The first through ninth radial derivatives of a harmonic function and gravity anomaly are derived in this paper. These derivatives can be used in the analytical continuation application. For the downward continuation ...The first through ninth radial derivatives of a harmonic function and gravity anomaly are derived in this paper. These derivatives can be used in the analytical continuation application. For the downward continuation of gravity anomaly, the Taylor series approach developed in the paper is equivalent theoretically to but more efficient and storage-saving computationally than the well-known gradient operator approach. Numerical simulation shows that Taylor series expansion constructed by the derived formulas for the radial derivatives of gravity disturbance is still convergent for height up to 4 km.展开更多
为提高电力系统暂态稳定分析效率,本文提出了多维阶数控制的多步Taylor级数暂态稳定快速计算方法。该方法基于多步Taylor级数展开理论,针对不同时间常数的机组及不同积分时刻的机组转角状态量,根据时域仿真计算精度建立了转角状态量的...为提高电力系统暂态稳定分析效率,本文提出了多维阶数控制的多步Taylor级数暂态稳定快速计算方法。该方法基于多步Taylor级数展开理论,针对不同时间常数的机组及不同积分时刻的机组转角状态量,根据时域仿真计算精度建立了转角状态量的高阶导数阶数差异化控制策略,并从理论上分析了忽略部分高阶导数对转角轨迹的影响。所提方法可实现状态变量时间和空间上的动态多维导数阶数控制,消除常规Taylor级数法暂态稳定分析的计算冗余。New England 10机39节点算例仿真验证了所提方法可灵活方便地实现Taylor级数法的时空多维阶数控制,能有效提高暂态稳定分析效率。展开更多
With increasing engineering demands,there need high order accurate schemes embedded with precise physical information in order to capture delicate small scale structures and strong waves with correct“physics”.There ...With increasing engineering demands,there need high order accurate schemes embedded with precise physical information in order to capture delicate small scale structures and strong waves with correct“physics”.There are two families of high order methods:One is the method of line,relying on the Runge-Kutta(R-K)time-stepping.The building block is the Riemann solution labeled as the solution element“1”.Each step in R-K just has first order accuracy.In order to derive a fourth order accuracy scheme in time,one needs four stages labeled as“1111=4”.The other is the one-stage Lax-Wendroff(LW)type method,which is more compact but is complicated to design numerical fluxes and hard to use when applied to highly nonlinear problems.In recent years,the pair of solution element and dynamics element,labeled as“2”,are taken as the building block.The direct adoption of the dynamics implies the inherent temporal-spatial coupling.With this type of building blocks,a family of two-stage fourth order accurate schemes,labeled as“22=4”,are designed for the computation of compressible fluid flows.The resulting schemes are compact,robust and efficient.This paper contributes to elucidate how and why high order accurate schemes should be so designed.To some extent,the“22=4”algorithm extracts the advantages of the method of line and one-stage LW method.As a core part,the pair“2”is expounded and LW solver is revisited.The generalized Riemann problem(GRP)solver,as the discontinuous and nonlinear version of LW flow solver,and the gas kinetic scheme(GKS)solver,the microscopic LW solver,are all reviewed.The compact Hermite-type data reconstruction and high order approximation of boundary conditions are proposed.Besides,the computational performance and prospective discussions are presented.展开更多
The conventional gravity gradient method to plot the geologic body location is fuzzy. When the depth is large and the geologic body is small, the Vzz and Vzx derivative errors are also large. We describe that using th...The conventional gravity gradient method to plot the geologic body location is fuzzy. When the depth is large and the geologic body is small, the Vzz and Vzx derivative errors are also large. We describe that using the status distinguishing factor to optimally determine the comer location is more accurate than the conventional higher-order derivative method. Thus, a better small geologic body and fault resolution is obtained by using the gravity gradient method and trial theoretical model calculation. The actual data is better processed, providing a better basis for prospecting and determination of subsurface geologic structure.展开更多
文摘The first through ninth radial derivatives of a harmonic function and gravity anomaly are derived in this paper. These derivatives can be used in the analytical continuation application. For the downward continuation of gravity anomaly, the Taylor series approach developed in the paper is equivalent theoretically to but more efficient and storage-saving computationally than the well-known gradient operator approach. Numerical simulation shows that Taylor series expansion constructed by the derived formulas for the radial derivatives of gravity disturbance is still convergent for height up to 4 km.
文摘为提高电力系统暂态稳定分析效率,本文提出了多维阶数控制的多步Taylor级数暂态稳定快速计算方法。该方法基于多步Taylor级数展开理论,针对不同时间常数的机组及不同积分时刻的机组转角状态量,根据时域仿真计算精度建立了转角状态量的高阶导数阶数差异化控制策略,并从理论上分析了忽略部分高阶导数对转角轨迹的影响。所提方法可实现状态变量时间和空间上的动态多维导数阶数控制,消除常规Taylor级数法暂态稳定分析的计算冗余。New England 10机39节点算例仿真验证了所提方法可灵活方便地实现Taylor级数法的时空多维阶数控制,能有效提高暂态稳定分析效率。
基金This work is supported by NSFC(nos.11771054,91852207)and Foundation of LCP.
文摘With increasing engineering demands,there need high order accurate schemes embedded with precise physical information in order to capture delicate small scale structures and strong waves with correct“physics”.There are two families of high order methods:One is the method of line,relying on the Runge-Kutta(R-K)time-stepping.The building block is the Riemann solution labeled as the solution element“1”.Each step in R-K just has first order accuracy.In order to derive a fourth order accuracy scheme in time,one needs four stages labeled as“1111=4”.The other is the one-stage Lax-Wendroff(LW)type method,which is more compact but is complicated to design numerical fluxes and hard to use when applied to highly nonlinear problems.In recent years,the pair of solution element and dynamics element,labeled as“2”,are taken as the building block.The direct adoption of the dynamics implies the inherent temporal-spatial coupling.With this type of building blocks,a family of two-stage fourth order accurate schemes,labeled as“22=4”,are designed for the computation of compressible fluid flows.The resulting schemes are compact,robust and efficient.This paper contributes to elucidate how and why high order accurate schemes should be so designed.To some extent,the“22=4”algorithm extracts the advantages of the method of line and one-stage LW method.As a core part,the pair“2”is expounded and LW solver is revisited.The generalized Riemann problem(GRP)solver,as the discontinuous and nonlinear version of LW flow solver,and the gas kinetic scheme(GKS)solver,the microscopic LW solver,are all reviewed.The compact Hermite-type data reconstruction and high order approximation of boundary conditions are proposed.Besides,the computational performance and prospective discussions are presented.
基金support by the "Eleventh Five-Year" National Science and Technology Support Program (No. 2006BAB01A02)the Pivot Program of the National Natural Science Fund (No. 40930314)
文摘The conventional gravity gradient method to plot the geologic body location is fuzzy. When the depth is large and the geologic body is small, the Vzz and Vzx derivative errors are also large. We describe that using the status distinguishing factor to optimally determine the comer location is more accurate than the conventional higher-order derivative method. Thus, a better small geologic body and fault resolution is obtained by using the gravity gradient method and trial theoretical model calculation. The actual data is better processed, providing a better basis for prospecting and determination of subsurface geologic structure.
