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Three regimes: near-, middle- and far-fields of underwater explosion are proposed in this study aiming at providing an overview on the responses of submerged slender structure by pulsating bubble. In the near-field, the material starts to yield, thus leading to structure breakdown immediately; remarkable structural global elastic deformation occurs in the middle-field as well as substantial movement; and a structure moves as a rigid body with negligible deformation for the far-field. Equivalent dimensionless parameters are obtained by two different dimensional analysis methods, among which a dominant similarity parameter is found out. Thus, a scaling law providing us with a relation between structural global response and the dominant similarity parameter is yielded, which can be used for demarcating the three regimes quantitatively. To demonstrate, three models corresponding to typical submarine parameters are performed in the case studies. Quantitative criterion of the three regimes is presented along with the regime diagrams. The structural global response features such as the deformation and maximal acceleration/speed of different regimes are provided as well. (C) 2015 Elsevier Ltd. All rights reserved.

The stability of a soil slope is usually analyzed by limit equilibrium methods, in which the identification of the critical slip surface is of principal importance. In this study the spline curve in conjunction with a genetic algorithm is used to search the critical slip surface, and Spencer's method is employed to calculate the factor of safety. Three examples are presented to illustrate the reliability and efficiency of the method. Slip surfaces defined by a series of straight lines are compared with those defined by spline curves, and the results indicate that use of spline curves renders better results for a given number of slip surface nodal points comparing with the approximation using straight line segments.

A theoretical expression for vertical profile-of horizontal velocity in terms of its depth-average is derived based on oscillatory boundary layer theory and estuarine flow characteristics. The derived theoretical profile is then incorporated into a vertical quasi-two-dimensional model, which is proved advantageous in more physical implications and less CPU time demand. To validate the proposed model, the calculated results are compared to the field data in the Yangtze River Estuary, exhibiting good agreement with observations. The proposed quasi-two-dimensional vertical model is used to study mixing process, especially dependence of salinity distribution and salt front strength on runoff and tides in estuaries.

We present an improved penalty immersed boundary (pIB) method for simulation of flow‐induced deformation of 3D elastic capsules. The membrane deformation takes full account of the bending and twisting effects as well as the stretching and shearing effects. Hence, the method of subdivision surfaces is adopted to generate the mesh of membrane and the corresponding shape functions, which are required to be C1 continuous. Using the proposed pIB method, the deformation of 3D elastic capsules in simple shear flow is studied in detail. For an initially spherical capsule the steady tank‐treading motion is formed, in which the capsule maintains constant shape and orientation but rotates around the interior fluid. Time histories of the deformation parameter at various dimentionless shear rates and reduced bending moduli are presented and compared with data from previous studies.

Dynamic formation and detachment of drop from a capillary tube at low flow rate was investigated by the method of numerical simulation. The full transient process of the formation and detachment of drop was simulated numerically by solving the Navier‐Stokes equations using an algorithm based on the finite volume method. The tracking of the free surface was achieved using the volume of fluid (VOF) technique and the geometric reconstruction was based on the technique of Piecewise‐Linear interface construction (PLIC). Dimensionless elongation length and dimensionless minimum radius were analyzed in the work and there is a good agreement between the numerical and experimental results. Not only the development of shape and axial velocity, but also the relationship between the formation and annihilation of the vortex rings in the droplet was investigated. The relation of the pressure on the axial line and the position of the neck and pinch‐off of the droplet was investigated by studying the variance of pressure on the axial line.

For the hypersonic vehicle, the aerodynamic performance becomes more intensive. Therefore, it is a significant event to optimize the shape of the hypersonic vehicle to achieve the project demands. It is a key technology to promote the performance of the hypersonic vehicle with the method of shape optimization. Based on the existing vehicle, the optimization to the upper surface of the Simplified hypersonic vehicle was done to obtain a shape which suits the project demand. At the cruising condition, the upper surface was parameterized with the B‐Spline curve method. The incremental parametric method and the reconstruction technology of the local mesh were applied here. The whole flow field was been calculated and the aerodynamic performance of the craft were obtained by the computational fluid dynamic (CFD) technology. Then the vehicle shape was optimized to achieve the maximum lift‐drag ratio at attack angle 3°, 4° and 5°. The results will provide the reference for the practical design.

Numerical simulation for the two models in cross‐wind was carried out in this paper. The three‐dimensional compressible Reynolds‐averaged Navier‐Stokes equations(RANS), combined with the standard k‐e turbulence model, were solved on multi‐block hybrid grids by second order upwind finite volume technique. The impact of fairing on aerodynamic characteristics of the train models was analyzed. It is shown that, the flow separates on the fairing and a strong vortex is generated, the pressure on the upper middle car decreases dramatically, which leads to a large lift force. The fairing changes the basic patterns around the trains. In addition, formulas of the coefficient of aerodynamic force at small yaw angles up to 24° were expressed.

Blunt leading edge with profiles of circular or power law shape is often used to decrease the aerodynamic heating of a vehicle when it flights into hypersonic regime. In order to further reduce the peak of heat flux of the leading edge, an inverse shape design method is presented in this paper. The leading edge is parameterized by using B-spline curve method. The hypersonic flow field and the heat flux distribution around the leading edge is evaluated by computational fluid dynamics. A homotopy method is developed as the optimizer. The computational heat flux distribution is driven by the optimizer to meet the objective. In order to verify the validity of the method, the inverse aerothermal design of a 2D leading edge with the thickness of 5 mm was carried out in the design condition Mach number is 6.5. The initial profile of the leading edge approximates to a circular arc. An H-type structured grid was used to discrete the computational domain. A 2D thin-layer Reynolds-averaged Navier-Stokes equations in strong conservation law form was employed as the solver. The results have shown that the peak value of the heat flux decreases about 4.6%.

We apply a Runge‐Kutta discontinuous Galerkin (RKDG) method to numerical solution of the reactive Euler equations. In order to keep conservation naturally, Taylor basis functions are utilized. We construct a new Taylor basis function which has smaller numerical error than previous Taylor basis function when the TVD limiter is used. The program is written with MPI for parallel computation. Numerical results of two‐dimensional unstable detonation waves demonstrate that the resulting RKDG method performs well in resolving detonation wave structures. Load imbalance due to different stiffness in different subzones is discussed.

A hybrid RANS‐LES method based on structural ensemble dynamics (SED) theory is presented, wherein coarse‐grained turbulent fluctuation amplitudes are re‐normalized using instantaneous values of an order function, i.e. mixing length, in the ensemble‐averaged Navier‐Stokes (EANS) equation. The re‐normalization procedure is applied throughout the channel (at wall friction Reynolds numbers Reτ = 1 050 and 2 000), to evade the common problem of log‐layer mismatch. The mean and rms velocity profiles show improved agreement with DNS at very coarse grids (40×49×20 for both Re’s). The method dissipates turbulent kinetic energy in the bulk flow, and increases turbulent fluctuations in the buffer region, mimicking the physical forcing of the sub‐grid scale term. The results demonstrate the feasibility to reconstruct the unsteady effect of wall‐bounded flows constrained by order functions.

We consider the two‐dimensional problem of steady natural convection in a circular cavity with constant volumetric heat flux filled with viscous fluid subject to constant temperature variation on the boundary. The solution is expanded for low Rayleigh number and extended to 16 terms by computer. Analysis of these expansions allows the exact computation for arbitrarily accuracy up to 50 000 figures. Although the range of the radius of convergence is small but pade approximation leads our result to be good even for higher value of the similarity parameter.

There are many vortex‐identification methods. We need to judge which criterion is better, and what motion a special criterion stands for. To study kinematics of different vortex criteria in detail, we analyze some common vortex criteria using decomposition of the velocity‐gradient tensor. First, a triple decomposition method (TDM) is use to distinguish three different elementary motions. Second, we introduce a quadruple decomposition method (QDM), which distinguishes pure shearing from other motion, decomposing fluid motion into for kinds: elongation, axial deformation, plane motion and pure shearing. QDM enables us to analyze vortex criteria from the relationship of pure rotation and axial deformation, thus get a deeper understanding of vortex and motions.

Viscous flow past two circular cylinders in tandem and side‐by‐side arrangements is investigated numerically. The solution to the Navier‐Stokes equations is obtained by means of a cell‐centred finite volume method (FVM) based on a structured Cartesian grid with collocated variable arrangement. The pressure‐velocity coupling is evaluated by using the SIMPLE algorithm. The 2D Cartesian cut cell mesh is generated on the horizontal plane, which is extended vertically to form the 3D grid. The simulations are based on the Reynolds number of 200, and the gap between the two cylinders are 1.5–3D for side‐by‐side arrangement and 3–4D for tandem. Instantaneous velocity contours of the flow around the cylinders and time histories of force coefficients are presented.

In this paper, using three‐dimensional laser‐doppler velocimeter (LDV) system, the turbulent flows in a rectangular channel with smooth and artificial rough surfaces are investigated experimentally over a wide Reynolds number range. The rough surfaces are composed of different amount roughness elements of transverse V‐shaped grooves with 120° vertex angle and 0.5 mm deep. Distributions of the mean velocity, turbulence intensities, and high‐order moments including the skewness and flatness factors in streamwise and wall‐normal directions on smooth and rough surfaces are all presented. The normalized statistical quantities on different surfaces exhibit significant differences in both the inner and outer region, which suggests that the roughness element has an important role on turbulent flow structure extending into the whole layer, and query the classical wall similarity hypothesis.

A hybrid prediction method for aerodynamic noise is performed using high order accuracy method in this paper. The method combines a two‐dimensional Unsteady Reynolds‐Averaged Navier‐Stokes(URANS) solver with the acoustic analogy method using Ffowcs Williams‐Hawkings equation with penetrable data surface (FW‐Hpds). Tandem cylinders are chosen to validate the prediction method. The computations are conducted at a Reynolds number of 1.66 × 105 based on the cylinder diameter. Both the aerodynamic and acoustic results show good agreement with the experimental data, showing a successful application of the hybrid prediction method using two‐dimensional URANS simulation.

Asymmetric water wave is a common phenomenon in coastal areas, which has a great influence on sediment transport and coast protection. However, previous studies mainly focused on symmetric wave motion. Therefore, it is of practical importance to manifest flow characteristics in asymmetric wave field. To begin with, we have formulated an LES model, by which we carry out numerical simulation of laminar flow induced by asymmetric waves showing reasonable agreement with analytical solution. Then, we apply the model to the cases of asymmetric waves in turbulent flow region. Numerical results of velocity profile and shear stress are obtained and compared with experimental data. We find that, in the case of asymmetric wave, the effect of Reynolds number and the degree of asymmetry are two crucial factors for governing the flows.

An analytical model describing a vortex ring for low Reynolds numbers (Re) proposed previously by Kaplanski and Rudi [Phys. Fluids,17, 087101 (2005)], is extended to a vortex rings for higher Reynolds numbers. The experimental results show that the vortex ring core takes the oblate ellipsoidal shape with increasing Re. In order to model this feature, we suggest an expression for the vorticity distribution, which corrects the linearized solution of the Navier‐Stokes equation, with two disposable nondimensional parameters λ and β governing the shape of the vortex core, and derive the new expressions for the streamfuction, circulation, energy and translation velocity on the basis of it. The appropriate values of λ and β are calculated by equating the nondimensional energy Ed and circulation Гd of the theoretical vortex to the corresponding values obtained from the experimental or numerical vortex ring. To validate the model, the data adapted from the numerical study of a vortex ring at Re = 1400 performed by...

The influence of the porosity of the structure on the wave‐induced seepage force on the bottom of porous vertical circular cylinder resting on porous elastic seabed in two layer ocean has been investigated. Under the assumptions of potential flow and linear wave theory, the analytical solutions to seepage pressure fields caused by surface wave and inner wave are respectively given by the eigenfunction expansion approach. Numerical results show that the porosity of the structure may lead to a reduction both in the horizontal wave forces and in the wave induced seepage forces, especially, leading to a significant reduction in the inner wave‐induced moment.

The geometric effects on the liquid flow were investigated in microchannel based on the numerical simulation method. Effects of geometry were shown obviously on the microflow by comparing the results of different geometric characteristics covering hydraulic diameter, length and aspect ratio. Thermal boundary conditions are the same for different cases in the numerical simulation.The geometric parameters except the aspect ratio have little effect on the friction factor but all of them obviously make the Nusselt number changed.

Evolution equation for nonlinear internal wave in stratified liquid film was derived based on boundary‐layer theory in this article. Firstly, the mathematical model was established for nonlinear internal wave (NLIW) in general stratified liquid film. Then, the model was simplified and the Long equation having viscosity term with boundary‐layer theory was yielded. Finally, the modified Long equation was calculated approximately by using of perturbation method, and the nonlinear evolution equation was obtained for internal wave in stratified liquid film with hypothesis of shallow water.

In this paper, the focused wave groups, which have been used in physical flumes for testing the survivability of offshore installations under extreme wave conditions, are generated numerically by using a recently developed two‐fluid free‐surface capturing code (AMAZON‐SC). The finite volume based method solves Navier‐Stokes equations for a variable density fluid on a Cartesian grid and the movement of the wave maker (a piston‐type paddle) is simulated efficiently and accurately by adopting a generic cut cell mesh approach for moving boundaries. Two test cases of the focused wave group with different frequency bandwidths have been calculated and results are in generally good agreements with the relevant experimental data.

A three‐dimensional (3D) Navier‐Stokes method is applied to calculate unsteady turbomachinery flows. The 4‐stage Runge‐Kutta time‐marching scheme and time‐consistent multi‐grid technique are adopted in the calculations. In this study, the multi‐passage computation and single passage computation are performed on the actual and scaled configurations respectively. The results from multi‐passage computation and singe passage computations are compared. Results in the form of isentropic efficiency, mass flow, entropy and unsteady aerodynamic force on the blades are presented. It has been found that the blade geometry scaling changes the axial position of the wakes, which leads to greater amplitude of efficiency fluctuation. The blade geometry scaling brings notable effects on the first four harmonics of unsteady tangential force.

In present paper, a design method for natural laminar flow (NLF) airfoils with a substantial amount of natural laminar flow on both surfaces by coupling inverse design method and optimal technique is developed. The N‐factor method is used to design the target pressure distributions before pressure recovery region with desired transition locations while maintaining aerodynamics constraints. The pressure in recovery region is designed according to Stratford separation criteria to prevent the laminar separation. In order to improve the off‐design performance in inverse design, a multi‐point inverse design is performed. An optimal technique based on response surface methodology (RSM) is used to calculate the target airfoil shapes according to the designed target pressure distributions. The set of design points is selected to satisfy the D‐optimality and the reduced quadratic polynomial RS models without the 2nd‐order cross items are constructed to reduce the computational cost. The design cases indicated that...

Stability of the channel flow with longitudinal wall‐oscillation is investigated by the Floquet theory. The stability equation, time‐dependent Orr‐Sommerfeld equation, is rewritten as a simple ordinary differential equation by the use of the collocation method. Using this ordinary equation, the Floquet exponents are defined. The velocity profiles for the Floquet analysis are given as superimposition of the two dimensional plane Poiseuille flow with the Stokes layer. Reynolds number is fixed at 10 000 which corresponds to supercritical condition. The parametric study shows that there is a stability spot on the parameter space in spite of the supercritical condition.

This paper focuses on the symplectic method for the Stokes flow through the superhydrophobic circular pipes with shearfree surfaces. Taking original variables (velocities) and their dual variables as the basic variables, the symplectic formulation can be introduced into stokes flow problems and put forward a direct method. The eigensolu‐tions corresponding to zeroeigenvalue and nonzero‐eigenvalues can be solved analytically, and the unknown expansion coefficients can be determined by using the end conditions based on the symplectic orthonormalization relationships. The examples show the applicability and validity of the symplectic approach for solving stokes flow problems.

Fluidity is an open source, general purpose, multi‐phase CFD code capable of solving numerically the Navier‐Stokes and accompanying field equations on arbitrary unstructured finite element meshes in one, two and three dimensions. It uses a moving finite element/control volume method which allows arbitrary movement of the mesh in time dependent problems. It has a wide range of finite element/control volume element choices including mixed formulations. Here, continuous Galerkin (CG) and control volumes (CV) solutions of the compressible Navier‐Stokes (N‐S) equations are presented for the stratified tests cases of the rising thermal bubble and inertia gravity waves. Results show good agreement with previously published literature and novel result presented here is the ability to dynamically adapt the mesh to increase resolution in the region of interest, thus reducing the number of degrees of freedom in the problem without decreasing the accuracy of the result. Finally, results from the case of a fully three dimensional rising thermal bubble are presented.

Firstly, a three‐dimensional model of WS‐80 vertical Woltmann water meter was created according to its geometrical parameters. And then the finite volume based SIMPLEC method and two different turbulence models (κ‐e RNG and κ‐e realizable) are used to get the internal flow of Water Meter, respectively. Finally, the details of flow, such as pressure loss, velocity vector and pressure distribution of flow field are derived. In addition, the numerical simulation of pressure loss was compared with experimental data. It has been found that numerical simulation results can really reflect the complicated internal flow of water meter, and they can be used as the guidance for the design and optimization of vertical Woltmann water meter.

This work presents a new Godunov‐type finite volume model for complex shallow flows over erodible bed with wetting and drying. The model solves the coupled shallow water and Exner equations, with the interface fluxes evaluated by an HLLC approximate Riemann solver. Well‐balanced solution is achieved by implementing the surface gradient method and wetting and drying are handled by a non‐negative reconstruction approach.

A newly developed statistical correlation structure is used to analyze compressible channel flows up to M = 3.0. Using velocity‐vorticity correlation structure (VVCS), the Mach number dependence of the characteristic scales of near wall structure are analyzed. The detailed results show that the length scale and the spanwise spacing of VVCS exponentially increase with Mach number in the near wall region. For example, for VVCSuωx, the length scale of the statistical streamwise structure is Lxuωx = e6.5 + M/2.8 + (M/4.1)2, and spacing between the structure is Dxuωx = 60eM/2.2 + 13.3, where the parameters 2.8, 4.1 and 2.2 are characteristic Mach numbers to be explained further. The geometrical features of the statistical structure are consistent with the observations of Coleman et al., and it is also argued that the quantitative relationship between the characteristic scales of VVCS and Mach number is important to consider in performing numerical computation of compressible flows. This study also suggests tha...

Effective slip lengths for pressure‐driven oscillatory flow through a parallel‐plate channel with boundary slip are deduced using a semi‐analytic method of eigenfunction expansions and point matching. The channel walls are each a superhydrophobic surface micropatterned with no‐shear alternating with no‐slip stripes which are aligned parallel to the flow. The slip lengths are complex quantities that are functions of the oscillation frequency, the channel height and the no‐shear area fraction of the wall. The dependence of the complex nature of the slip length on the oscillation frequency is investigated in particular.

This paper presents a family of high order finite volume schemes for solving Navier‐Stokes equations on unstructured grids. The k‐exact reconstruction is performed on every control volume as the primary reconstruction. On a cell of interest, besides the primary reconstruction, additional candidate reconstruction polynomials are provided by means of very simple and efficient “secondary” reconstructions. The weighted average procedure of the WENO scheme is then applied to the primary and secondary reconstructions to ensure the shock capturing capability of the scheme. A quadrature‐free way is proposed to perform WENO schemes for saving computation. Several test cases are presented to validate the accuracy and non‐oscillation property of the proposed schemes.

A structured finite volume Euler solver for non‐hydrostatic term, free‐surface flows has been developed to simulate nonlinear water waves. A semi‐implicit projection method which splits the pressure term into hydrostatic and non‐hydrostatic parts is employed. A vertically shifted staggered grid is designed to accommodate a new Gaussian discharge calculator and to the application of a non‐hydrostatic free‐surface boundary condition. The Gaussian discharge calculator on the shifted grid increases the dispersion accuracy compared to traditional approaches that calculate discharges on a regular staggered grid. Numerical results are presented to demonstrate the improvements of these methods.

The problem involving the scattering of surface water waves by small undulation of a sea‐bed has been solved completely, by utilizing the eigenfunction expansion method leading to the mathematical problem of solving over‐determined system of linear algebraic equations. Such an over‐determined system of linear algebraic equations is best solved by the method of least‐squares and numerical results for useful practical quantities such as the reflection and transmission coefficients are obtained.

To study the phenomena of two‐phase flow with salt‐out in centrifugal pump, it is important to investigate the real flow in the pump with clear water. Based on the Reynolds‐averaged N‐S equations and standard κ‐e two‐equation turbulent model, the 3D turbulent flow was simulated through the full flow passage by the fluid dynamics software FLUENT.PIV was also applied to measure the flow inside the modified centrifugal pump. Relative velocity distributions in the impeller were obtained. Combined with the results from numerical simulation and experiment, preliminary analysis of inner flow field in the centrifugal pump was presented. The experiment results also show that standard κ‐e turbulent model used in simulation coincides with the inner flow of the pump basically.

A simple and rapid simulation of freak wave generation is attempted. This scheme is based on sideband instability in the evolution of wave trains. The modified four‐order nonlinear Schrodinger equation is employed as a mathematical model. And the superimposed wave trains by carrier wave and sideband disturbances are applied to this equation as initial conditions. In the simulation, variations of wave steepness, scale factor and sideband disturbance parameter are respectively considered to explore the generation of freak waves. Results show that some values of parameters are very helpful to form freak waves. And according to this, the rapid numerical experiment is performed, and an example of freak wave generation are provided.

The lattice-Boltzmann method is employed to solve the none‐Newtonian microporous flow field in the porescale under various rheological properties. The calculated local viscosity distribution in microporous structures corresponds with the non‐Newtonian rheological properties. For the shear thinning fluid of power‐law exponent n ≤ 1, the fluid viscosity near the block surface is smaller. The flow rate through the porous structure is linear proportional to the applied pressure difference in logarithmic coordinates, keeping with the modified Blake‐Kozeny equation.

Flow behavior of time periodic electro‐osmotic flow (EOF) of non‐Newtonian (Jeffrey) fluids in a circular microtube is investigated based on a linearized Poisson‐Boltzmann equation, together with the Cauchy momentum equation and the Jeffrey constitutive equation. Taking near‐wall depletion effects of macromolecules into account, we divided the flow region into skimming layer and the bulk. Analytical solutions of EOF velocity distribution are obtained. By numerical computations, the influences of the related parameters on the velocity amplitude are studied.

We develop the Hamilton‐Pontryagin principle for Lagrangians with advective parameters, which yields an implicit analogue of Euler‐Poincare equations with advective parameters. Then, we derive the reduced Hamilton‐Pontryagin principle and illustrate it with the example of incompressible ideal fluids, where the configuration space is given by the group of (volume preserving) diffeomorphisms. Incorporating pressure and momentum densities as Lagrange multipliers into the Hamilton‐Pontryagin principle, we finally show that the dynamics of incompressible ideal fluids can be effectively formulated in the context of implicit Euler‐Poincare equations.

This paper discusses the physical meanings of various parameters in multi‐fractal spectrum and offers the thermo‐mechanical formula in calculating the multi‐fractal spectrum. Besides it works out the sets of multi‐fractal Cantor, the multi‐fractal spectrum of turbulence data of Rayleigh‐Benard convection and DNA series by means of wavelet transform maximum modulus (WTMM). In the end, it arrives at the conclusions that the means of WTMM is plausible on the application of multi‐fractal research, multi‐fractal spectrum offers function α∼f(α), which describes all the sub‐collections’ characters. So it gives specific information of a system. Turbulence is similar to DNA’s multi‐fractal character. The latter is more uneven and complex. Multi‐fractal spectrum analysis can reveal the uneven overall distribution information of the series (or sets). But it has a limited description of the local position information of signal singularity and concrete local structure.

In this study, a centrifugal fan design with two flow outlets is investigated. This design aims to provide high mass flow rate but low noise performance. Two dimensional unsteady flow simulation with CFD code (FLUENT 6.3) is carried out to analyze the fan flow dynamics and its acoustics. The calculations were done using the unsteady Reynolds averaged Navier Stokes (URANS) approach in which effects of turbulence were accounted for using κ‐e model. This work aims to provide an insight how the dominant noise source mechanisms vary with a key fan geometrical paramters, namely, the ratio between cutoff distance and the radius of curvature of the fan housing. Four new fan designs were calculated. Simulation results show that the unsteady flow‐induced forces on the fan blades are found to be the main noise sources. The blade force coefficients are then used to build the dipole source terms in Ffowcs Williams and Hawkings (FW‐H) Equation for estimating their noise effects. It is found that one design is able to deliver a mass flow 34% more, but with sound pressure level (SPL) 10 dB lower, than the existing design .

A Reynolds‐averaged Navier‐stokes equations (RANS) model using the body force method (BFM) has been developed to simulate open‐channel flows over gravel beds. The momentum equation is modified by introducing the form drag as an extra body force term to represent the gravel‐bed resistance. By applying the body force within the roughness layer of the flow over small‐scale roughness, it is found that the body force coefficient frk varies inversely with the roughness length scale ks. The method is robust, not sensitive to mesh resolution and is easily extended to deal with large scale roughness.

A forward stepwise method of inflow generation for large‐eddy simulation (LES) is developed. The method was tested by simulating plane channel flows, and validated using DNS data in the literature and LES data with periodic boundary conditions.

Stability analyses of two‐dimension conventional Burnett and Woods equations were carried out. The characteristic stability equations of these two equations were first derived and the characteristic curves were achieved. The linearized stability analyses show that the two‐dimension conventional Burnett and Woods equations are not stable. The critical Knudsen numbers for these two extended hydrodynamic equations are 0.353 and 0.130, respectively. The critical Knudsen numbers are smaller than those of one‐dimension equations. The two‐dimension extended hydrodynamic equations are more unstable than one‐dimension equations.

In this paper, the symplectic method is presented for solving Stokes flow in closed sectorial domain. The dual equations are built by variational principle, in which the velocities and stresses are dual variables in the symplectic space. The solution of the problem can be expanded by eigensolutions, and the expansion coefficients are determined via ortho‐normalization relations of the eigensolutions. The velocities and stresses of the case are obtained directly with this method, which can be applied in some other low Reynolds problem too.

A high‐order accurate and highly‐efficient finite difference algorithm for numerical simulation of the incompressible viscous flows has been developed. This algorithm is based on the pseudo‐compressibility formulation, which combines the preconditioning technique for accelerating the time marching for stiff hyperbolic equations. Third‐, fifth‐ and seventh‐order accurate WENO schemes are used to discrete the inviscid fluxes and fourth‐ and sixth‐order central schemes are employed for the viscous fluxes and metric terms. Implicit lower‐upper symmetric Gauss‐Seidel (LU‐SGS) time marching procedure is performed for temporal discretization. The accuracy and the efficiency of the proposed method are demonstrated for several numerical test cases.

Different methods have been used to derive Green function in a two‐layer fluid model, which has been treated in different ways. In a two‐layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the free surface and the interface. This is because the density does change in the vertical direction of the water in special areas such as lakes, fjords or estuaries, due to variation in salinity and/or temperature where loads on underwater structures are interesting. The fluid in this case is considered to be inviscid, incompressible and the flow is irrotational. In this paper, derived Green functions in three dimensional case of a stationary source oscillating are presented. The source point is located either in the upper or lower part of a two‐layer fluid of finite depths. The method of singularities was used to arrive at the desired Green functions. This method has an advantage because it involves representing the potential as a sum of singularities or multipole...

A new model to estimate the flow in a fracture has been developed in this paper. This model used two sinusoidal‐varying walls with different phases to replace the flat planes in the cubic law model. The steady laminar flow between non‐symmetric sinusoidal surfaces was numerically solved. The relationships between the effective hydraulic apertures and the phase retardation for different amplitudes and wavelengths are investigated respectively. Finally, a formula of the effective hydraulic aperture of the fracture was carried out based on the numerical results.

Large eddy simulation (LES) of fully developed, compressible turbulent channel flows is performed in the present paper. The turbulent statistics agree well with those from other direct numerical simulation (DNS) results, indicating that the LES method established in the present paper is reliable. Through the analysis of the turbulent fluctuations, the Morkovin's hypothesis is basically validated, and consequently the dominant compressibility effect is that due to mean property variations. When properly scaled, the turbulence statistics such as mean steamwise velocity, root‐mean‐square (RMS) velocity fluctuations are found to agree well with the incompressible DNS results.