A novel high resolution model without open boundary conditions applied to the China Seas: first investigation on tides

We developed a Global Ocean Circulation and Tide Model （GOCTM） with coarse grids in the open deep ocean degrading ‘smoothly’ into the highly resolved China Seas （CS） of refined grids to study the tides and circulation there.GOCTM is based on the framework of the Finite Volume approach for better mass conservation through improved transports across the discrete individual control volume.It also takes a full advantage of the geometric flexibility of unstructured mesh using a realistic global topography including the Arctic Ocean.The CS are given a special focus by refining the unstructured grids,but they are embedded into global domain naturally.Furthermore,GOCTM not only successfully avoids the treatment of the open boundaries,but also optimizes the trade-off between computational cost and model accuracy.Meanwhile,GOCTM is driven by the astronomical tide-generating potential and the secondary tide-generating potential directly,together with the wind stress and heat flux.GOCTM succeeds in reproducing the global eight principal tidal harmonic constants.Particularly,the simulated tidal results in the CS are improved compared to some other regional models with the discrepancy of 3.9 cm for M 2 tide.This idea of GOCTM can also be referred for other regional ocean study.

Inversion of two-dimensional tidal open boundary conditions of M_2 constituent in the Bohai and Yellow Seas

Two-dimensional tidal open boundary conditions of the M2 constituent in the Bohai and Yellow Seas(BYS) have been estimated by assimilating T/P altimeter data.During inversion,independent point(IP) strategy was used,in which several IPs on the open boundary is assumed,values at these IPs can be optimized with an adjoint method,and those at other grid points are determined by linearly interpolating the values at IPs.The reasonability and feasibility of the model are tested by ideal twin experiments.In the practical experiment(PE) after assimilation,the cost function may reach 1% or less of its initial value.Mean absolute errors in amplitude and phase can be less than 5 cm and 5°,respectively,and the obtained co-chart can show the character of the M2 constituent in the BYS.The results of the PE indicate that using only two IPs on the open boundary can yield better simulated results.

Integrability of N-Component Bariev Model Under Open Boundary Conditions

N-component Bariev model for correlated hopping under open boundary conditions in one dimension is studied in the framework of Bethe ansatz method. The energy spectrum and the related Bethe ansatz equations are obtained.

Ocean Model Open Boundary Conditions with Volume, Heat and Salinity Conservation Constraints

Open boundary conditions （OBCs） for a regional ocean model that can be integrated stably over a long timeframe, as well as satisfy the volume, heat and salinity conservation constraints, were developed. First, the idea that the inward and outward flux information can be treated separately in the OBCs was adopted. Second, in order to maintain the property that the volume, heat and salinity remains conserved in the simulation domain, conservation constraints were added to the OBCs, and an inverse method utilized to solve the constraint equations. Ideal experiments were designed to investigate the conservation property, and the OBCs were found to work efficiently to maintain the volume, heat and salinity conservation. It was found that simulations were comparable to observations when the OBCs were applied to a regional ocean model.

AN ADAPTIVE OPEN BOUNDARY CONDITION

A significant improvement of the open boundary condition which was originally studied by Engquist and Majda is given.The method given here is applicable without limitation of the angle between the direction of the incident wave and the normal to the boundary.It also improves the precision of the method from order one to two.The test examples show that this method is much better than the method mentioned above.

Thermodynamics of 1D N-Component Bariev Model Under Open Boundary Conditions

The thermodynamic Bethe ansatz equations and free energy for 1D N-component Bariev model under open boundary conditions are derived based on the string hypothesis for both, a repulsive and an attractive interaction. These equations are discussed in some limiting cases, such as the ground state, weak and strong couplings.

The High Precision Open Boundary Conditions Designed for Transient Waves

In Rels. [2-4] there is an Adaptive. Open Boundary Condition (AOBC) designed for transient waves which overcomes the limitation of the existing Open BoundaryCondition (OBC) and can be used for the cases of waves with arbitrary incidentangles. In this article a new family of high order AOBC has been designed on the basisof the above mentioned AOBC with the first order.In comparison with all other OBC with the same order, this new family of AOBC has the highest precision.

A Simplified Approach of Open Boundary Conditions for the Smoothed Particle Hydrodynamics Method

In this paper,we propose a simplified approach of open boundary conditions for particle-based fluid simulations using the weakly compressible smoothed-particle hydrodynamics(SPH)method.In this scheme,the values of the inflow/outflow particles are calculated as fluid particles or imposed desired values to ensure the appropriate evolution of the flow field instead of using a renormalization process involving the fluid particles.We concentrate on handling the generation of new inflow particles using several simple approaches that contribute to the flow field stability.The advantages of theδ^(+).-SPH scheme,specifically the particle shifting technique,were successfully applied to correct the position,velocity,and pressure terms of the particles.Therefore,unexpected errors were removed and tensile instabilities of the particles were prevented.The proposed technique is validated for several benchmark test cases,and the tests show that the results match the reference solutions well.A viscous open-channel flow is used to demonstrate the stability of the flow field during the computational time.Based on this stability,we compress the computational domain to a lower resolution in a second test case while preserving the accuracy of the simulation.Flow over a backward-facing step is used to highlight the challenges of inflow boundary conditions with prescribed or non-prescribed values.The developed technique is well suited to the wall boundaries and the evolution of the flow field.The results demonstrate the robustness and versatility of the proposed technique for a variety of simulations.

Numerical analysis for cooling effect of open boundary ripped-rock embankment on Qinghai-Tibetan railway

The heat convection of fluid inside the ballast layer and ripped-rock layer,which are re-garded as porous media in railway embankment,is a process of heat and mass transfer.At present,the ripped-rock embankment,as a new type of embankment structure,has widely been used in the construction of Qinghai-Tibetan railway.However,because its ripped-rock layer is almost open in two bilateral boundaries and closed at top and bottom,and air can flow into/out of the ballast layer and ripped-rock layer,the convection and transfer heat patterns are very complicated in the embankment.Therefore,based on the temperature and geology conditions of the Qinghai-Tibetan Plateau,a nu-merical approach of the unsteady two-dimensional continuity,momentum(non-Darcy flow)and en-ergy equations of heat convection for incompressible fluid in porous media is provided to analyze the velocity and temperature characteristics of the ripped-rock embankment with different embankment heights under open boundary condition for the coming 50 years in this paper.The calculated results indicate that,due to the influence of the outside wind,the convective heat transfer mainly relies on the forced convection in the open ripped-rock embankment.Even if the air temperature will be warmed up by 2.6℃in the coming 50 years,it still has a better cooling effect on the underlying soils and a low temperature frozen-soil core is formed in the permafrost below it if the embankment is constructed in the regions whose present mean annual air temperature is?4.0℃.Furthermore,the cooling effect of high ripped-rock embankment is better than that of low embankment.This is because the wider bot-tom of high embankment has a more influence dimension on the underlying frozen soil.However,cardinal winds on the Qinghai-Tibetan Plateau disturb its convection pattern,so that an asymmetric temperature distribution occurs under high embankment and it is possible to induce a transverse un-even deformation of embankment,but no similar situation occurs under low embankment.This asymmetric temperature field problem should be considered when ripped-rock embankment is de-signed and constructed.

2-D CHARACTERISTICS LIKE MODEL AND OPEN BOUNDARY CONDITION FOR UNSTEADY OPEN CHANNEL FLOW MODELING

A characteristic like model is presented to calculate the two dimensional flow in open channels with finite or infinite dimensions. The comparisons between the computational results and experimental data show the model to be robust in simulating two dimensional unsteady flows. The comparisons also show the effectiveness of the open boundary condition in simulation of wave propagation process in an infinite domain with computational domain of finite dimension.

ANALYTIC METHOD FOR INVERSING THE OPEN BOUNDARY CONDITIONS IN A SEMI-CLOSED SEA AREA—CASE I FOR INVERSING THE TIDAL LEVELS AT OPEN BOUNDARY

In this paper, a computational case was employed to describe thecomputational procedure for inversing the tidal level open boundary conditions using an analyticmethod. The area for finding the solution is a circular area with a circular arc with the openingangle 60°-being the open boundary and the other circular arc being the solid wall boundary.Proceeding from the reestablished elliptic partial differential equation satisfied by the tidallevel function, the extended spectrum method was used to derive the general solution of the equationfor the sea of constant depth, and the impermeable solid wall condition (the second class boundarycondition) and the adequately specified open boundary conditions were then applied to determine theundetermined coefficients of the general solution, thus obtaining the tidal level distributionfunction. In this way, both the first and second class boundary values at the solid wall boundarywere obtained. With the above boundary values as the boundary conditions, the tidal level values atthe open boundary were then inversed by means of the general solution of tidal wave equation. Thevalidity of inversion method could be verified by comparing the inversed tidal level distributionswith the originally specified open boundary values.

An SPH wave-current flume using open boundary conditions

In this paper, a novel numerical wave-current flume is implemented based on the Smoothed Particle Hydrodynamics (SPH) method. The proposed flume is more stable and computationally efficient than conventional ones because it cancels wave paddles or sponge layers while using a non-reflective open boundary condition to simultaneously generate and absorb waves and currents. Numerical tests of nonlinear regular waves interacting with steady currents in the same/opposite directions indicate that the wave-current interactions mainly affect the horizontal velocity distributions in the water body, with little influence on the vertical movements. Water particle trajectories are stretched, and the mass transportation effects are enhanced when the waves and currents are in the same direction. When the directions are opposed, the trajectories, as well as the mass transportation, are compressed, suppressed and even reversed. The applications of solitary wave-current interaction over a submerged bump further show that the relative direction between the wave and the current has remarkable influence on the wave breaking pattern over an underwater obstacle.

ON THE HIGH PRECISION ADAPTIVE OPEN BOUNDARY CONDITIONS FOR TRANSIENT WAVES

The adaptive open boundary conditions (AOBC) designed by Chen and Zou for transient waves overcome the limitation of the existing open boundary conditions (OBC) and can be used for the cases of waves with arbitrary incident angles. In this paper a new family of AOBC has been designed on the basis of the AOBC with first order mentioned above. In comparing with all other OBC with the same order, this new family of AOBC has the highest precision. It can be generalized into 3D problems without difficulty and its forms in different curvilinear coordinate systems can be got very easily. The distinguished advantages above mentioned of the AOBC will be discussed in this paper.

Spectrum of the Open Asymmetric Simple Exclusion Process with Arbitrary Boundary Parameters

We study the one-dimensional asymmetric simple exclusion process （ASEP） with generic open boundaries （in- cluding current-counting deformation）, and obtain the exact solutions of this ASEP via the off-diagonal Bethe ansatz method. In particular, numerical results for the small size asymmetric simple exclusion process indicate that the spectrum obtained by the Bethe ansatz equations is complete. Moreover, we present the eigenvalue of the totally asymmetric exclusion process and the corresponding Bethe ansatz equations.

Entanglement in an anisotropic spin-1 Heisenberg chain

The entanglement in an anisotropic spin-1 Heisenberg chain with a uniform magnetic field is investigated. The ground-state entanglement will undergo two different kinds of transitions when the anisotropy △ and the amplitude of the magnetic field B are varied. The thermal entanglement of the nearest neighbour always declines when B increases no matter what the value of the anisotropy is. It is very interesting to note that the entanglement of the next-nearest neighbour can increase to a maximum at a certain magnetic field. Regardless of the boundary condition, the nearestneighbour entanglement always decreases and approaches to a constant value when the size of the system is very large. The constant value of open boundary condition is much larger than that of periodic boundary condition.

Computational Techniques of 2D Tidal Flow in Estuaries and Bays

Some problems in the numerical calculation of tidal flow in estuaries and bays, such as distribution bed roughness, relationship between model moving boundary and water volume balance, remedy of certain shortage under open boundary conditions, smooth transfer of the controlling message for the inner boundaries of nested model, can not be solved usually by means of the fundamental equations and computing mode adopted in the numerical model, but can be done by the measures which not only satisfy the physical features but also are convenient for operation. Based on the calculated samples of some areas of Modaomen, Lingdingyang and Huangmaohai of the Pearl River Estuary, and Shuidong Bay (a typical barrier- lagoon tidal channel) in Guangdong Province, method and process of calculation for the above mentioned problems are briefly presented in this paper.

STUDY ON THE ADJOINT METHOD IN DATA ASSIMILATION AND THE RELATED PROBLEMS

It is not reasonable that one can only use the adjoint of model in data assimilation. The simulated numerical experiment shows that for the tidal model, the result of the adjoint of equation is almost the same as that of the adjoint of model: the averaged absolute difference of the amplitude between observations and simulation is less than 5.0 cm and that of the phase-lag is less than 5.0°. The results are both in good agreement with the observed M2 tide in the Bohai Sea and the Yellow Sea. For comparison, the traditional methods also have been used to simulate M2 tide in the Bohai Sea and the Yellow Sea. The initial guess values of the boundary conditions are given first, and then are adjusted to acquire the simulated results that are as close as possible to the observations. As the boundary conditions contain 72 values, which should be adjusted and how to adjust them can only be partially solved by adjusting them many times. The satisfied results are hard to acquire even gigantic efforts are done. Here, the automation of the treatment of the open boundary conditions is realized. The method is unique and superior to the traditional methods. It is emphasized that if the adjoint of equation is used, tedious and complicated mathematical deduction can be avoided. Therefore the adjoint of equation should attract much attention.

Numerical study of the effects of Planetary Boundary Layer structure on the pollutant dispersion within built-up areas

The effects of different Planetary Boundary Layer（PBL） structures on pollutant dispersion processes within two idealized street canyon configurations and a realistic urban area were numerically examined by a Computational Fluid Dynamics（CFD） model. The boundary conditions of different PBL structures/conditions were provided by simulations of the Weather Researching and Forecasting model. The simulated results of the idealized 2D and 3D street canyon experiments showed that the increment of PBL instability favored the downward transport of momentum from the upper flow above the roof to the pedestrian level within the street canyon. As a result, the flow and turbulent fields within the street canyon under the more unstable PBL condition are stronger. Therefore, more pollutants within the street canyon would be removed by the stronger advection and turbulent diffusion processes under the unstable PBL condition. On the contrary, more pollutants would be concentrated in the street canyon under the stable PBL condition. In addition, the simulations of the realistic building cluster experiments showed that the density of buildings was a crucial factor determining the dynamic effects of the PBL structure on the flow patterns. The momentum field within a denser building configuration was mostly transported from the upper flow, and was more sensitive to the PBL structures than that of the sparser building configuration. Finally, it was recommended to use the Mellor-Yamada-Nakanishi-Niino（MYNN） PBL scheme, which can explicitly output the needed turbulent variables, to provide the boundary conditions to the CFD simulation.

THE EXPLICIT SOLUTIONS OF C_(p,q)^(k+α)-FORM FOR THE -EQUATIONS ON PSEUDOCONVEX OPEN SETS

In this paper, we study the integral solution operators for the -equations on pseudoconvex domains. As a generalization of [1] for the -dequations on pseudoconvex domains with boundary of class C∞, we obtain the explicit integral operator solutions of C -form for the -equations on pseudoconvex open sets with boundary of Ck (k≥0) and the sup-norm estimates of which solutions have similar as that [1] in form.