A high order boundary scheme to simulate complex moving rigid body under impingement of shock wave

In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff(ILW) procedure developed in the previous work(TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15),6023–6036(2011)), in which the authors only considered the translation of the rigid body,we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.

Applicability of Temperature Discrete Equation to NMRF Boundary Layer Scheme in GRAPES Model

By deriving the discrete equation of the parameterized equation for the New Medium-Range Forecast(NMRF)boundary layer scheme in the GRAPES model,the adjusted discrete equation for temperature is obviously different from the original equation under the background of hydrostatic equilibrium and adiabatic hypothesis.In the present research,three discrete equations for temperature in the NMRF boundary layer scheme are applied,namely the original(hereafter NMRF),the adjustment(hereafter NMRF-gocp),and the one in the YSU boundary-layer scheme(hereafter NMRF-TZ).The results show that the deviations of height,temperature,U and V wind in the boundary layer in the NMRF-gocp and NMRF-TZ experiments are smaller than those in the NMRF experiment and the deviations in the NMRF-gocp experiment are the smallest.The deviations of humidity are complex for the different forecasting lead time in the three experiments.Moreover,there are obvious diurnal variations of deviations from these variables,where the diurnal variations of deviations from height and temperature are similar and those from U and V wind are also similar.However,the diurnal variation of humidity is relatively complicated.The root means square errors of 2m temperature(T2m)and 10m speed(V10m)from the three experiments show that the error of NMRF-gocp is the smallest and that of NMRF is the biggest.There is also a diurnal variation of T2m and V10m,where T2m has double peaks and V10m has only one peak.Comparison of the discrete equations between NMRF and NMRF-gocp experiments shows that the deviation of temperature is likely to be caused by the calculation of vertical eddy diffusive coefficients of heating,which also leads to the deviations of other elements.

Development of a Single-Column Model in RegCM4 and Its Preliminary Application for Evaluating PBL Schemes in Simulating the Dry Convection Boundary Layer

A single-column model(SCM)is developed in the regional climate model RegCM4.The evolution of a dry convection boundary layer(DCBL)is used to evaluate this SCM.Moreover,four planetary boundary layer(PBL)schemes,namely the Holtslag-Boville scheme(HB),Yonsei University scheme(YSU),and two University of Washington schemes(UW01,Grenier-Bretherton-Mc Caa scheme and UW09,Bretherton-Park scheme),are compared by using the SCM approach.A large-eddy simulation(LES)of the DCBL is performed as a benchmark to examine how well a PBL parameterization scheme reproduces the LES results,and several diagnostic outputs are compared to evaluate the schemes.The results show that the SCM is properly constructed.In general,with the DCBL case,the YSU scheme performs best for reproducing the LES results,which include well-mixed features and vertical sensible heat fluxes;the simulated wind speed,turbulent kinetic energy,entrainment flux,and height of the entrainment zone are all underestimated in the UW09;the UW01 has all those biases of the UW09 but larger,and the simulated potential temperature is not well mixed;the HB is the least skillful scheme,by which the PBL height,entrainment flux,height of the entrainment zone,and the vertical gradients within the mixed layer are all overestimated,and a inversion layer near the top of the surface layer is wrongly simulated.Although more cases and further testing are required,these simulations show encouraging results towards the use of this SCM framework for evaluating the simulated physical processes by the RegCM4.

Numerical Experiments of Three Boundary Layer Parameterization Schemes on Simulation Results of Low-vortex Rainstorm Weather in Langfang Region

Using mesoscale numerical model WRFV3.7,simulation tests of a low-vortex rainstorm were carried out in Langfang area,and simulation results of three boundary layer parameterization schemes(MYJ,YSU,ACM2)were contrasted.The results showed that the rainstorm in Langfang area had better dynamic condition.By the influence of northeast cold vortex,cold vortex at high altitude cooperated with the surface wind speed convergence,which provided better dynamic condition for strong convective rainfall.Three boundary layer parameterization schemes all simulated surface wind speed convergence of rainstorm center.Simulation results of 24-h rainfall distribution showed that the simulation of YSU scheme was better than ACM2 and MYJ.The simulation results of flow field and temperature field also verified that YSU scheme was better than other schemes.

Limitations of Lattice Boltzmann Modeling of Micro-Flows in Complex Nanopores

The multiscale transport mechanism of methane in unconventional reservoirs is dominated by slip and transition flows resulting from the ultra-low permeability of micro/nano-scale pores,which requires consideration of the microscale and rarefaction effects.Traditional continuum-based computational fluid dynamics(CFD)becomes problematic when modeling micro-gaseous flow in these multiscale pore networks because of its disadvantages in the treatment of cases with a complicated boundary.As an alternative,the lattice Boltzmann method(LBM),a special discrete form of the Boltzmann equation,has been widely applied to model the multi-scale and multi-mechanism flows in unconventional reservoirs,considering its mesoscopic nature and advantages in simulating gas flows in complex porous media.Consequently,numerous LBM models and slip boundary schemes have been proposed and reported in the literature.This study investigates the predominately reported LBM models and kinetic boundary schemes.The results of these LBM models systematically compare to existing experimental results,analytical solutions of Navier-Stokes,solutions of the Boltzmann equation,direct simulation of Monte Carlo(DSMC)and information-preservation DSMC(IP_DSMC)results,as well as the numerical results of the linearized Boltzmann equation by the discrete velocity method(DVM).The results point out the challenges and limitations of existing multiple-relaxation-times LBM models in predicting micro-gaseous flow in unconventional reservoirs.

Impacts of boundary layer parameterization schemes and air-sea coupling on WRF simulation of the East Asian summer monsoon

The planetary boundary layer （PBL） scheme in the regional climate model （RCM） has a significant impact on the interactions and exchanges of moisture, momentum, and energy between land, ocean, and atmosphere; however, its uncertainty will cause large systematic biases of RCM. Based on the four different PBL schemes （YSU, ACM2, Boulac, and MYJ） in Weather Research and Forecasting （WRF） model, the impacts of these schemes on the simulation of circulation and precipitation during the East Asian summer monsoon （EASM） are investigated. The simulated results of the two local turbulent kinetic energy （TKE） schemes, Boulac and MYJ, are more consistent with the observations than those in the two nonlocal closure schemes, YSU and ACM2. The former simulate more reasonable low-level southwesterly flow over East China and west pacific subtropical high （WPSH） than the latter. As to the modeling of summer monsoon precipitation, both the spatial distributions and temporal evolutions from Boulac and MTT are also better than those in YSU and ACM2 schemes. In addition, through the comparison between YSU and Boulac experiments, the differences from the results of EASM simulation are more obvious over the oceanic area. In the experiments with the nonlocal schemes YSU and ACM2, the boundary layer mixing processes are much stronger, which lead to produce more sea surface latent heat flux and enhanced convection, and finally induce the overestimated precipitation and corresponding deviation of monsoon circulation. With the further study, it is found that the absence of air-sea interaction in WRF may amplify the biases caused by PBL scheme over the ocean. Consequently, there is a reduced latent heat flux over the sea surface and even more reasonable EASM simulation, if an ocean model coupled into WRF.

EXPLICIT DISSIPATIVE SCHEMES FOR BOUNDARY PROBLEMS OF GENERALIZED SCHRDINGER SYSTEMS

In this paper, the author constructs a class of explicit schemes, spanning two time levels, forthe initial--boundary-value problems of generalized nonlinear Schrodinger systems, and proves theconvergence of these schemes with a series of prior estimates. For a single Schrodinger equation, theschemes are identical with those of the article [1].

A Consistent Fourth-Order Compact Finite Difference Scheme for Solving Vorticity-Stream Function Form of Incompressible Navier-Stokes Equations

The inconsistent accuracy and truncation error in the treatment of boundary usually leads to performance defects,such as decreased accuracy and even numerical instability,of the entire computational method,especially for higher order methods.In this work,we construct a consistent fourth-order compact finite difference scheme for solving two-dimensional incompressible Navier-Stokes(N-S)equations.In the pro-posed method,the main truncation error term of the boundary scheme is kept the same as that of the interior compact finite difference scheme.With such a feature,the nu-merical stability and accuracy of the entire computation can be maintained the same as the interior compact finite difference scheme.Numerical examples show the effec-tiveness and accuracy of the present consistent compact high order scheme in L^(∞).Its application to two dimensional lid-driven cavity flow problem further exhibits that un-der the same condition,the computed solution with the present scheme is much close to the benchmark in comparison to those from the 4^(th)order explicit scheme.The compact finite difference method equipped with the present consistent boundary technique im-proves much the stability of the whole computation and shows its potential application to incompressible flow of high Reynolds number.

Effects of local and non-local closure PBL schemes on the simulation of Super Typhoon Mangkhut(2018)

With the convection-permitting simulation of Super Typhoon Mangkhut(2018)with a 3 km resolution for 10.5 days using mesoscale numerical model,Weather Research and Forecasting Model Version 4.1(WRFV4.1),the influences of local closure QNSE planetary boundary layer(PBL)scheme and non-local closure GFS planetary boundary layer scheme on super typhoon Mangkhut are mainly discussed.It is found that in terms of either track or intensity of typhoon,the local closure QNSE scheme is better than the non-local closure GFS scheme.Local and non-local closure PBL schemes have a large influence on both the intensity and the structure of typhoon.The maximum intensity difference of the simulated typhoon is 50 hPa.The intensity of typhoon is closely related to its variations in structure.In the rapid intensification stage,the typhoon simulated by the QNSE scheme has a larger friction velocity,stronger surface latent heat flux,sensible heat flux and vapor flux,related to a higher boundary height and stronger vertical mixing.The latent heat flux and sensible heat flux on the surface conveyed energy upward for the typhoon while the water vapor was transported upward through vertical mixing.While the water vapor condensed,the latent heat was released,which further warmed the typhoon eyewall,strengthening the convection.The stronger winds also intensified the vertical mixing and the warm-core structure,further strengthened the typhoon.The differences in surface layer schemes dominated the differences between the two simulations.