations, which are solved numerically on a nonuniform, staggered Cartesian grid by a finite difference method. The free surface as well as the body boundary is immersed in the computational domain. The numerical results of the water entry and exit force, the free surface deformation and the vertical motion of the cylinder are compared with experimental results, and favorable agreement is obtained.

Development of magnetohydrodynamic simulation code using the constrained interpolation profile method

A three-dimensional masnetohydrodynamic (MHD) simulation code has been newly developed. In this code, the physical variables are defined in the staggered mesh system and each of the MHD equations is split into the advection phase and the non-advection phase. The constrained interpolation profile method, which gives a highly accurate solution with less numerical diffusion, is applied to the calculation for the advection phase. In contrast, the non-advection phase is calculated using the finite difference method. The developed code is tested for the relaxation processes of the mass density, plasma pressure and magnetic field in the Large Helical Device (LHD).

Implementation of the Perfect Matched Layer to the CIP Method

The perfect matched layer (PML) is formulated for the use in the constrained interpolation profile (CIP) method. Numerical results are presented to examine the performance of the proposed formulation of the PML in the case of two-dimensional TM wave. The results show that the proposed methods suppress the reflection effectively in comparison with the natural absorbing boundary condition of the CIP method. We have two methods to formulate the PML, and it is shown that the both methods have equal characteristics.

Application of CIP Method for Strongly Nonlinear Marine Hydrodynamics

A CFD approach based on the CIP (Constrained Interpolation Profile) method has been developed for predicting strongly nonlinear marine hydrodynamics. The numerical model uses a Cartesian grid for numerical solution and applies the CIP method for the flow solver and the free-surface interface capturing. An efficient interface capturing method by using a conservative CIP scheme is applied to two-dimensional sloshing. For strongly nonlinear wave-body interactions, a Cartesian grid method, in which the body surface is approximated by distributing virtual particles on it, treats the boundary condition at the body surface. A three-dimensional numerical simulation on a ship moving in large waves is presented.

Analysis of Absorbing Characteristics of One-Layer EM-Absorber Using CIP Method

In this paper, Constrained Interpolation Profile (CIP) method is applied to Maxwell's equation including complex permittivity and permeability and the validity of CIP method applied to the equation is confirmed compared with the FDTD method. And the dependency on CFL (Courant-Friedrich-Lewy) condition, cell size and estimates of ∂e ∂x, ∂μ ∂x and ∂σ ∂x of the absorbing characteristics of one-layer EM-absorber are calculated using CIP method and compared with that by FDTD method. As a result, it is confirmed that the characteristics obtained by CIP method is different from that by FDTD method.

Analytical study of rectangle wave propagation in electromangetic field using FDTD, CIP, and R-CIP methods

In this article, constrained interpolation profile (CIP) and rational function-interpolation profile (R-CIP) methods are applied to electromagnetic field analysis for the fundamental examination. The dependency of Courant Friedrichs Lewy (CFL) condition is examined using FDTD, CIP, and R-CIP method when a rectangle wave propagates. As a result, it is confirmed that the computational values by three methods agree well with that of theoretical one when CFL condition is equal to 1, however, the computational value is oscillated in FDTD method and that is diffused in CIP and R-CIP methods when CFL condition is less than 1; and the calculated results using FDTD, CIP, and R-CIP methods in rectangle wave propagation is confirmed. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 1940–1943, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21819

Numerical study on characteristics of ship wave according to shape of waterway section

The ship wave phenomena in the restricted waterway were investigated by a numerical analysis. The Euler and continuity equations were employed for the present study. The boundary fitted and moving grid system was adopted to enhance the computational efficiency. The convective terms in the governing equations and the kinematic free surface boundary condition were solved by the Constrained Interpolated Profile (CIP) algorithm in order to solve accurately wave heights in far field as well as near field. The advantage of the CIP method was verified by the comparison of the computed results by the CIP and the Maker and Cell (MAC) method. The free surface flow simulation around Wigley hull was performed and compared with the experiment for the sake of the validation of the numerical method. The present numerical scheme was applied to the free surface simulation for various canal sections in order to understand the effect of the sectional shape of waterways on the ship waves. The wave heights on the side wall and the shape of the wave patterns with their characteristics of flow are discussed.

Numerical study on breaking phenomena of ships? waves in narrow and shallow waterways

The environmental impact of a ship’s waves, such as the risk of erosion of coasts and riverbanks, and unacceptable ship movements in a restricted waterway, is now a significant ship design criterion. Therefore, it is necessary to predict ship-wave phenomena accurately in a restricted waterway. In this study, a numerical investigation of the breaking phenomena of a ship’s waves in restricted waterways was carried out. Incompressible Navier–Stokes and continuity equations were employed. The equations are discretized by a finite-difference method in a curvilinear coordinate system. The interface capturing method was applied to simulation of a ship’s waves, including wave-breaking. A modification of the level-set method is proposed to find the free surface shape clearly and without difficulty of the implemation of the boundary conditions for the distance function. In order to obtain a high resolution of wave height, a constrained interpolated profile (CIP) algorithm is adopted. In order to check the advantage of the CIP method, computations by two numerical methods, the CIP and the 3rd-order up-wind scheme, were compared. The computations for a Wigley hull in restricted waterways were performed and compared with experiments. The phenomena of ships’ waves in restricted waterways are discussed in order to understand the mechanism of wave-breaking in relation to the change in water depth along a waterway.

A New Paradigm of Computer Graphics by Universal Solver for Solid, Liquid and Gas

We propose a new algorithm for producing computer graphics of melting and evaporation process of matter. Such a computation becomes possible by a universal solver for solid, liquid and gas based on the CIP (Cubic-Interpolated Propagation / Constrained Interpolation Profile) method proposed by one of the authors. This method can also be applied to the movement, deformation and even break up of solid, liquid and gas in one simple algorithm. Therefore seamless computation of all the phases of matter becomes possible. This enables us to reproduce natural phenomena in some instances by computation. In order to demonstrate this reality, we show how precisely the computational result replicates the movies of real phenomena. The flattering motions of metal disk in water and thin name card in air are treated showing accuracy of force calculation on the surface of sub-grid scale. Although the CIP uses semi-Lagrangian form algorithm, the exact mass conservation is guaranteed by additional tool. By using this scheme, separation of a bubble in bifurcation tube and splashing of water surface are successfully simulated.

Accurate basis set by the CIP method for the solutions of the Schrödinger equation

In this paper, we propose a basis set approach by the Constrained Interpolation Profile (CIP) method for the calculation of bound and continuum wave functions of the Schrödinger equation. This method uses a simple polynomial basis set that is easily extendable to any desired higher-order accuracy. The interpolating profile is chosen so that the subgrid scale solution approaches the local real solution by the constraints from the spatial derivative of the original equation. Thus the solution even on the subgrid scale becomes consistent with the master equation. By increasing the order of the polynomial, this solution quickly converges. The method is tested on the one-dimensional Schrödinger equation and is proven to give solutions a few orders of magnitude higher in accuracy than conventional methods for the lower-lying eigenstates. The method is straightforwardly applicable to various types of partial differential equations.

A note on the basis set approach in the constrained interpolation profile method

We propose a simple polynomial basis set that is easily extendable to any desired higher-order accuracy. This method is based on the Constrained Interpolation Profile (CIP) method and the profile is chosen so that the subgrid scale solution approaches the real solution by the constraints from the spatial derivative of the original equation. By adopting the higher-order derivatives of the master equations as constraints to generate a self-consistent subgrid profile, this solution quickly converges. 3rd and 5th order polynomials are tested on the one-dimensional Schrödinger equation and are proved to give solutions a few orders of magnitude higher in accuracy than conventional methods for lower-lying eigenstates.

328 CIP 法の基底関数

We propose a simple polynomial basis-set that is easily extendable to any desired higher-order accuracy. This method, i. e. the CIP-BS method, is based on the Constrained Interpolation Profile (CIP) method and the profile is chosen so that the subgrid scale solution approaches the real solution with the constraints from the spatial derivative of the original equation. Thus the solution even on the subgrid scale becomes consistent with the master equation. By increasing the order of the polynomial, this solution quickly converges. The governing equation is transformed into the discretized form by taking scalar products with each basis function.

New numerical method for the solutions of the MCDF equations based on the CIP method

Abstract A new numerical method based on the constrained interpolation profile (CIP) method to solve the Multiconfiguration Dirac–Fock (MCDF) equations is presented. The radial wave functions are represented by the values and the spatial derivatives on an arbitrary grid system, and approximated by cubic polynomials. Owing to this representation, the values and the spatial derivatives of the effective charge distribution and inhomogeneous term are calculated using the previous cycle's wave functions. Then the homogeneous MCDF equations are integrated to obtain two linearly independent solutions, which are used to construct the Green function, by the adaptive stepsize controlled Runge–Kutta method controlling the truncation errors within a prescribed accuracy. The radial wave function is improved by taking the convolution of the Green function and the inhomogeneous term. The effectiveness of this numerical procedure is investigated after implementing it into the relativistic atomic structure code GRASP92.

Accurate numerical method for the solutions of the Schrödinger equation and the radial integrals based on the CIP method

A new accurate numerical method based on the constrained interpolation profile (CIP) method to solve the Schrödinger wave equation for bound and free states in central fields and to calculate radial integrals is presented. The radial wave equation is integrated on an arbitrary grid system by the adaptive stepsize controlled Runge–Kutta method controlling the truncation errors within a prescribed accuracy. For the continuum orbitals in the highly oscillating region, the non-linear radial wave equation in the phase-amplitude representation is used. In the evaluation of the derivatives of the radial wave function, the potential energy is approximated by the CIP method. In addition, the radial integrals encountered in the computation of various atomic process are accomplished with the CIP method using the values and their analytical derivatives at the grids. This numerical procedure can be extended in a straightforward way to solve the Dirac wave equation.

452 CIP 法によるシュレディンガー、ディラック方程式の数値解法

A new accurate numerical method based on the constrained interpolation profile (CIP) method to solve the Schrodinger and Dirac radial wave equation for the bound and free states in central fields and to calculate the radial integrals is presented. The radial integrals encountered in the computation of the various atomic processes are accomplished with the CIP method using the values and their analytical derivatives at the grids.

The Constrained Interpolation Profile Method for Multiphase Analysis

We present a review of the constrained interpolation profile (CIP) method that is known as a general numerical solver for solid, liquid, gas, and plasmas. This method is a kind of semi-Lagrangian scheme and has been extended to treat incompressible flow in the framework of compressible fluid. Since it uses primitive Euler representation, it is suitable for multiphase analysis. The recent version of this method guarantees the exact mass conservation even in the framework of a semi-Lagrangian scheme. We provide a comprehensive review of the strategy of the CIP method, which has a compact support and subcell resolution, including a front-capturing algorithm with functional transformation, a pressure-based algorithm, and other miscellaneous physics such as the elastic–plastic effect and surface tension. Some practical applications are also reviewed, such as milk crown or coronet, laser-induced melting, and turbulent mixing layer of liquid–gas interface.