On the approximate solution of synoptic flow equation with discontinuous boundary conditions

In the present paper we investigate existence and uniqueness generalized solution for initial boundary value problem of synoptic flow equation with discontinuous boundary conditions. We consider Rothe-Galerkin method for given problem and reduce numerical calculations.

Approximate Formulation and Numerical Solution for Hypersingular Boundary Integral Equations in Plane Elasticity

Based on the fact that the singular boundary integrals in the sense of Cauchy principal value can be represented approximately by the mean values of two companion nearly singular boundary integrals, a vary general approach was developed in the paper. In the approach, the approximate formulation before discretization was constructed to cope with the difficulties encountered in the corner treatment in the formulations of hypersingular boundary integral equations. This makes it possible to solve the hypersingular boundary integral equation numerically in a non regularized form and in a local manner by using conforming C 0 quadratic boundary elements and standard Gaussian quadratures similar to those employed in the conventional displacement BIE formulations. The approximate formulation is very convenient to use because the corner information is comprised naturally in the representations of those approximate integrals. Numerical examples in plane elasticity show that with the present approach, the compatible or better results can be achieved in comparison with those of the conventional BIE formulations.

The Exact and Approximate Solutions of Some Boundary Value Problems in Domains with Angular Points of the Boundary

On the basis of the exact solution of biharmonic problems of elasticity theory in a half-strip one possible reason is shown of those problems that arise when an approximate or numerical approaches leading the solution of boundary value problems to infinite systems of linear algebraic equations. Construction of exact solutions of some boundary value problems for differential equations in partial derivatives is not possible without their extensions to Riemann surfaces. Moreover, each of the boundary value problem corresponds to its Riemann surface. This fact is important to consider when developing an effective approximate and numerical methods of solving boundary value problems.

Solution of the Euler Equations with Approximate Boundary Conditions for Thin Airfoils

This paper presents an efficient numerical method for solving the Euler equations on rectilinear grids. Wall boundary conditions on the surface of an airfoil are implemented by using their first order expansions on the airfoil chord line, which is placed along a grid line. However, the method is not restricted to flows with small disturbances since there are no restrictions on the magnitude of the velocity or pressure perturbations. The mathematical formulation and the numerical implementation of the wall boundary conditions in a finite volume Euler code are described. Steady transonic flows are calculated about the NACA 0006, NACA 0012 and NACA 0015 airfoils, corresponding to thickness ratios of 6%, 12%, and 15%, respectively. The computed results, including surface pressure distributions, the lift coefficient, the wave drag coefficient, and the pitching moment coefficient, at angles of attack from 0° to 8° are compared with solutions at the same conditions by FLO52, a well established Euler code using body fitted curvilinear grids. Results demonstrate that the method yields acceptable accuracies even for the relatively thick NACA 0015 airfoil and at high angles of attack. This study establishes the potential of extending the method to computing unsteady fluid structure interaction problems, where the use of a stationary rectilinear grid offers substantial advantages in both computer time and human work since it would not require the generation of time dependent body fitted grids.

Different Turbulent Regimes and Vertical Turbulence Structures of the Urban Nocturnal Stable Boundary Layer

Turbulence in the nocturnal boundary layer(NBL)is still not well characterized,especially over complex underlying surfaces.Herein,gradient tower data and eddy covariance data collected by the Beijing 325-m tower were used to better understand the differentiating characteristics of turbulence regimes and vertical turbulence structure of urban the NBL.As for heights above the urban canopy layer(UCL),the relationship between turbulence velocity scale(VTKE)and wind speed(V)was consistent with the“HOckey-Stick”(HOST)theory proposed for a relatively flat area.Four regimes have been identified according to urban nocturnal stable boundary layer.Regime 1 occurs where local shear plays a leading role for weak turbulence under the constraint that the wind speed V<VT(threshold wind speed).Regime 2 is determined by the existence of strong turbulence that occurs when V>VT and is mainly driven by bulk shear.Regime 3 is identified by the existence of moderate turbulence when upside-down turbulence sporadic bursts occur in the presence of otherwise weak turbulence.Regime 4 is identified as buoyancy turbulence,when V>VT,and the turbulence regime is affected by a combination of local wind shear,bulk shear and buoyancy turbulence.The turbulence activities demonstrated a weak thermal stratification dependency in regime 1,for which within the UCL,the turbulence intensity was strongly affected by local wind shear when V<VT.This study further showed typical examples of different stable boundary layers and the variations between turbulence regimes by analyzing the evolution of wind vectors.Partly because of the influence of large-scale motions,the power spectral density of vertical velocity for upsidedown structure showed an increase at low frequencies.The upside-down structures were also characterized by the highest frequency of the stable stratifications in the higher layer.

Temperature oscillations observed in the stable boundary layer over four different underlying surfaces

Nocturnal temperature is crucial in stability determination, as well as parameterization in numerical models. In the present research, data from four tall towers are used to investigate the temperature oscillations observed in the stable boundary layer, including the 307-m Boseong Tower on the southern coast of Korea, a 100-m tower in a grassland area of northern China, a 70-m tower in a desert area in northwestern China, and the 32S-m Beijing Tower. Large temperature oscillations, with amplitudes of about 2℃ and periods of several minutes to tens of minutes, are detected. Using the empirical mode decomposition method working as a high-pass filter, the oscillations of temperature are extracted from the original non-stationary and nonlinear temperature data. The daily variations and vertical distribution of the temperature oscillations are discussed. Generally strong temperature oscillations are found at tens of meters high during nighttime in the coastal area, in the steppe, and in the desert, when stable conditions have formed. Much weaker nocturnal temperature oscillations are observed in Beijing, where the large heat capacity of buildings and streets and artificial heat sources prevent the boundary layer conditions from becoming stable. Static stability expressed by the Brunt-Vaisala frequency is found to be an important factor for such temperature oscillation events, which is worthy of model parameterization.

Euler Solutions Using Approximate Boundary Conditions for Thin Airfoil with Small Oscillations

This paper presents an efficient numerical method for solving the unsteady Euler equations on stationary Cartesian grids. Wall boundary conditions are implemented on non moving mean wall positions by assuming the airfoil being thin and undergoing small deformation, but the mean angle of attack of the body can still be large and we use the full nonlinear Euler equation in the field for accurate resolution of shock waves and vorticity. The method does not require the generation of moving body fitted grids and thus can be easily deployed in any fluid structure interaction problem involving relatively small deformation of a thin body. We use the first order wall boundary conditions in solving the full Euler equation. Unsteady transonic flow is calculated about an oscillating NACA 0012 airfoil at free stream Mach number M ∞ =0.755, mean angle of attack α m =0.016, amplitude of pitching oscillation α 0 =2.51, reduced frequency κ = 0.081 4. The computed results, including surface pressure distribution, instantaneous lift and moment coefficients are compared with known experimental data. It is shown that the first order boundary conditions are satisfactory for airfoils of typical thicknesses with small deformation for unsteady calculations.

Approximate Analytic Solution for a Class of Generalized Nonlinear Singularly Perturbed Time-delay Model in the Critical Case

Based on the boundary layer corrective method, a class of generalized nonlinear perturbed model in the critical case is studied. The asymptotic solution for the original equation is constructed. And the method is of significance to seek approximate solutions to other nonlinear models.

Approximate solution of the flow over a nonlinear magneto-hydrodynamic stretching sheet

The approximate solution of the magneto-hydrodynamic （MHD） boundary layer flow over a nonlinear stretching sheet is obtained by combining the Lie symmetry method with the homotopy perturbation method. The approximate solution is tabulated, plotted for the values of various parameters and compared with the known solutions. It is found that the approximate solution agrees very well with the known numerical solutions, showing the reliability and validity of the present work.

A New Approximate Fundamental Solution for Orthotropic Plate

A weight double trigonometric series is presented as an approximate fundamental solution for orthotropic plate.Integral equation of orthotropic plate bending is solved by a new method, which only needs one basic boundary integral Eq., puts one fictitious boundary outside plate domain. Examples show that the approximate fundamental solution and solving method proposed in this paper are simple, reliable and quite precise. And they are applicable for various boundary conditions.

Approximate Solution of the Singular-Perturbation Problem on Chebyshev-Gauss Grid

Matrix methods, now-a-days, are playing an important role in solving the real life problems governed by ODEs and/or by PDEs. Many differential models of sciences and engineers for which the existing methodologies do not give reliable results, these methods are solving them competitively. In this work, a matrix methods is presented for approximate solution of the second-order singularly-perturbed delay differential equations. The main characteristic of this technique is that it reduces these problems to those of solving a system of algebraic equations, thus greatly simplifying the problem. The error analysis and convergence for the proposed method is introduced. Finally some experiments and their numerical solutions are given.

Partial approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls

In this paper,we propose the concept of partial approximate boundary synchronization for a coupled system of wave equations with Dirichlet boundary controls,and make a deep discussion on it.We analyze the relationship between the partial approximate boundary synchronization and the partial exact boundary synchronization,and obtain sufficient conditions to realize the partial approximate boundary synchronization and necessary conditions of Kalman’s criterion.In addition,with the help of partial synchronization decomposition,a condition that the approximately synchronizable state does not depend on the sequence of boundary controls is also given.

An implicit algorithm based on iterative modified approximate factorization method coupling with characteristic boundary conditions for solving subsonic viscous flows

An algorithm composed of an iterative modified approximate factorization(MAF(k)) method with Navier-Stokes characteristic boundary conditions(NSCBC) is proposed for solving subsonic viscous flows.A transformation on the matrix equation in MAF(k) is made in order to impose the implicit boundary conditions properly.To be in consistent with the implicit solver for the interior domain,an implicit scheme for NSCBC is formulated.The performance of the developed algorithm is investigated using spatially evolving zero pressure gradient boundary layer over a flat plate and a wall jet mixing with a cross flow over a flat plate with a square hole as the test cases.The numerical results are compared to the existing experimental datasets and a number of general correlations,together with other available numerical solutions,which demonstrate that the developed algorithm possesses promising capacity for simulating the subsonic viscous flows with large CFL number.

Approximate Boundary Conditions for Patch Antennas Mounted on Thin Dielectric Layers

In this paper we discuss scattering problems inherent in curved microstrip structures mounted on thin dielectric structures.We provide approximate boundary conditions for such structures in the framework of integral equations.

Sufficiency of Kalman's Rank Condition for the Approximate Boundary Controllability on an Annular Domain

In this paper the author establishes the sufficiency of Kalman’s rank condition on the approximate boundary controllability at a finite time for diagonalizable systems on an annular domain in higher dimensional case.

A PARAMETERIZED STUDY ON THE LOCAL SIMILARITY THEORY IN THE STABLE BOUNDARY LAYER MODEL

A 1-dimensional K-model parameterized by the local similarity theory is used to study the structure of the stably stratified boundary layer. The computed results are quite consistent with those of the second-order moments model. Thus, the model can be used to improve the simulated results and the parameterized accuracy.

ON SIMILARITY AND THE TURBULENT STRUCTURE IN THE STABLE BOUNDARY LAYER

In the stably stratified boundary layer,the vertical flux profiles for momentum and heat can be obtained from an atmospheric boundary layer model which includes parameterization of the long-wave radiation,In addi- tion,the Monin-Obukhov similarity theory can be extended to the whole boundary layer by using the local tur- bulent scales L(z),U_*(z)and 0_*(z)in place of surface layer scales.The similarity predictions are in good agreement with observational data.

Seismicity modulation by external stress perturbations in plate boundary vs.stable plate interior

Characterization of critically stressed seismogenic fault systems in diverse tectonic settings can be used to explore the stress/frictional condition of faults,along with its sensitivity for seismicity modulation by periodic stress perturbation.However,the process of seismicity modulation in response to external stress perturbation remains debated.In this paper,the characteristic difference in the seismicity modulation due to resonance destabilization phenomenon governed by rate-and-state friction is presented and val-idated with the globally reported cases of seismicity modulation in diverse tectonic settings.The rela-tively faster-moving plate boundary regions are equally susceptible for both shorter-period(e.g.,semi-diurnal,diurnal,and other small tidal constituents)and long-period(e.g.,semi-annual,annual,pole tide and pole wobble)seismicity modulation processes in response to stress perturbations from natural har-monic forcing,including tidal,semi-annual,annual,or multi-annual time scales.In contrast,slowly deforming stable plate interior regions and diffuse deformation zones appear to be more sensitive for long-period seismicity modulation of semi-annual,annual,or even multi-annual time scales but less sen-sitive for short-period seismicity modulation.This finding is also supported by the theoretical model pre-dictions from the resonance destabilization process and worldwide documented natural observations of seismicity modulation in diverse types of tectonic settings.

Stable Boundary Layer Height Parameterization: Learning from Artificial Neural Networks

Artificial neural networks (ANN) are employed using different combinations among the surface friction velocity u*, surface buoyancy flux Bs, free-flow stability N, Coriolis parameter f, and surface roughness length z0 from large-eddy simulation data as inputs to investigate which variables are essential in determining the stable boundary layer(SBL) height h. In addition, the performances of several conventional linear SBL height parameterizations are evaluated. ANN results indicate that the surface friction velocity u* is the most predominant variable in the estimation of SBL height h. When u* is absent, the secondly important variable is the surface buoyancy flux Bs. The relevance of N, f, and z0 to h is also discussed;f affects more than N does, and z0 shows to be the most insensitive variable to h.

Observation of Stable Marine Boundary Layer by Shipborne Coherent Doppler Lidar and Radiosonde over Yellow Sea

Shipborne observations obtained with the coherent Doppler lidar(CDL)and radiosonde during 2014 campaign were used to study the structure of marine boundary layer in the Yellow Sea.Vertical wind profiles corrected for ship motion was used to derive higher-order statistics,showing that motion correction is required and significant for turbulence analysis.During a day with weak mesoscale activity,a complexed three-layer structure system was observed.The lowest layer showed a typical stable boundary layer structure feature.An aerosol layer with abrupt variation in wind speed and relative humidity always appeared at the middle layer,the formation of which may be due to Kelvin-Helmholz instability.The top layer encountered a dramatic change in wind direction,which may result from the warm advection from the Eurasian continent on the basis of backward trajectory analysis.Furthermore,the MABL height in stable regime was derived from potential temperature,CDL signal-to-noise ratio(SNR)and CDL vertical velocity variance,respectively.The stable boundary layer(SBL)height in SBL can be derived from the inversion layer of potential temperature profile,and the mixing height in SBL can be retrieved from the vertical velocity variance gradient method.Neither the SBL height nor the mixing height is in agreement with the height retrieved from CDL SNR gradient method because of different definition and criterion.One of the limitations of SNR gradient method for MABL retrieval is that it is easier to be affected by the lofted decoupled aerosol layer,where the retrieved result is less suitable.Finally,the higher-order vertical velocity statistics within the marine stable boundary layer were investigated and compared with the previous studies,and different turbulence mechanisms have an important effect on the statistics deviation.