An analysis of the hydromagnetic free convective flow past a vertical infinite porous plate in a rotating fluid is carried out. The temperatures involved are assumed to be very large so that the radiative heat transfe...An analysis of the hydromagnetic free convective flow past a vertical infinite porous plate in a rotating fluid is carried out. The temperatures involved are assumed to be very large so that the radiative heat transfer is significant, which renders the problem very non-linear even on the assumption of a differential approximation for the radiative flux. The temperature and velocity fields are computed using a generic software tool based on the Nakamura finite difference scheme. The genericity of the software tool is in the sense that it is a common solution to the category of time dependent laminar fluid flows expressed in one spatial coordinate. The input equations, together with other relevant parameters, are transformed into postfix code which will be farther interpreted in the computation process. The influence of the various parameters entering into the problem is shown graphically followed by a discussion of results.展开更多
The fully anisotropic molecular overall tumbling model with methyl conformation jumps internal rotation among three equivalent sites is proposed,the overall tumbling rotation rates and the methyl internal rotation rat...The fully anisotropic molecular overall tumbling model with methyl conformation jumps internal rotation among three equivalent sites is proposed,the overall tumbling rotation rates and the methyl internal rotation rates of ponicidin are computed with this model from ~C relaxation parameters.展开更多
With the aid of symbolic computation Maple, the discrete Ablowitz–Ladik equation is studied via an algebra method, some new rational solutions with four arbitrary parameters are constructed. By analyzing related para...With the aid of symbolic computation Maple, the discrete Ablowitz–Ladik equation is studied via an algebra method, some new rational solutions with four arbitrary parameters are constructed. By analyzing related parameters, the discrete rogue wave solutions with alterable positions and amplitude for the focusing Ablowitz–Ladik equations are derived. Some properties are discussed by graphical analysis, which might be helpful for understanding physical phenomena in optics.展开更多
Poisson's equation is solved numerically by two direct methods, viz. Block Cyclic Reduction (BCR) method and Fourier Method. Qualitative and quantitative comparison between the numerical solutions obtained by two ...Poisson's equation is solved numerically by two direct methods, viz. Block Cyclic Reduction (BCR) method and Fourier Method. Qualitative and quantitative comparison between the numerical solutions obtained by two methods indicates that BCR method is superior to Fourier method in terms of speed and accuracy. Therefore. BCR method is applied to solve (?)2(?)= ζ and (?)2X= D from observed vorticity and divergent values. Thereafter the rotational and divergent components of the horizontal monsoon wind in the lower troposphere are reconstructed and are com pared with the results obtained by Successive Over-Relaxation (SOR) method as this indirect method is generally in more use for obtaining the streamfunction ((?)) and velocity potential (X) fields in NWP models. It is found that the results of BCR method are more reliable than SOR method.展开更多
A configurable U-Net architecture is trained to solve the multi-scale elliptical partial differential equations.The motivation is to improve the computational cost of the numerical solution of Navier-Stokes equations...A configurable U-Net architecture is trained to solve the multi-scale elliptical partial differential equations.The motivation is to improve the computational cost of the numerical solution of Navier-Stokes equations–the governing equations for fluid dynamics.Building on the underlying concept of V-Cycle multigrid methods,a neural network framework using U-Net architecture is optimized to solve the Poisson equation and Helmholtz equations–the characteristic form of the discretized Navier-Stokes equations.The results demonstrate the optimized U-Net captures the high dimensional mathematical features of the elliptical operator and with a better convergence than the multigrid method.The optimal performance between the errors and the FLOPS is the(3,2,5)case with 3 stacks of UNets,with 2 initial features,5 depth layers and with ELU activation.Further,by training the network with the multi-scale synthetic data the finer features of the physical system are captured.展开更多
In this article,we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the...In this article,we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the modified simple equation method.The proposed method is so powerful and effective to solve nonlinear space-time fractional differential equations by with modified Riemann–Liouville derivative.展开更多
Simulation of flow and transport through rough walled rock fractures is investigated using the latticeBoltzmann method （LBM） and random walk （RW）, respectively. The numerical implementation isdeveloped and validat...Simulation of flow and transport through rough walled rock fractures is investigated using the latticeBoltzmann method （LBM） and random walk （RW）, respectively. The numerical implementation isdeveloped and validated on general purpose graphic processing units （GPGPUs）. Both the LBM and RWmethod are well suited to parallel implementation on GPGPUs because they require only next-neighbourcommunication and thus can reduce expenses. The LBM model is an order of magnitude faster onGPGPUs than published results for LBM simulations run on modern CPUs. The fluid model is verified forparallel plate flow, backward facing step and single fracture flow; and the RWmodel is verified for pointsourcediffusion, Taylor-Aris dispersion and breakthrough behaviour in a single fracture. Both algorithmsplace limitations on the discrete displacement of fluid or particle transport per time step to minimise thenumerical error that must be considered during implementation. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.展开更多
The time accuracy of the exponentially accurate Fourier time spectral method（TSM） is examined and compared with a conventional 2nd-order backward difference formula（BDF） method for periodic unsteady flows. In part...The time accuracy of the exponentially accurate Fourier time spectral method（TSM） is examined and compared with a conventional 2nd-order backward difference formula（BDF） method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth subsonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the prediction of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higherorder harmonic contents to the local pressure fluctuations,a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method.The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.展开更多
文摘An analysis of the hydromagnetic free convective flow past a vertical infinite porous plate in a rotating fluid is carried out. The temperatures involved are assumed to be very large so that the radiative heat transfer is significant, which renders the problem very non-linear even on the assumption of a differential approximation for the radiative flux. The temperature and velocity fields are computed using a generic software tool based on the Nakamura finite difference scheme. The genericity of the software tool is in the sense that it is a common solution to the category of time dependent laminar fluid flows expressed in one spatial coordinate. The input equations, together with other relevant parameters, are transformed into postfix code which will be farther interpreted in the computation process. The influence of the various parameters entering into the problem is shown graphically followed by a discussion of results.
文摘The fully anisotropic molecular overall tumbling model with methyl conformation jumps internal rotation among three equivalent sites is proposed,the overall tumbling rotation rates and the methyl internal rotation rates of ponicidin are computed with this model from ~C relaxation parameters.
基金Supported by the Beijing Natural Science Foundation under Grant No.1153004China Postdoctoral Science Foundation under Grant No.2015M570161the Natural Science Foundation of China under Grant No.61471406
文摘With the aid of symbolic computation Maple, the discrete Ablowitz–Ladik equation is studied via an algebra method, some new rational solutions with four arbitrary parameters are constructed. By analyzing related parameters, the discrete rogue wave solutions with alterable positions and amplitude for the focusing Ablowitz–Ladik equations are derived. Some properties are discussed by graphical analysis, which might be helpful for understanding physical phenomena in optics.
文摘Poisson's equation is solved numerically by two direct methods, viz. Block Cyclic Reduction (BCR) method and Fourier Method. Qualitative and quantitative comparison between the numerical solutions obtained by two methods indicates that BCR method is superior to Fourier method in terms of speed and accuracy. Therefore. BCR method is applied to solve (?)2(?)= ζ and (?)2X= D from observed vorticity and divergent values. Thereafter the rotational and divergent components of the horizontal monsoon wind in the lower troposphere are reconstructed and are com pared with the results obtained by Successive Over-Relaxation (SOR) method as this indirect method is generally in more use for obtaining the streamfunction ((?)) and velocity potential (X) fields in NWP models. It is found that the results of BCR method are more reliable than SOR method.
文摘A configurable U-Net architecture is trained to solve the multi-scale elliptical partial differential equations.The motivation is to improve the computational cost of the numerical solution of Navier-Stokes equations–the governing equations for fluid dynamics.Building on the underlying concept of V-Cycle multigrid methods,a neural network framework using U-Net architecture is optimized to solve the Poisson equation and Helmholtz equations–the characteristic form of the discretized Navier-Stokes equations.The results demonstrate the optimized U-Net captures the high dimensional mathematical features of the elliptical operator and with a better convergence than the multigrid method.The optimal performance between the errors and the FLOPS is the(3,2,5)case with 3 stacks of UNets,with 2 initial features,5 depth layers and with ELU activation.Further,by training the network with the multi-scale synthetic data the finer features of the physical system are captured.
文摘In this article,we establish new and more general traveling wave solutions of space-time fractional Klein–Gordon equation with quadratic nonlinearity and the space-time fractional breaking soliton equations using the modified simple equation method.The proposed method is so powerful and effective to solve nonlinear space-time fractional differential equations by with modified Riemann–Liouville derivative.
文摘Simulation of flow and transport through rough walled rock fractures is investigated using the latticeBoltzmann method （LBM） and random walk （RW）, respectively. The numerical implementation isdeveloped and validated on general purpose graphic processing units （GPGPUs）. Both the LBM and RWmethod are well suited to parallel implementation on GPGPUs because they require only next-neighbourcommunication and thus can reduce expenses. The LBM model is an order of magnitude faster onGPGPUs than published results for LBM simulations run on modern CPUs. The fluid model is verified forparallel plate flow, backward facing step and single fracture flow; and the RWmodel is verified for pointsourcediffusion, Taylor-Aris dispersion and breakthrough behaviour in a single fracture. Both algorithmsplace limitations on the discrete displacement of fluid or particle transport per time step to minimise thenumerical error that must be considered during implementation. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.
基金supported by the State Scholarship Fund of the China Scholarship Council (Grant 2009629129)
文摘The time accuracy of the exponentially accurate Fourier time spectral method（TSM） is examined and compared with a conventional 2nd-order backward difference formula（BDF） method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth subsonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the prediction of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higherorder harmonic contents to the local pressure fluctuations,a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method.The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.
