Constrained Interpolation Profile Research Articles

Numerical analysis of three-dimensional acoustic field with background flow using constrained interpolation profile method

Our study group is investigating the acoustic simulation with background flow using the constrained interpolation profile (CIP) method. The CIP method is a type of method of characteristics (MOC) used for time domain numerical analysis. In this study, we examine the calculation method considering background flow using the type-C and type-M CIP methods. The type-C CIP method involves the calculation of all advection equations using the cubic Hermite interpolation, whereas the type-M CIP method involves the calculation of advection equations of spatial differential value perpendicular to the propagation direction using linear interpolation. We compare the calculation results with those of other methods and evaluate calculation accuracy, calculation time, and memory cost. Results show that our proposed method maintains high accuracy under various environmental conditions and that the proposed method is superior in terms of calculation time and memory cost.

Numerical study on interaction of a solitary wave with the submerged obstacle

The extremely nonlinear interaction between waves and marine structures is one of most challenging problems in ocean engineering. In this study, the propagation of a solitary wave over a submerged vertical obstacle is investigated by a developed two-dimensional multi-phase viscous model. The constrained interpolation profile (CIP) based on Cartesian grid method is introduced to solve the Navier-Stokes equations, and free surface is captured accurately by the Tangent of Hyperbola for INterface Capturing (THINC) scheme. First, the free surface motions and velocity fields of a solitary wave interacting with a submerged obstacle are simulated. The present calculations fit fairly well with the measurements through whole wave propagation over the submerged obstacle. Second, the corresponding vorticity fields are calculated to illustrate characteristics of vortex generation and evolution. Third, wave forces acting on the submerged obstacle are calculated, and the results agree well with existing computations. Finally, the effectiveness of the submerged obstacle as a targeted breakwater is estimated by evaluating the reflection and transmission coefficients. The presented computations confirm that the CIP-based Cartesian grid method is capable of reproducing strongly nonlinear interaction of a solitary wave with the submerged obstacle and performing predictions of comprehensive flow-field information accurately.

Development of a simulation method for evaluating Marangoni convection with free surface for tungsten divertor

A tungsten (W) divertor has been developed for tokamak-type nuclear fusion reactors, such as ITER. Because the divertor will be repetitively subjected to high heat flux when plasma disruption or edge localized mode occurs, W at the surface of the divertor will be melted and solidified during reactor operation. The surface shape of the W divertor after or during such a heat load strongly influences its lifetime. Thus, evaluating the behavior of W in such conditions is important. An important driving force in molten metal is Marangoni convection due to a difference in surface tension resulting from a temperature gradient at the surface. To clarify the mechanism of Marangoni convection in molten W, a simulation method that can simultaneously treat surface deformation and convection in molten W, including Marangoni convection, is required. We have been developing such a simulation code based on the constrained interpolation profile combined unified procedure method. In this paper, we simulated molten W under a given temperature gradient or heat load and validated the model by simulating the flow in a molten W pool with a temperature gradient. The development process of Marangoni convection in molten W with a free surface was evaluated.

An adaptive multi-moment FVM approach for incompressible flows

In this study, a multi-moment finite volume method (FVM) based on block-structured adaptive Cartesian mesh is proposed for simulating incompressible flows. A conservative interpolation scheme following the idea of the constrained interpolation profile (CIP) method is proposed for the prolongation operation of the newly created mesh. A sharp immersed boundary (IB) method is used to model the immersed rigid body. A moving least squares (MLS) interpolation approach is applied for reconstruction of the velocity field around the solid surface. An efficient method for discretization of Laplacian operators on adaptive meshes is proposed. Numerical simulations on several test cases are carried out for validation of the proposed method. For the case of viscous flow past an impulsively started cylinder (Re=3000,9500), the computed surface vorticity coincides with the result of the body-fitted method. For the case of a fast pitching NACA 0015 airfoil at moderate Reynolds numbers (Re=10000,45000), the predicted drag coefficient (CD) and lift coefficient (CL) agree well with other numerical or experimental results. For 2D and 3D simulations of viscous flow past a pitching plate with prescribed motions (Re=5000,40000), the predicted CD, CL and CM (moment coefficient) are in good agreement with those obtained by other numerical methods.

A Fundamental Study of Supercritical Flow at Sudden Expansion Structure by Using Numerical Model

In the design of hydraulic structures, it is common to deal with the supercritical flow. Abrupt expansion structure represents a type of transition often constructed in manmade hydraulic structure (e.g. chutes in dam structures, sewer or drainage system, an irrigation channel, etc.) to cater the geometry difference. It is important to cater to the design of such transition especially it involves flow with high velocity. The flow features of high-velocity flow at sudden expansion channel are studied. A two-dimensional depth-averaged model (DA model) incorporate with Constrained Interpolation Profile (CIP) scheme is developed to simulate the supercritical flow at the abrupt expansion channel. The numerical model is able to reproduce the flow features of supercritical flow at the abrupt expansion structure. The simulated results are compared with the analytical solution with a different degree of agreement is observed. The same numerical setup is applied to the model generated by FLOW-3D model. The numerical results from the DA model and FLOW-3D model are compared with previous experimental results. The simulated results from the DA model showed better agreement with the experimental results.

Mathematical Modelling of One-Dimensional Overland Flow on a Porous Surface

Due to rapid urbanization, surface water drainage systems are designed to perform as natural drainage acting as water storage areas that allow infiltration and evaporation and to solve issues caused by traditional drainage system As there is an increase of attention on Sustainable Urban Drainage system (SuDs) to manage storm water, a simple yet efficient numerical model for flow over porous media is needed. The purpose of this research is to develop a numerical model for the simulation of flow over porous media. The model solves the unsteady one-dimensional Saint-Venant equation for the surface flow. The advection term in the momentum equation is solved using the Constrained Interpolation Profile (CIP) scheme which is of the third order accuracy. Averaged infiltration rate is estimated from the physical model experiment. The model is then used to simulate dam-break flow over porous bed and the result is verified against the experiment. The author found that the numerical model performed satisfactorily in terms of surface flow profile and the loss of total fluid volume through infiltration.

Numerical Simulations for Large Deformation of Geomaterials Using Molecular Dynamics

From the microperspective, this paper presents a model based on a new type of noncontinuous theoretical mechanical method, molecular dynamics (MD), to simulate the typical soil granular flow. The Hertzian friction formula and viscous damping force are introduced in the MD governing equations to model the granular flow. To show the validity of the proposed approach, a benchmark problem of 2D viscous material flow is simulated. The calculated final flow runout distance of the viscous material agrees well with the result of constrained interpolated profile (CIP) method as reported in the literature. Numerical modeling of the propagation of the collapse of three‐dimensional axisymmetric sand columns is performed by the application of MD models. Comparison of the MD computational runout distance and the obtained distance by experiment shows a high degree of similarity. This indicates that the proposed MD model can accurately represent the evolution of the granular flow. The model developed may thus find applications in various problems involving dense granular flow and large deformations, such as landslides and debris flow. It provides a means for predicting fluidization characteristics of soil large deformation flow disasters and for identification and design of appropriate protective measures.

Numerical study of dam-break induced tsunami-like bore with a hump of different slopes

Numerical simulation of dam-break wave, as an imitation of tsunami hydraulic bore, with a hump of different slopes is performed in this paper using an in-house code, named a Constrained Interpolation Profile (CIP)-based model. The model is built on a Cartesian grid system with the Navier Stokes equations using a CIP method for the flow solver, and employs an immersed boundary method (IBM) for the treatment of solid body boundary. A more accurate interface capturing scheme, the Tangent of hyperbola for interface capturing/Slope weighting (THINC/SW) scheme, is adopted as the interface capturing method. Then, the CIP-based model is applied to simulate the dam break flow problem in a bumpy channel. Considerable attention is paid to the spilling type reflected bore, the following spilling type wave breaking, free surface profiles and water level variations over time. Computations are compared with available experimental data and other numerical results quantitatively and qualitatively. Further investigation is conducted to analyze the influence of variable slopes on the flow features of the tsunami-like bore.

Computation of Lightning Electromagnetic Pulses Using a Hybrid Constrained Interpolation Profile and Transmission Line Modeling Method

In this paper, a hybrid approach of the constrained interpolation profile (CIP) method and the transmission line modeling (TLM) method has been proposed for analyzing lightning electromagnetic fields and surges in the three-dimensional Cartesian coordinate system. The TLM method is employed locally in the working space for representing thin-wire conductors, and the CIP method is used for computing fields in the rest of the working space. Waveforms of lightning electromagnetic fields and surges computed using the CIP-TLM hybrid method agree well with corresponding ones computed using exact analytical expressions or with the finite-difference time-domain method.

A numerical study of water entry of asymmetric wedges using a CIP-based model

The two-dimensional water entry of wedges with different inclination angles is numerically investigated using a constrained interpolation profile (CIP)-based model, which is developed on the ground of a fixed Cartesian grid and governed by the Navier-Stokes (N-S) equations. A high-order finite difference method is employed as the flow solver, where the CIP method is used to discretize the convective term. The tangent of hyperbola for interface capturing/slope weighting (THINC/SW) is adopted to capture the free surface/interface, and an immersed boundary method is applied to simulate the motion of bodies. The present numerical model involving symmetric water entry is verified in comparison with the previous numerical and experimental results in the literature. The results of the asymmetric water entry are provided in terms of the penetration depth, velocity, pile-up coefficients, impact force of wedges, and velocity and pressure distributions of fluid. Considerable attention is paid into the effects of deadrise and inclination angles. It is found that the presence of the inclination angle significantly influences both the velocity and pressure field, and further regulates the penetration depth, velocity, pile-up coefficients, and impact force on the wedge. Specifically, wedges entering into the water with small deadrise angles are found to be more sensitive to the inclination angle than those with large deadrise angle.

A New Method for Analysing the Pressure Response Delay in a Pneumatic Brake System Caused by the Influence of Transmission Pipes

This study aims to propose an analysis method for resolving the pressure response of a pneumatic brake circuit considering the effect of a transmission pipe. Pneumatic brake systems (PBS) are widely used in commercial vehicles. The pressure response characteristic of the PBS is the key factor affecting braking performance. By using the thermodynamics of a variable-quality system, the pressure response model of the brake chamber is established, which includes the dynamic model of the pipe considering the unsteady friction and heat transfer. The partial-differential control equations of pipe are solved by introducing the constrained interpolation profile (CIP) method, and a virtual chamber model is proposed to set the boundary condition so as to solve the pressure response in the brake chamber simultaneously. Thus, the regularity of the brake pressure response is obtained by considering the influence of the pipe. Lastly, the model is verified experimentally. The present study indicates that the main factors that affect the pressure response delay are the pipe length and the combination forms of the sonic conductances of the orifices inlet and outlet. Furthermore, it helps to verify that the CIP method is an effective way of solving the pressure response of a brake circuit because of its high accuracy. The present study serves as a foundation for the design and analysis of a PBS.

Constrained Interpolation Profile Conservative Semi-Lagrangian Scheme Based on Third-Order Polynomial Functions and Essentially Non-Oscillatory (CIP-CSL3ENO) Scheme

AbstractWe propose a fully conservative and less oscillatory multi-moment scheme for the approximation of hyperbolic conservation laws. The proposed scheme (CIP-CSL3ENO) is based on two CIP-CSL3 schemes and the essentially non-oscillatory (ENO) scheme. In this paper, we also propose an ENO indicator for the multimoment framework, which intentionally selects non-smooth stencil but can efficiently minimize numerical oscillations. The proposed scheme is validated through various benchmark problems and a comparison with an experiment of two droplets collision/separation. The CIP-CSL3ENO scheme shows approximately fourth-order accuracy for smooth solution, and captures discontinuities and smooth solutions simultaneously without numerical oscillations for solutions which include discontinuities. The numerical results of two droplets collision/separation (3D free surface flow simulation) show that the CIP-CSL3ENO scheme can be applied to various types of fluid problems not only compressible flow problems but also incompressible and 3D free surface flow problems.

A numerical study of tsunami wave impact and run-up on coastal cliffs using a CIP-based model

Abstract. There is a general lack of understanding of tsunami wave interaction with complex geographies, especially the process of inundation. Numerical simulations are performed to understand the effects of several factors on tsunami wave impact and run-up in the presence of gentle submarine slopes and coastal cliffs, using an in-house code, a constrained interpolation profile (CIP)-based model. The model employs a high-order finite difference method, the CIP method, as the flow solver; utilizes a VOF-type method, the tangent of hyperbola for interface capturing/slope weighting (THINC/SW) scheme, to capture the free surface; and treats the solid boundary by an immersed boundary method. A series of incident waves are arranged to interact with varying coastal geographies. Numerical results are compared with experimental data and good agreement is obtained. The influences of gentle submarine slope, coastal cliff and incident wave height are discussed. It is found that the tsunami amplification factor varying with incident wave is affected by gradient of cliff slope, and the critical value is about 45°. The run-up on a toe-erosion cliff is smaller than that on a normal cliff. The run-up is also related to the length of a gentle submarine slope with a critical value of about 2.292 m in the present model for most cases. The impact pressure on the cliff is extremely large and concentrated, and the backflow effect is non-negligible. Results of our work are highly precise and helpful in inverting tsunami source and forecasting disaster.

Wave transformation over submerged breakwaters by the constrained interpolation profile method

A multiphase flow model based on the Navier–Stokes equations using a constrained interpolation profile based Cartesian grid method is applied to estimate the wave interaction with a submerged breakwater. The free surface is captured by the Tangent of Hyperbola for Interface Capturing scheme. Wave transformations around submerged breakwaters are simulated with this model. Two kinds of waves (regular wave and solitary wave) and two shapes of submerged structures (rectangle and trapezoid) are investigated to verify the ability of the presented wave model to simulate the flow characteristics in these wave-structure interaction problems. Comparisons with experimental results show good agreements. It is demonstrated that the numerical wave model with the constrained interpolation profile method can reproduce the nonlinear flow phenomena and capture the complex free surface of wave transformation around submerged breakwaters accurately.

Numerical simulation of viscous flow past an oscillating square cylinder using a CIP-based model

The flow past an in-line forced oscillating square cylinder at Reynolds number of 200 is studied using an in-house code, named constrained interpolation profile method developed in Zhejiang University (CIP-ZJU). The model is established in the Cartesian coordinate system using the CIP method to discretise the Navier-Stokes equations. The fluid-structure interaction is treated as a multiphase flow of the liquid and solid phases to be solved simultaneously. An immersed boundary method is used to deal with the boundary of the solid body. The CFD model is first applied to the computation of the flow past a fixed square cylinder for its validation. Computations are then performed for the flow past a square cylinder oscillating in the streamwise direction. Considerable attention is paid to the symmetric and anti-symmetric modes of the vortex shedding in the oscillating square cylinder wake. Various oscillation amplitudes and frequencies are simulated and their effects on the vortex shedding modes are analyzed via Lissajous patterns of the unsteady lift coefficient. The relationship among the lift coefficient, the drag coefficient and the lock-on range is also investigated quantitatively.

Evaluation of numerical simulation of acoustic wave propagation using method of characteristics-based constrained interpolation profile (CIP-MOC) method with non-uniform grids

Evaluation of numerical simulation of acoustic wave propagation using method of characteristics-based constrained interpolation profile (CIP-MOC) method with non-uniform grids

Numerical simulation of bubble deformation in magnetic fluids by finite volume method

Bubble deformation in magnetic fluids under magnetic field is investigated numerically by an interface capturing method. The numerical method consists of a coupled level-set and VOF (Volume of Fluid) method, combined with conservation CIP (Constrained Interpolation Profile) method with the self-correcting procedure. In the present study considering actual physical properties of magnetic fluid, bubble deformation under given uniform magnetic field is analyzed for internal magnetic field passing through a magnetic gaseous and liquid phase interface. The numerical results explain the mechanism of bubble deformation under presence of given magnetic field.

A fully conservative high‐order upwind multi‐moment method using moments in both upwind and downwind cells

SummaryWe propose a fully conservative high‐order upwind multi‐moment method for the conservation equation. The proposed method is based on a third‐order polynomial interpolation function and semi‐Lagrangian formulation and is a variant of the constrained interpolation profile conservative semi‐Lagrangian scheme with third‐order polynomial function method. The third‐order interpolation function is constructed based on three constraints in the upwind cell (two boundary values and a cell average) and a constraint in the downwind cell (a cell center value). The proposed method shows fourth‐order accuracy in a benchmark problem (sine wave propagation). We also propose a less oscillatory formulation of the proposed method. The less oscillatory formulation can minimize numerical oscillations. These methods were validated through scalar transport problems, and compressible flow problems (shock tube and 2D explosion problems). Copyright © 2016 John Wiley & Sons, Ltd.

Lightning Electromagnetic Field Calculation Using the Constrained Interpolation Profile Method With a Subgridding Technique

The constrained interpolation profile (CIP) method has been recently applied to analyzing lightning electromagnetic fields. This method has an advantage that it is capable of computing electromagnetic fields reasonably accurately even when a relatively coarse grid is used. However, in analyzing small structures (in comparison with grid size) in the field point, this advantage of the CIP method is no longer valid and a locally fine grid would need to be employed. In this letter, a subgridding technique is applied to analyzing lightning electromagnetic fields in the three-dimensional space with the CIP method.

Multi-dimensional numerical simulation of sound propagation with background flow using constrained interpolation profile method

To date, numerical simulation for sound wave propagation has been widely investigated as a result of advances in computer technology. For acoustic imaging and prediction, the development of accurate and effective analysis methods in time domain has become an important technical issue. The constrained interpolation profile (CIP) method, a novel low-dispersive numerical scheme, is a type of method of characteristics (MOC) employing a co-located grid system. In our past study, we have applied the CIP method to solving the linearized sound propagation equation. MOC is the calculation method which transforms governing equations of acoustic field into advection equations to solve the acoustic fields. Therefore, the method should be suitable for solving sound propagation considering the background flow effect, e.g., prediction of sound noise environment generated from a propulsion system of aircrafts or rockets. In the study, we proposed and examined the calculation method of sound propagation in an arbitrary background flow using CIP method. We made a numerical comparison between proposed method and the linearized Euler equations (LEE) method. The presentation has clarified that the CIP method is more accurate and effective for solving sound propagation in a strong and/or heterogeneous background flow.