The local time-stepping(LTS)algorithm is an adaptive method that adjusts the time step by selecting suitable intervals for different regions based on the spatial scale of each cell and water depth and flow velocity be...The local time-stepping(LTS)algorithm is an adaptive method that adjusts the time step by selecting suitable intervals for different regions based on the spatial scale of each cell and water depth and flow velocity between cells.The method can be optimized by calculating the maximum power of two of the global time step increments in the domain,allowing the optimal time step to be approached throughout the grid.To verify the acceleration and accuracy of LTS in storm surge simulations,we developed a model to simulate astronomical storm surges along the southern coast of China.This model employs the shallow water equations as governing equations,numerical discretization using the finite volume method,and fluxes calculated by the Roe solver.By comparing the simulation results of the traditional global time-stepping algorithm with those of the LTS algorithm,we find that the latter fit the measured data better.Taking the calculation results of Typhoon Sally in 1996 as an example,we show that compared with the traditional global time-stepping algorithm,the LTS algorithm reduces computation time by 2.05 h and increases computation efficiency by 2.64 times while maintaining good accuracy.展开更多
The effect of ionospheric delay on the ground-based augmentation system under normal conditions can be mitigated by determining the value of the nominal ionospheric gradient(σvig).The nominal ionospheric gradient is ...The effect of ionospheric delay on the ground-based augmentation system under normal conditions can be mitigated by determining the value of the nominal ionospheric gradient(σvig).The nominal ionospheric gradient is generally obtained from Continuously Operating Reference Stations data by using the spatial single-difference method(mixed-pair,station-pair,or satellite-pair)or the temporal single-difference method(time-step).The time-step method uses only a single receiver,but it still contains ionospheric temporal variations.We introduce a corrected time-step method using a fixed-ionospheric pierce point from the geostationary equatorial orbit satellite and test it through simulations based on the global ionospheric model.We also investigate the effect of satellite paths on the corrected time-step method in the region of the equator,which tends to be in a more north–south direction and to have less coverage for the east–west ionospheric gradient.This study also addresses the limitations of temporal variation correction coverage and recommends using only the correction from self-observations.All processes are developed under simulations because observational data are still difficult to obtain.Our findings demonstrate that the corrected time-step method yieldsσvig values consistent with other approaches.展开更多
A backward differentiation formula (BDF) has been shown to be an effective way to solve a system of ordinary differential equations (ODEs) that have some degree of stiffness. However, sometimes, due to high-frequency ...A backward differentiation formula (BDF) has been shown to be an effective way to solve a system of ordinary differential equations (ODEs) that have some degree of stiffness. However, sometimes, due to high-frequency variations in the external time series of boundary conditions, a small time-step is required to solve the ODE system throughout the entire simulation period, which can lead to a high computational cost, slower response, and need for more memory resources. One possible strategy to overcome this problem is to dynamically adjust the time-step with respect to the system’s stiffness. Therefore, small time-steps can be applied when needed, and larger time-steps can be used when allowable. This paper presents a new algorithm for adjusting the dynamic time-step based on a BDF discretization method. The parameters used to dynamically adjust the size of the time-step can be optimally specified to result in a minimum computation time and reasonable accuracy for a particular case of ODEs. The proposed algorithm was applied to solve the system of ODEs obtained from an activated sludge model (ASM) for biological wastewater treatment processes. The algorithm was tested for various solver parameters, and the optimum set of three adjustable parameters that represented minimum computation time was identified. In addition, the accuracy of the algorithm was evaluated for various sets of solver parameters.展开更多
If a traditional explicit numerical integration algorithm is used to solve motion equation in the finite element simulation of wave motion, the time-step used by numerical integration is the smallest time-step restric...If a traditional explicit numerical integration algorithm is used to solve motion equation in the finite element simulation of wave motion, the time-step used by numerical integration is the smallest time-step restricted by the stability criterion in computational region. However, the excessively small time-step is usually unnecessary for a large portion of computational region. In this paper, a varying time-step explicit numerical integration algorithm is introduced, and its basic idea is to use different time-step restricted by the stability criterion in different computational region. Finally, the feasibility of the algorithm and its effect on calculating precision are verified by numerical test.展开更多
Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However,the finite-differ...Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However,the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap,combined with variable grid-size and time-step,this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.展开更多
There are two models in use today to analyze structural responses when subjected to earthquake ground motions, the Displacement Input Model （DIM） and the Acceleration Input Model （AIM）. The time steps used in dire...There are two models in use today to analyze structural responses when subjected to earthquake ground motions, the Displacement Input Model （DIM） and the Acceleration Input Model （AIM）. The time steps used in direct integration methods for these models are analyzed to examine the suitability of DIM. Numerical results are presented and show that the time-step for DIM is about the same as for AIM, and achieves the same accuracy. This is contrary to previous research that reported that there are several sources of numerical errors associated with the direct application of earthquake displacement loading, and a very small time step is required to define the displacement record and to integrate the dynamic equilibrium equation. It is shown in this paper that DIM is as accurate and suitable as, if not more than, AIM for analyzing the response of a structure to uniformly distributed and spatially varying ground motions.展开更多
The numerical time step integrations of PDEs are mainly carried out by the finitedifference method to date. However,when the time step becomes longer, it causes theproblem of numerical instability,. The explicit integ...The numerical time step integrations of PDEs are mainly carried out by the finitedifference method to date. However,when the time step becomes longer, it causes theproblem of numerical instability,. The explicit integration schemes derived by the singlepoint precise integration method given in this paper are proved unconditionally stable.Comparisons between the schemes derived by the finite difference method and theschemes by the method employed in the present paper are made for diffusion andconvective-diffusion equations. Nunierical examples show the superiority of the singlepoint integration method.展开更多
基金National Natural Science Foundation of China(No.52071306)the Natural Science Foundation of Shandong Province(No.ZR2019MEE050)the Natural Science Foundation of Zhejiang Province(No.LZ22E090003).
文摘The local time-stepping(LTS)algorithm is an adaptive method that adjusts the time step by selecting suitable intervals for different regions based on the spatial scale of each cell and water depth and flow velocity between cells.The method can be optimized by calculating the maximum power of two of the global time step increments in the domain,allowing the optimal time step to be approached throughout the grid.To verify the acceleration and accuracy of LTS in storm surge simulations,we developed a model to simulate astronomical storm surges along the southern coast of China.This model employs the shallow water equations as governing equations,numerical discretization using the finite volume method,and fluxes calculated by the Roe solver.By comparing the simulation results of the traditional global time-stepping algorithm with those of the LTS algorithm,we find that the latter fit the measured data better.Taking the calculation results of Typhoon Sally in 1996 as an example,we show that compared with the traditional global time-stepping algorithm,the LTS algorithm reduces computation time by 2.05 h and increases computation efficiency by 2.64 times while maintaining good accuracy.
基金funding from BRIN through the Research Collaboration Program with ORPA(No.2/III.1/HK/2024)Prayitno Abadi is participating in this study as part of a Memorandum of Understanding for Research Collaboration on Regional Ionospheric Observation at Telkom University(No.092/SAM3/TE-DEK/2021).
文摘The effect of ionospheric delay on the ground-based augmentation system under normal conditions can be mitigated by determining the value of the nominal ionospheric gradient(σvig).The nominal ionospheric gradient is generally obtained from Continuously Operating Reference Stations data by using the spatial single-difference method(mixed-pair,station-pair,or satellite-pair)or the temporal single-difference method(time-step).The time-step method uses only a single receiver,but it still contains ionospheric temporal variations.We introduce a corrected time-step method using a fixed-ionospheric pierce point from the geostationary equatorial orbit satellite and test it through simulations based on the global ionospheric model.We also investigate the effect of satellite paths on the corrected time-step method in the region of the equator,which tends to be in a more north–south direction and to have less coverage for the east–west ionospheric gradient.This study also addresses the limitations of temporal variation correction coverage and recommends using only the correction from self-observations.All processes are developed under simulations because observational data are still difficult to obtain.Our findings demonstrate that the corrected time-step method yieldsσvig values consistent with other approaches.
文摘A backward differentiation formula (BDF) has been shown to be an effective way to solve a system of ordinary differential equations (ODEs) that have some degree of stiffness. However, sometimes, due to high-frequency variations in the external time series of boundary conditions, a small time-step is required to solve the ODE system throughout the entire simulation period, which can lead to a high computational cost, slower response, and need for more memory resources. One possible strategy to overcome this problem is to dynamically adjust the time-step with respect to the system’s stiffness. Therefore, small time-steps can be applied when needed, and larger time-steps can be used when allowable. This paper presents a new algorithm for adjusting the dynamic time-step based on a BDF discretization method. The parameters used to dynamically adjust the size of the time-step can be optimally specified to result in a minimum computation time and reasonable accuracy for a particular case of ODEs. The proposed algorithm was applied to solve the system of ODEs obtained from an activated sludge model (ASM) for biological wastewater treatment processes. The algorithm was tested for various solver parameters, and the optimum set of three adjustable parameters that represented minimum computation time was identified. In addition, the accuracy of the algorithm was evaluated for various sets of solver parameters.
基金National Natural Science Foundation of China (50178065), 973 Program (2002CB412706), National Social Com-monweal Research Foundation (2002DIB30076) and Joint Seismological Science Foundation (101066).
文摘If a traditional explicit numerical integration algorithm is used to solve motion equation in the finite element simulation of wave motion, the time-step used by numerical integration is the smallest time-step restricted by the stability criterion in computational region. However, the excessively small time-step is usually unnecessary for a large portion of computational region. In this paper, a varying time-step explicit numerical integration algorithm is introduced, and its basic idea is to use different time-step restricted by the stability criterion in different computational region. Finally, the feasibility of the algorithm and its effect on calculating precision are verified by numerical test.
基金supported by the National Basic Research Program of China (No. 2013CB228604)the National Science and Technology Major Project (No. 2011ZX05030-004-002,2011ZX05019-003)the National Natural Science Foundation (No. 41004050)
文摘Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However,the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap,combined with variable grid-size and time-step,this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.
文摘There are two models in use today to analyze structural responses when subjected to earthquake ground motions, the Displacement Input Model （DIM） and the Acceleration Input Model （AIM）. The time steps used in direct integration methods for these models are analyzed to examine the suitability of DIM. Numerical results are presented and show that the time-step for DIM is about the same as for AIM, and achieves the same accuracy. This is contrary to previous research that reported that there are several sources of numerical errors associated with the direct application of earthquake displacement loading, and a very small time step is required to define the displacement record and to integrate the dynamic equilibrium equation. It is shown in this paper that DIM is as accurate and suitable as, if not more than, AIM for analyzing the response of a structure to uniformly distributed and spatially varying ground motions.
文摘The numerical time step integrations of PDEs are mainly carried out by the finitedifference method to date. However,when the time step becomes longer, it causes theproblem of numerical instability,. The explicit integration schemes derived by the singlepoint precise integration method given in this paper are proved unconditionally stable.Comparisons between the schemes derived by the finite difference method and theschemes by the method employed in the present paper are made for diffusion andconvective-diffusion equations. Nunierical examples show the superiority of the singlepoint integration method.
