A Family of High_order Accuracy Explicit Difference Schemes for Solving 2-D Parabolic Partial Differential Equation

A family of high_order accuracy explicit difference schemes for solving 2_dimension parabolic P.D.E. are constructed. Th e stability condition is r=Δt/Δx 2=Δt/Δy 2【1/2 and the truncation err or is O(Δt 3+Δx 4).

Stability of finite difference numerical simulations of acoustic logging-while-drilling with different perfectly matched layer schemes

In acoustic logging-while-drilling （ALWD） finite difference in time domain （FDTD） simulations, large drill collar occupies, most of the fluid-filled borehole and divides the borehole fluid into two thin fluid columns （radius -27 mm）. Fine grids and large computational models are required to model the thin fluid region between the tool and the formation. As a result, small time step and more iterations are needed, which increases the cumulative numerical error. Furthermore, due to high impedance contrast between the drill collar and fluid in the borehole （the difference is 〉30 times）, the stability and efficiency of the perfectly matched layer （PML） scheme is critical to simulate complicated wave modes accurately. In this paper, we compared four different PML implementations in a staggered grid finite difference in time domain （FDTD） in the ALWD simulation, including field-splitting PML （SPML）, multiaxial PML（M- PML）, non-splitting PML （NPML）, and complex frequency-shifted PML （CFS-PML）. The comparison indicated that NPML and CFS-PML can absorb the guided wave reflection from the computational boundaries more efficiently than SPML and M-PML. For large simulation time, SPML, M-PML, and NPML are numerically unstable. However, the stability of M-PML can be improved further to some extent. Based on the analysis, we proposed that the CFS-PML method is used in FDTD to eliminate the numerical instability and to improve the efficiency of absorption in the PML layers for LWD modeling. The optimal values of CFS-PML parameters in the LWD simulation were investigated based on thousands of 3D simulations. For typical LWD cases, the best maximum value of the quadratic damping profile was obtained using one do. The optimal parameter space for the maximum value of the linear frequency-shifted factor （a0） and the scaling factor （β0） depended on the thickness of the PML layer. For typical formations, if the PML thickness is 10 grid points, the global error can be reduced to 〈1% using the optimal PML parameters, and the error will decrease as the PML thickness increases.

Parallel EOI algorithm with different insertion schemes

A parallel embedding overlapped iterative (EOI) algorithm about classicimplicit equations with asymmetric Saul'yev schemes (CIS-EOI) to solve one-dimensional diffusionequations is discussed to improve the properties of the segment classic implicit iterative (SCII)algorithm. The structure of CIS-EOI method is given and the stability of scheme and convergence ofiteration are proved by matrix method. The property of gradual-approach convergence is alsodiscussed. It has been shown that the convergent rate is faster and the property of gradual-approachconvergence also becomes better with the increasing of the net point in subsystems than with theSCII algorithm. The simulation examples show that the parallel iterative algorithm with a differentinsertion scheme CIS-EOI is more effective.

Application of the two different salinity parameterization schemes in the sea ice model

In this study, we mainly introduce two salinity parameterization schemes used in Sea Ice Simulator （SIS）, that is, isosaline scheme and salinity profile scheme. Comparing the equation of isosaline scheme with that of salinity profile scheme, we found that there was one different term between the two schemes named the salinity different term. The thermodynamic effect of the salinity difference term on sea ice thickness and sea ice concentration showed that： in the freezing processes from November to next May, the sea ice temperature could rise on the influence of the salinity difference term and restrain sea ice freezing; at the first melting phase from June to August, the upper ice melting rate was faster than the lower ice melting rate. Then sea ice temperature could rise and accelerate the sea ice melting; at the second melting phase from September to October, the upper ice melting rate was slower than the lower ice melting rate, then sea ice temperature could decrease and restrain sea ice melting. However, the effect of the salinity difference term on the sea ice thickness and sea ice concentration was weak. To analyze the impacts of the salinity different term on Arctic sea ice thickness and sea ice concentration, we also designed several experiments by introducing the two salinity parameterizations to the ice-ocean coupled model, Modular Ocean Model （MOM4）, respectively. The simulated results confirmed the previous results of formula derivation.

Stability Analysis of Inverse Lax-Wendroff Procedure for a High order Compact Finite Difference Schemes

This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary even order of accuracy.The main idea is to make use of the lower order compact schemes recursively,so as to obtain the high order compact schemes formally.Moreover,the schemes can be implemented efficiently by solving a series of tridiagonal systems recursively or the fast Fourier transform(FFT).With mathematical induction,the eigenvalues of the proposed differencing operators are shown to be bounded away from zero,which indicates the positive definiteness of the operators.To obtain numerical boundary conditions for the high order schemes,the simplified inverse Lax-Wendroff(SILW)procedure is adopted and the stability analysis is performed by the Godunov-Ryabenkii method and the eigenvalue spectrum visualization method.Various numerical experiments are provided to demonstrate the effectiveness and robustness of our algorithms.

The Sensitivity of Numerical Simulation of the East Asian Monsoon to Different Cumulus Parameterization Schemes

In this paper, a 5-level spectral AGCM is used to examine the sensitivity of simulated East Asian summer monsoon circulation and rainfall to cumulus parameterization schemes. From the simulated results of East Asian monsoon circulations and rainfalls during the summers of 1987 and 1995, it is shown that the Kuo′s convective parameterization scheme is more suitable for the numerical simulation of East Asian summer monsoon rainfall and circulation. This may be due to that the cumulus in the rainfall system is not strong in the East Asian monsoon region.

Intercomparison of different physics schemes in the WRF model over the Asian summer monsoon region

Enhancing the ability of the WRF model in simulating a large area covering the West Pacific Ocean, China's Mainland, and the East Indian Ocean is very important to improve prediction of the East Asian monsoon climate. The objective of this study is to identify a reasonable configuration of physical parameterization schemes to simulate the precipitation and temperature in this large area. The Mellor-Yamada-Janjic （MYJ） and Yonsei University （YSU） PBL schemes, the WSM3 and WSM5 microphysics schemes, and the Betts-Miller-Janjic （BMJ） and Tiedtke cumulus schemes are compared through simulation of the regional climate of summer 2008. All cases exhibit a similar spatial distribution of temperature as observed, and the spatial correlation coefficients are all higher than 0.95. The cases combining MY J, WSM3/WSM5, and BMJ have the smallest biases of temperature. The choice of PBL scheme has a significant effect on precipitation in such a large area. The cases with MYJ reproduce a better distribution of rain belts, while YSU strongly overestimates the precipitation intensity. The precipitation simulated using WSM3 is similar to that using WSM5. The BMJ cumulus scheme combined with the MYJ PBL scheme has a smaller bias of precipitation. However, the Tiedtke scheme reproduces the precipitation pattern better, especially over the ITCZ.

MJO ensemble prediction in BCC-CSM1.1(m)using different initialization schemes

The Madden–Julian Oscillation（MJO）is a dominant mode of tropical intraseasonal variability（ISV）and has prominent impacts on the climate of the tropics and extratropics.Predicting the MJO using fully coupled climate system models is an interesting and important topic.This paper reports upon a recent progress in MJO ensemble prediction using the climate system model of the Beijing Climate Center,BCC-CSM1.1（m）;specifically,the development of three different initialization schemes in the BCC ISV/MJO prediction system,IMPRESS.Three sets of 10-yr hindcasts were separately conducted with the three initialization schemes.The results showed that the IMPRESS is able to usefully predict the MJO,but is sensitive to the initialization scheme used and becomes better with the initialization of moisture.In addition,a new ensemble approach was developed by averaging the predictions generated from the different initialization schemes,helping to address the uncertainty in the initial values of the MJO.The ensemble-mean MJO prediction showed significant improvement,with a valid prediction length of about 20 days in terms of the different criteria,i.e.,a correlation score beyond 0.5,a RMSE lower than 1.414,or a mean square skill score beyond 0.This study indicates that utilizing the different initialization schemes of this climate model may be an efficient approach when forming ensemble predictions of the MJO.

Sensitivity Study of the South China Sea Summer Monsoon in 1998 to Different Cumulus Parameterization Schemes

In this study, the improved high-resolution regional climate model of the China National Climate Center （RegCM_NCC） is used to examine the sensitivity of the simulated circulation and rainfall during the South China Sea summer monsoon （SCSSM） period during 1998 in an effort to compare to other cumulus param- eterization schemes. The investigation has indicated that the model is capable of simulating the seasonal march of the SCSSM and that the results were very sensitive to the choice of cumulus parameterization schemes. It seems that the Kuo cumulus parameterization scheme simulates the process of the SCSSM onset reasonably well, which can reproduce the onset timing and dramatic changes before and after the onset, especially the upper- and lower-level wind-fields. However, there are still some discrepancies between the simulations and observations. For example, the model can not completely simulate the intensity of the rainfall or the location of the western Pacific subtropical high as well as the feature of the rapid northward propagation of seasonal rain belt.

Impacts of different radiation schemes on the prediction of solar radiation and photovoltaic power

The output power of a photovoltaic system largely depends on the amount of solar radiation that can be received by the photovoltaic panel, and the solar radiation energy reaching the ground is affected by the radiation transmission process. However, in engineering practice, numerical simulation prediction schemes tend to adopt a kind of radiation scheme, and the prediction of solar radiation and photovoltaic power cannot always meet the prediction accuracy. In this paper, NCEP-NCAR reanalysis data are used as the initial field, and a variety of radiation parameterization schemes are used to produce simulations for the Xinjiang area. Through analysis of examples, it is found that the simulation results differ greatly depending on the radiation parameterization scheme employed, with the maximum absolute error of the total radiation and the predicted power being 106.67 W m-2 and 3.5 MW, respectively. Meanwhile, the mean absolute percentage error of the total radiation ranges from 8.6% to 17.3%, and that of the predicted power from 11.3% to 20.2%. Having analyzed the simulation results of the different radiation parameterization schemes, we conclude that the RRTM/Dudhia and CAM （Community Atmospheric Model） schemes are the most appropriate when under clear-weather conditions.

Uncertainty in Dust Budget over East Asia Simulated by WRF/Chem with Six Different Dust Emission Schemes

In this study, the dependence of dust budgets on dust emission schemes is investigated through the simulation of dust storm events, which occurred during 14–25 March 2002, over East Asia, by the Weather Research and Forecasting with Chemistry(WRF/Chem) model coupled with six dust emission schemes. Generally, this model can reasonably reproduce the spatial distribution of surface dust concentration; however, the simulated total dust budget differs significantly with different emission schemes. Moreover, uncertainties in the simulated dust budget vary among regions. It is suggested that the dust emission scheme affects the regional dust budget directly through its impact on the total emitted dust amount; however, the inflow and outflow of dust aerosols simulated by different schemes within a region also depend on the geographical location of the dust emission region. Furthermore, the size distribution of dust particles for a specific dust emission scheme has proven to be important for dust budget calculation due to the dependence of dust deposition amount on dust size distribution.

Impact of Different Cloud Microphysics Parameterization Schemes on Typhoon Intensity and Structure

The impact of different cloud microphysics parameterization schemes on the intensity and structure of the Super-strong Typhoon Rammasun(1409)in 2014 is investigated using the Weather Research and Forecasting model version 3.4 with eight cloud microphysics parameterization schemes.Results indicate that the uncertainty of cloud microphysics schemes results in typhoon forecast uncertainties,which increase with forecast time.Typhoon forecast uncertainty primarily affects intensity predictions,with significant differences in predicted typhoon intensity using various cloud microphysics schemes.Typhoon forecast uncertainty also affects the predicted typhoon structure.Greater typhoon intensity is accompanied by smaller vortex width,tighter vortex structure,stronger wind in the middle and lower troposphere,greater height of the strong wind region,smaller thickness of the eyewall and the outward extension of the eyewall,and a warmer warm core at upper levels of the eye.The differences among the various cloud microphysics schemes lead to different amounts and distributions of water vapor and hydrometeors in clouds.Different hydrometeors have different vertical distributions.In the radial direction,the maxima for the various hydrometeors forecast by a single cloud microphysics scheme are collocated with each other and with the center of maximum precipitation.When the hydrometeor concentration is high and hydrometeors exist at lower altitudes,more precipitation often occurs.Both the vertical and horizontal winds are the strongest at the location of maximum precipitation.Results also indicate that typhoon intensities forecast by cloud microphysics schemes containing graupel processes are noticeably greater than those forecast by schemes without graupel processes.Among the eight cloud microphysics schemes investigated,typhoon intensity forecasts using the WRF Single-Moment 6-class and Thompson schemes are the most accurate.

THE IMPACT OF CUMULUS PARAMETERIZATIONS AND MICROPHYSICS SCHEMES UNDER DIFFERENT COMBINATIONS ON TYPHOON TRACK PREDICTION

This study examines the effects of cumulus parameterizations and microphysics schemes on the track forecast of typhoon Nabi using the Weather Research Forecast model. The study found that the effects of cumulus parameterizations on typhoon track forecast were comparatively strong and the typhoon track forecast of Kain-Fritsch (KF) was superior to that of Betts-Miller (BM). When KF was selected, the simulated results would be improved if microphysics schemes were selected than otherwise. The results from Ferrier, WSM6, and Lin were very close to those in the best track. KF performed well with the simulations of the western extension and eastern contraction changes of a North Pacific high as well as the distribution and strength of the typhoon wind field.

A FAMILY OF HIGH-ORDER ACCURACY EXPLICIT DIFFERENCE SCHEMES WITH BRANCHING STABILITY FOR SOLVING 3-D PARABOLIC PARTIAL DIFFERENTIAL EQUATION

A family of high-order accuracy explict difference schemes for solving 3-dimension parabolic P. D. E. is constructed. The stability condition is r = Deltat/Deltax(2) Deltat/Deltay(2) = Deltat/Deltaz(2) < 1/2 ,and the truncation error is 0(<Delta>t(2) + Deltax(4)).

Comparative Studies of Different Mesoscale Convection Parameterization Schemes in the Simulation of Mei-Yu Front Heavy Rain

The mei-yu front heavy rainstorms occurred over Nanjing on 3 5 and 8 9 July 2003 and were simulated in this paper using the Weather Research and Forecasting Model (WRFv3.1) with various mesoscale convection parameterization schemes (MCPSs). The simulations show that the temporal and spatial evolution and distribution of rainstorms can be modeled; however, there was incongruity between the comparative simulations of four different MCPSs and the observed data. These disparities were exhibited in the simulations of both the 24-hour surface rainfall total and the hourly precipitation rate. Further analysis revealed that the discrepancies of vertical velocity and the convective vorticity vector (CVV) between the four simulations were attributed to the deviation of rainfall values. In addition, the simulations show that the mid-scale convection, particularly the mesoscale convection system (MCS) formation, can be well simulated with the proper mesoscale convection parameterization schemes and may be a crucial factor of the mei-yu front heavy rainstorm. These results suggest that, in an effort to enhance simulation and prediction of heavy rainfall and rainstorms, subsequent studies should focus on the development and improvement of MCPS.

Theoretical and Numerical Study of Stress and Thermo-Optic in Photonic Crystal Fiber Laser in Different Pump Schemes

In this paper, we present a study of thermal, average power scaling, change in index of refraction and stress in photonic crystal fiber lasers with different pump schemes: forward pump scheme, backward pump scheme, forward pump scheme with reflection of 98%, backward pump scheme with reflection of 98% and bi-directional pump scheme. We show that management of thermal effects in fiber lasers will determine the efficiency and success of scaling-up efforts. In addition, we show that the most suitable scheme is the bi-directional.

Sensitivity of Numerical Simulations of the East Asian Summer Monsoon Rainfall and Circulation to Different Cumulus Parameterization Schemes

A 5-level spectral AGCM (ImPKU-SLAGCM) is used to examine the sensitivity of the simulated results of the summer monsoon rainfall and circulation in East Asia to different cumulus parameterization schemes in the climatological-mean case and in the cases of weak and strong Asian summer monsoons, respectively. The results simulated with the Arakawa-Schubert's(hereafter A-S's), Kuo's and Manabe's cumulus parameterization schemes show that these simulated distributions of the summer monsoon rainfall and circulation in East Asia depend strongly on the cumulus parameterization schemes either in the climatological-mean case or in the cases of weak and strong Asian summer monsoons. From the simulated results, it might be shown that the Kuo scheme appears to be more suitable for the simulation of the summer monsoon rainfall and circulation in East Asia than the A-S scheme or the Manabe scheme, although the A-S scheme is somewhat better in the simulations of the tropical rainfall. This might be due to that the Kuo's cumulus parameterization scheme is able to reflect well the characteristics of rainfall cloud system in the East Asian summer monsoon region, where the rainfall system used to be a mixing of cumulus and stratus.

Numerical Investigation of Different Airflow Schemes in a Real Operating Theatre

A study on performances of different ventilation schemes provided by vertical and horizontal uni-directional air flow was carried out in a standard orthopaedic operating theatre (OT). Starting from our previous studies of a real OT under operating use conditions, in this research different air flow configurations, considering some air curtain solutions on the ceiling and at the sliding door always assumed to be open as a basic boundary condition, were investigated by numerical simulations. Indoor air quality (IAQ) indexes and thermal comfort parameters, deduced from simulation results were calculated and discussed referring to the best performance and efficacy between the air flow schemes to contrast the incorrect use conditions of the OT. Referring to the studied schemes, the reciprocal comparison emphasizes that a successful outcome in preventing surgical site infection can depend as much on resolving human factors (i.e. operational use conditions, door opening/closing), as on overcoming physical and technical obstacles.

Unconditionally Explicit Stable Difference Schemes for Solving Some Linear and Non-Linear Parabolic Differential Equation

We present the numerical method for solution of some linear and non-linear parabolic equation. Using idea [1], we will present the explicit unconditional stable scheme which has no restriction on the step size ratio k/h2 where k and h are step sizes for space and time respectively. We will also present numerical results to justify the present scheme.

Analysis of Extreme Rainfall Event with Different Microphysics and Parameterization Schemes in WRF Model

In the present study, the imitation of heavy rainfall event which occurred over Jharkhand during 18 August 2016 was taken as a case study. Weather Research and Forecasting (WRF) model has been utilized for this study. National Centers for Environmental Prediction (NCEP) analysis data is compared with GSMaP data with different combination of physical parameterization scheme like microphysics (MP) and cumulus parameterization (CP). In the present study, three MP schemes: Kessler scheme, Lin et al. scheme and WRF Single-moment 6-class scheme with combination of three CP schemes: Betts-Miller-Janjic scheme, Multi-scale Kain-Fritsch scheme and New simplified Arakawa-Schubert scheme have been used. The model predicted humidity, temperature and precipitation were compared with the GSMaP product. The model nicely depicted the cloud pattern and recognized the rain event spatially. The obtained result shows that the model overestimates the precipitation for all the schemes.