Cubic Interpolated Pseudo-particle Method Research Articles

Prediction of thermal distribution and fluid flow in the domain with multi-solid structures using Cubic-Interpolated Pseudo-Particle model.

A nanofluid is a suspension of very small solid particles in a continuous fluid with significant improvement of heat transfer characteristics in the main liquid. In general, in industrial equipment, the heat transfer rate can be improved with optimization of equipment including the domain structure and using the different types of nanofluids. Still, there is a big challenge to analyze the heat transfer and fluid circulation in the domain. Having nanofluids with experimental observation as using sensors and probes are destructive for the liquid stream and they are costly to observe the details of particles and the original fluid. Over the 20 years, different numerical methods have been implemented in the modeling of the heat and fluid distribution in industrial equipment containing nanofluids. Among all mathematical and numerical methods, Cubic-Interpolated Pseudo-Particle (CIP) model provides a strong potential in the prediction of the fluid structure and heat analysis, when there is a complex structure of thermal walls and high concentration of nanoparticles. However, this method is not frequently used by researchers in nanofluids analysis. In this study, the Cubic-Interpolated Pseudo-Particle model is applied to predict the flow in the square domain. different thermal walls (multi-solid structure) and hot cylindrical wall are specifically used to observe the fluid flow and heat distribution in the domain. Additionally, for a better understanding of the flow in the domain, different numbers of cylinders are used and also different amounts of nanofluid in the continuous fluid are added. The results show that adding more walls in the domain causes the change in the vortex structure. Furthermore, using nanofluid results in better heat transfer rate in the system. The CIP method is also a capable tool to predict the heat and fluid flow in the multi-solid structure domain.

Numerical Analysis Of Braided Rivers and Alluvial Fan Deltas

Understanding the processes of morphological behavior in braided rivers and alluvial fan deltas is very important for river engineering purposes to manage hydraulic structures and prevent disasters from flood, and environmental purposes to maintain river ecosystem. A two-dimensional numerical model was developed to simulate braided rivers and alluvial fan deltas with erodible bed and banks. A moving boundary-fitted coordinate system was employed to calculate water flow, bed change, and bank erosion. CIP (Cubic Interpolated Pseudo-particle) method was used to calculate flow, which introduced little numerical diffusion. Sediment transport equation in the streamline and transverse wise, considering the secondary flow, was used to estimate bed and bank evolution in time. Bank erosion was simulated by following the procedure proposed by Shimizu (2002). Braided river in laboratory was reproduced for verifying the numerical model in the channel filled with nearly uniform sandy materials. Comparison of numerical results and experimental data has shown relatively good agreements. The evolution processes of the alluvial fan deltas were investigated numerically by controlling the sediment inflow, and the model reproduced the features of alluvial fan deltas, i.e., the successive aggradation, avulsion and then migration of a river.

Numerical simulation for braided rivers with erodible banks

Understanding the process and mechanism of morphological behavior in braided rivers is very important for river engineering purposes to manage hydraulic structures and prevent disaster from flood, and environmental purposes to maintain river ecosystem and landscape. A two-dimensional numerical model was developed to simulate braided rivers with erodible bed and banks composed of well sorted-sandy materials. A moving boundary-fitted coordinate system was employed to calculate water flow, bed change, and bank erosion. CIP (Cubic Interpolated Pseudo-particle) method was used to calculate flow, which introduced little numerical diffusion. Sediment transport equation in the streamline and transverse wise, considering the secondary flow, was used to estim ate bed and bank evolution in time. Bank erosion was simulated when the gradient in the cross-sectional direction of the banks was steeper than the submerged angle of repose because of the bed erosion in the vicinity of banks. Braided river in laboratory was reproduced for verifying the numerical model in the channel filled with nearly uniform sandy materials. Comparison of numerical results and experimental data has shown relatively good agreements.

Implementation of the CIP as the Advection Solver in the MM5

Abstract A semi-Lagrangian-type advection scheme, cubic-interpolated pseudoparticle (CIP) method is implemented to the fifth-generation Pennsylvania State University–NCAR Mesoscale Model (MM5, version 3.4). A dimensional splitting CIP algorithm, with spatial third-order and temporal second-order accuracy, is derived to compute the advection in the MM5. The modified model is evaluated with ideal tests and real case studies in comparing with the leapfrog scheme, which was originally employed in the MM5. The CIP method appears remarkably superior to the leapfrog scheme in respect to both dissipative and dispersive errors, especially when discontinuities or large gradients exist in the advected quantity. Two real cases of severe mesoscale phenomena were simulated by using both the CIP scheme and the leapfrog scheme. In the advection dominant regions, the CIP shows remarkable advantages in capturing the detail structures of the predicted field. As computations with high resolution become more and more popular ...

Liquefaction induced lateral spread analysis using the CIP method

Abstract This paper presents a CIP (cubic interpolated pseudoparticle) based numerical method for liquefaction induced lateral spread analysis in the framework of fluid dynamics. Previously, the authors presented similar methods using a SIMPLE-VOF based commercial code but were not able to extend such a code to simulate lateral spread of liquefied ground with an overlaying non-liquefied layer, which is the most common and more practical post liquefaction problem. In this study, the CIP method is used because it is able to treat solid, liquid and gas together, can correctly define the flow behavior at interfaces of multi-fluids and can also be used as a unified scheme for both compressible and incompressible materials. A Bingham model that takes the undrained strength of soils into account is used as the basic constitutive model. A CIP based numerical scheme, which has been successfully used in fluid dynamics problems, is modified by incorporating the Bingham viscosity and an implicit calculation procedure for pressure terms. The Poisson equation is used to compute the pressure over the whole domain. The current numerical method is validated and good agreement is produced in comparison with experimental results. A previously verified similitude for liquefied ground flow is also reproduced by this method. The method is, finally, used to simulate shaking table tests on a liquefied subsoil model with an overlaying non-liquefied layer. From the results of simulations, the numerical method is found to satisfactorily reproduce the time histories of ground surface velocity and displacement and depth distribution of displacement.

Verification of GSMAC-CIP Method by the Unsteady Separated Flows around a Impulsive Started Circular Cylinder.

We have extended the CIP (Cubic Interpolated Pseudo-particle) method to the FEM (Finite-Element method) in our previous works. The previous verifcations of GSMAC-CIP scheme were, however, done by using the orthogonal meshes and we don't make use of the characteristic of the FEM. In the present work, GSMAC-CIP scheme is applied to the flow around a circuler cylinder and employs arbirary meshes. That flow is a famous problem which has been studied by many investigators. Therefore, good numerical and experimental data, for example the experimental data obtained by Bouard and Coutanceu, are available easily. The Reynolds numbers are Re=550, 3 000 and 9 500. The numerical results are compared with the experimental data obtained by Bouard and Coutanceu, and the effetiveness of the present scheme is shown. Moreover, we point out the mistakes of their experimental data for the velocity profile on the center axis behind a cylinder at Re=9 500.

Verification of CIP Finite-Element Method by 2D-Advection Diffusion Equations.

The conventional shape function for the finite-element method (FEM) is a linear one, which is inadequate for analyzing numerically complex flows for high Reynolds numbers. In the present study, we suppose CIP-FEM scheme using 3rd order shape function which requires continuity of the value of the function and its first space derivative in whole space and is formulated a finite element method for the cubic interpolated pseudo-particle (CIP) method which was developed in the field of finite difference method. The CIP method is used to analyze Advection equations with high accuracy. We verify the effectiveness of this new scheme by 1-D and 2D-Advection Diffusion equations which have the exact solution. The numerical results of these problems are good agreement with each of exact one we could confirm the effectiveness of CIP-FEM scheme.

Finite-Element Method for CIP Method. Verification of Three-D Advection Equation.

The conventional shape function for the finite-element method (FEM) is a linear one, which is inadequate for analyzing numerically complex flows at high Reynolds numbers. In the present study, we aim to formulate a finite element method for the cubic interpolated pseudo-particle (CIP) method which was developed in the field of finite difference method. The CIP method is used to analyze advection equations with high accuracy. We modify this CIP method and discretize it with FEM. We propose third order shape functions which require continuity of the value of the function and its first space derivative in whole space. The shape function is written as a product of the conventional linear shape function and new second order shape function. Using this new shape function, we analyze some rotating problems in 3D which are a good example of the use of advection equation.

Constructing oscillation preventing scheme for advection equation by rational function

A numerical scheme for solving advection equations is presented. The scheme is derived from a rational interpolation function. Some properties of the scheme with respect to convex-concave preserving and monotone preserving are discussed. We find that the scheme is attractive in suppressing overshoots and undershoots even in the vicinities of discontinuity. The scheme can also be easily switched as the CIP (Cubic interpolated Pseudo-Particle) method to get a third-order accuracy in smooth region. Numbers of numerical tests are carried out to show the non-oscillatory and less diffusive nature of the scheme.

The compact CIP (cubic-interpolated pseudo-particle) method as a general hyperbolic solver

Abstract A new universal solver is proposed for general hyperbolic equations; multi-dimensional, linear and nonlinear equations with dissipative and dispersive terms. The scheme uses piecewise cubic polynomial interpolation inside meshes. The physical quantity and its spatial derivative are advanced in time according to the given equation. The scheme not only describes a sharp discontinuity with only one mesh but also reproduces the traveling wave train in the dispersive media. The extension to higher dimensions is straightforward.