Numerical Comparison for Focused Wave Propagation Between the Fully Nonlinear Potential Flow and the Viscous Fluid Flow Models

Numerical simulations on focused wave propagation are carried out by using three types of numerical models,including the linear potential flow,the nonlinear potential flow and the viscous fluid flow models.The wave-wave interaction of the focused wave group with different frequency bands and input wave amplitudes is examined,by which the influence of free surface nonlinearity and fluid viscosity on the related phenomenon of focused wave is investigated.The significant influence of free surface nonlinearity on the characteristics of focused wave can be observed,including the increased focused wave crest,delayed focused time and downstream shift of focused position with the increase of input amplitude.It can plot the evident difference between the results of the nonlinear potential flow and linear potential flow models.However,only a little discrepancy between the nonlinear potential flow and viscous fluid flow models can be observed,implying the insignificant effect of fluid viscosity on focused wave behavior.Therefore,the nonlinear potential flow model is recommended for simulating the non-breaking focused wave problem in this study.

A fast multipole boundary element method for three-dimensional potential flow problems

A fast multipole methodology (FMM) is developed as a numerical approach to reduce the computational cost andmemory requirements in solving large-scale problems. It is applied to the boundary element method (BEM) for three-dimensional potential flow problems. The algorithm based on mixed multipole expansion and numerical integration isimplemented in combination with an iterative solver. Numerical examinations, on Dirichlet and Neumann problems,are carried out to demonstrate the capability and accuracy of the present method. It has been shown that the methodhas evident advantages in saving memory and computing time when used to solve huge-scale problems which may beprohibitive for the traditional BEM implementation.

Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations

A three-dimensional （3D） predictor-corrector finite difference method for standing wave is developed. It is applied to solve the 3D nonlinear potential flow equa- tions with a free surface. The 3D irregular tank is mapped onto a fixed cubic tank through the proper coordinate transform schemes. The cubic tank is distributed by the staggered meshgrid, and the staggered meshgrid is used to denote the variables of the flow field. The predictor-corrector finite difference method is given to develop the difference equa- tions of the dynamic boundary equation and kinematic boundary equation. Experimental results show that, using the finite difference method of the predictor-corrector scheme, the numerical solutions agree well with the published results. The wave profiles of the standing wave with different amplitudes and wave lengths are studied. The numerical solutions are also analyzed and presented graphically.

A Potential Flow Based Flight Simulator for an Underwater Glider

Underwater gliders are recent innovative types of autonomous underwater vehicles （AUVs） used in ocean exploration and observation. They adjust their buoyancy to dive and to return to the ocean surface. During the change of altitude, they use the hydrodynamic forces developed by their wings to move forward. Their flights are controlled by changing the position of their centers of gravity and their buoyancy to adjust their trim and heel angles. For better flight control, the understanding of the hydrodynamic behavior and the flight mechanics of the underwater glider is necessary. A 6-DOF motion simulator is coupled with an unsteady potential flow model for this purpose. In some specific cases, the numerical study demonstrates that an inappropriate stabilizer dimension can cause counter-steering behavior. The simulator can be used to improve the automatic flight control. It can also be used for the hydrodynamic design optimization of the devices.

Dissipative free-surface solver for potential flow around hydrofoil distributed with doublets

A doublet integral equation is formulated for the two-dimensional dissipative potential flow around a hydrofoil submerged below a free-water surface. The free-water surface is assumed to involve energy dissipation, and thus it is the source of damping. A doublet panel method is developed from incorporation of the dissipative Green function approach and the doublet distributions on the hydrofoil surface. Numerical computations are implemented, and the derived numerical results are in good agreement with analytic solutions and experimental measurements.

RELATIVE ENTROPY AND COMPRESSIBLE POTENTIAL FLOW

Compressible （full） potential flow is expressed as an equivalent first-order system of conservation laws for density ρ and velocity v. Energy E is shown to be the only nontrivial entropy for that system in multiple space dimensions, and it is strictly convex in ρ, v if and only if ｜v｜ 〈 c. For motivation some simple variations on the relative entropy theme of Dafer- mos/DiPerna are given, for example that smooth regions of weak entropy solutions shrink at finite speed, and that smooth solutions force solutions of singular entropy-compatible per- turbations to converge to them. We conjecture that entropy weak solutions of compressible potential flow are unique, in contrast to the known counterexamples for the Euler equations.

GENERAL EXACT SOLUTION OF INCOMPRESSIBLE POTENTIAL FLOWS AROUND TWO CIRCLES

Three exact solutions are obtained for 2-D incompressible potential flows around two moving circles in three cases: (i) expansion (or contraction) of themselves, (ii) approaching (or departing from) each other, (iii) moving perpendicularly to the line connecting the centres in opposite directions. Meanwhile, an- other set of two exact solutions is obtained for 2-D incompressible potential flows between two moving eccen- tric circles in two cases: moving parallelly or perpendicularly to the line connecting the centres.

A General Boundary Solution Method for Potential Flow around a 2D Semi-infinite Body

By using Cauchy's integral formula of analytical complex function and the third order complex spline function, a general boundary solution method for solving the complex potential field of the flow field around a 2D semi infinite body is presented in this paper. The pressure coefficients obtained by the present method agree well with those given by Acrivous, showing the validity of our method.

Study on Mooring Design and Calculation Method of Ocean Farm Based on Time-Domain Potential Flow Theory

In order to calculate the mooring force of a new semi-submerged Ocean Farm quickly and accurately,based on the unsteady time-domain potential flow theory and combined the catenary model,the control equation of mooring cable is established,and the mooring force of the platform under the wave spectrum is calculated.First of all,based on the actual situation of the ocean environment and platform,the mooring design of the platform is carried out,and the failure analysis and sensitivity analysis of the single anchor chain by the time domain coupling method are adopted:including different water depth,cycle,pretension size,anchor chain layout direction and wind speed,etc.The analysis results confirm the reliability of anchoring method.Based on this,the mooring point location of the platform is determined,the force of each anchor chain in the anchoring process is calculated,and the mooring force and the number of mooring cables are obtained for each cable that satisfies the specification,the results of this paper can provide theoretical calculation methods for mooring setting and mooring force calculation of similar offshore platforms.

Viscoelastic potential flow instability theory of Rivlin-Ericksen electrified fluids of cylindrical interface

A linear electrohydrodynamic Kelvin-Helmholtz instability of the interface between two viscoelastic Rivlin-Ericksen fluids enclosed by two concentric horizontal cylinders has been studied via the viscoelastic potential flow theory.The dispersion equation of complex coefficients for asymmetric disturbance has been obtained by using normal mode technique.the stability criteria are analyzed theoretically and illustrated graphically.The imaginary part of growth rate is plotted versus the wave number.The influences of dynamic viscoelastic,uniform velocities,Reynolds number,electric field,dynamic viscosity,density fluids ratio,dielectric constant ratio and inner fluid fraction on the stability of the system are discussed.The study finds its significance in Ocean pipelines to transfer oil or gas such as Eastern Siberia-Pacific Ocean oil pipeline.

Numerical solution of potential flow equations with a predictor-corrector finite difference method

We develop a numerical solution algorithm of the nonlinear potential flow equations with the nonlinear free surface boundary condition.A finite difference method with a predictor-corrector method is applied to solve the nonlinear potential flow equations in a two-dimensional (2D) tank.The irregular tank is mapped onto a fixed square domain with rectangular cells through a proper mapping function.A staggered mesh system is adopted in a 2D tank to capture the wave elevation of the transient fluid.The finite difference method with a predictor-corrector scheme is applied to discretize the nonlinear dynamic boundary condition and nonlinear kinematic boundary condition.We present the numerical results of wave elevations from small to large amplitude waves with free oscillation motion,and the numerical solutions of wave elevation with horizontal excited motion.The beating period and the nonlinear phenomenon are very clear.The numerical solutions agree well with the analytical solutions and previously published results.

Real-time solution of nonlinear potential flow equations for lifting rotors

Analysis of rotorcraft dynamics requires solution of the rotor induced flow field.Often,the appropriate model to be used for induced flow is nonlinear potential flow theory（which is the basis of vortex-lattice methods）.These nonlinear potential flow equations sometimes must be solved in real time––such as for real-time flight simulation,when observers are needed for controllers,or in preliminary design computations.In this paper,the major effects of nonlinearities on induced flow are studied for lifting rotors in low-speed flight and hover.The approach is to use a nonlinear statespace model of the induced flow based on a Galerkin treatment of the potential flow equations.

The Full Multi-wake Vortex Lattice Method:a detached flow model based on Potential Flow Theory

One of the main issues concerning the standard Vortex Lattice Method is its application to partially or fully detached flow conditions,where non-linear aerodynamic characteristics appear as the angle of attack increases and/or the aspect ratio decreases.In order to solve such limitations,a pure numerical approach based entirely on the Vortex Lattice Method concepts has been developed.The so-called steady“Full Multi-wake Vortex Lattice Method”comes from the main hypothesis that each discretized element on the body’s surface detaches their own wakes downstream.The obtained results match for lift,drag and moment coefficients for the entire aspect ratio range configurations(under straight wakes and inviscid assumptions).Future unsteady versions of such a multi-wake approach could improve the current results obtained through Vortex Element Methods(as vortons or isolated vortex filaments).

A BOUNDARY INTEGRAL EQUATION AND ITS NUMERICAL SOLUTION OF POTENTIAL FLOW AROUND SURFACE-IRREGULA-RITIES

In this paper,using complex functional theory,the authors turn the potential flow around the surface irregularities in a pressure conduit and semi-infinite platforms into Dirichlet problem.Based on Schwarz formula and by the application of Plemelj's formula,the authors change the problem into the integration of a Cauchy boundary integral equation in the flow plane through the substitution of variables.Using numerical integration,the authors obtain the velocity distribution and pressure coefficient along surface irregularities and platforms.The physical concept of this method is clear,the convergent speed is rapid and the computative effi- ciency is high.The calculated values agree well with the measured results.It is an effective and simple method in solving potential flow.

Reduced Basis Approximation and Error Bounds for Potential Flows in Parametrized Geometries

In this paper we consider(hierarchical,Lagrange)reduced basis approximation and a posteriori error estimation for potential flows in affinely parametrized geometries.We review the essential ingredients:i)a Galerkin projection onto a lowdimensional space associated with a smooth“parametric manifold”in order to get a dimension reduction;ii)an efficient and effective greedy sampling method for identification of optimal and numerically stable approximations to have a rapid convergence;iii)an a posteriori error estimation procedure:rigorous and sharp bounds for the linearfunctional outputs of interest and over the potential solution or related quantities of interest like velocity and/or pressure;iv)an Offline-Online computational decomposition strategies to achieve a minimum marginal computational cost for high performance in the real-time and many-query(e.g.,design and optimization)contexts.We present three illustrative results for inviscid potential flows in parametrized geometries representing a Venturi channel,a circular bend and an added mass problem.

Negative Stiffness Mechanism on An Asymmetric Wave Energy Converter by Using A Weakly Nonlinear Potential Model

Salter's duck,an asymmetrical wave energy converter(WEC)device,showed high efficiency in extracting energy from 2D regular waves in the past;yet,challenges remain for fluctuating wave conditions.These can potentially be addressed by adopting a negative stiffness mechanism(NSM)in WEC devices to enhance system efficiency,even in highly nonlinear and steep 3D waves.A weakly nonlinear model was developed which incorporated a nonlinear restoring moment and NSM into the linear formulations and was applied to an asymmetric WEC using a time domain potential flow model.The model was initially validated by comparing it with published experimental and numerical computational fluid dynamics results.The current results were in good agreement with the published results.It was found that the energy extraction increased in the range of 6%to 17%during the evaluation of the effectiveness of the NSM in regular waves.Under irregular wave conditions,specifically at the design wave conditions for the selected test site,the energy extraction increased by 2.4%,with annual energy production increments of approximately 0.8MWh.The findings highlight the potential of NSM in enhancing the performance of asymmetric WEC devices,indicating more efficient energy extraction under various wave conditions.

Identification of Potential Sites of Debris Flows in the Upper Min River Drainage,Following Environmental Changes Caused by the Wenchuan Earthquake

The Wenchuan earthquake caused numerous landslides and collapses that provide abundant unconsolidated material for future mobilization as debris flows.Debris flows will be very active and cause considerable damage for some time in the affected area.Because of environmental changes related to the earthquake,many potentially dangerous debris flow gullies have yet to be identified.This paper selects the upper Min River from Yinxiu to Wenchuan as the study area,interprets the unconsolidated deposits,and discusses their relationship to distance from the fault.Then,applying that information and the values of other factors relating to debris flow occurrence,the locations of potential debris flows are analyzed by multi-factor comprehensive identification and rapid identification.The multi-factor comprehensive identification employs fuzzy matter-element extension theory.The volume of unconsolidated material in the study area is about 3.28 × 108 m3.According to the analysis by multi-factor comprehensive identification,47 gullies have a high probability for potential debris flow,8 gullies have a moderate probability,and 1 gully has a low probability.

THE VERIFICATION OF THE CURRENT TRANSIENT EQUATION AT TUBULAR ELECTRODES IN A FLOWING FLUID UNDER POTENTIAL STEP

The equation derived for the response of the current transients in the flowing fluid is verified experimentally.

Momentum-Dependent Symmetry Potential from Nuclear Collective Flows in Heavy Ion Collisions at Intermediate Energies

Within the isospin-dependent quantum molecular dynamics model, we investigate the nuclear collective flows produced in semi-central 197 Au＋197 Au collisions at intermediate energies. The neutron proton differential flows and difference of neutron proton collective flows are sensitive to the momentum-dependent symmetry potential. This sensitivity is less affected by both the isoscalar part of nuclear equation of state and in-medium nucleon- nucleon cross sections. Moreover, this sensitivity becomes pronounced with increasing the rapidity cut.

Numerical Calculation of Supercavitating Flows over the Disk Cavitator of a Subsonic Underwater Projectile

To deal with the effect of compressible fluids on the supercavitating flow over the subsonic disk cavitator of a projectile, a finite volume method is formulated based on the ideal compressible potential theory. By using the continuity equation and Tait state equation as well as Riabouchinsky closure model, an“inverse problem”solution is presented for the supercavitating flow. According to the impenetrable condition on the surface of supercavity, a new iterative method for the supercavity shape is designed to deal with the effect of compressibility on the supercavity shape, pressure drag coefficient and density field. By this method, the very low cavitation number can be computed. The calculated results agree well with the experimental data and empirical formula. At the subsonic condition, the fluid compressibility will make supercavity length and radius increase. The supercavity expands, but remains spheroid. The effect on the first 1/3 part of supercavity is not obvious. The drag coefficient of projectile increases as the cavitation number or Mach number increases. With Mach number increasing, the compressibility is more and more significant. The compressibility must be considered as far as the accurate calculation of supercavitating flow is concerned.