In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state pr...In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.展开更多
Slope limiters play an essential role in maintaining the non-oscillatory behavior of high-resolution methods for nonlinear conservation laws.The family of minmod limiters serves as the prototype example.Here,we revisi...Slope limiters play an essential role in maintaining the non-oscillatory behavior of high-resolution methods for nonlinear conservation laws.The family of minmod limiters serves as the prototype example.Here,we revisit the question of non-oscillatory behavior of high-resolution central schemes in terms of the slope limiter proposed by van Albada et al.(Astron Astrophys 108:76–84,1982).The van Albada(vA)limiter is smoother near extrema,and consequently,in many cases,it outperforms the results obtained using the standard minmod limiter.In particular,we prove that the vA limiter ensures the one-dimensional Total-Variation Diminishing(TVD)stability and demonstrate that it yields noticeable improvement in computation of one-and two-dimensional systems.展开更多
为改善风火打捆系统的暂态稳定性,提出将具有串补功能的复合型故障限流器(Fault Current Limiter,FCL)接入到风火打捆系统中。将双馈风电机组(Doubly-Fed Induction Generator,DFIG)对系统的影响用等效外特性参数表示,在分析DFIG接入系...为改善风火打捆系统的暂态稳定性,提出将具有串补功能的复合型故障限流器(Fault Current Limiter,FCL)接入到风火打捆系统中。将双馈风电机组(Doubly-Fed Induction Generator,DFIG)对系统的影响用等效外特性参数表示,在分析DFIG接入系统对暂态稳定的影响和复合型FCL工作原理的基础上,分析带复合型FCL的风火打捆系统的功率特性方程,通过分析在不同运行状态下复合型FCL对功率特性方程中输入阻抗、转移阻抗的影响,确定其对传输功率极限的作用,分析其提高暂态稳定性的机理。制定了故障发生前、中、后不同阶段,复合型FCL提高风火打捆系统暂态稳定性的控制策略。正常运行及故障切除后发挥复合型FCL的串补功能;故障状态下通过确定目标功率差与触发角之间的关系,通过控制限流电抗,发挥FCL限制短路电流、提高母线电压的作用,达到提高功率输送能力,改善暂态稳定性的目的。仿真分析表明机理分析和所提控制策略的有效性。展开更多
Recent works have shown that neural networks are promising parameter-free limiters for a variety of numerical schemes(Morgan et al.in A machine learning approach for detect-ing shocks with high-order hydrodynamic meth...Recent works have shown that neural networks are promising parameter-free limiters for a variety of numerical schemes(Morgan et al.in A machine learning approach for detect-ing shocks with high-order hydrodynamic methods.et al.in J Comput Phys 367:166-191.,2018;Veiga et al.in European Conference on Computational Mechanics andⅦEuropean Conference on Computational Fluid Dynamics,vol.1,pp.2525-2550.ECCM.,2018).Following this trend,we train a neural network to serve as a shock-indicator function using simulation data from a Runge-Kutta discontinuous Galer-kin(RKDG)method and a modal high-order limiter(Krivodonova in J Comput Phys 226:879-896.,2007).With this methodology,we obtain one-and two-dimensional black-box shock-indicators which are then coupled to a standard limiter.Furthermore,we describe a strategy to transfer the shock-indicator to a residual distribution(RD)scheme without the need for a full training cycle and large data-set,by finding a mapping between the solution feature spaces from an RD scheme to an RKDG scheme,both in one-and two-dimensional problems,and on Cartesian and unstruc-tured meshes.We report on the quality of the numerical solutions when using the neural network shock-indicator coupled to a limiter,comparing its performance to traditional lim-iters,for both RKDG and RD schemes.展开更多
Due to its significant attributes,the liquid metal current limiter(LMCL)is considered a new strategy for limiting short-circuit current in the power grid.A resistive wall liquid metal current limiter(RWLMCL)is designe...Due to its significant attributes,the liquid metal current limiter(LMCL)is considered a new strategy for limiting short-circuit current in the power grid.A resistive wall liquid metal current limiter(RWLMCL)is designed to advance the starting current-limiting time.Experiments are performed to investigate the dynamic behaviors of liquid metal,and the influence of different currents on the liquid metal self-shrinkage effect is compared and analyzed.Furthermore,the liquid metal self-shrinkage effect is mathematically modeled,and the reason for the formation of arc plasma is obtained by simulation.The laws of arc plasma formation and the current transfer in the cavity are revealed,and the motion mechanisms are explained by physical principles.The simulations are in accordance with the test data.It is demonstrated that the sudden change of the current density at both ends of the wall causes the liquid metal to shrink and depress under the electromagnetic force,and the current starts to transfer from the liquid metal path to the wall resistance path.The RWLMCL can effectively advance the starting current-limiting time.展开更多
This paper proposes a new version of the high-resolution entropy-consistent(EC-Limited)flux for hyperbolic conservation laws based on a new minmod-type slope limiter.Firstly,we identify the numerical entropy productio...This paper proposes a new version of the high-resolution entropy-consistent(EC-Limited)flux for hyperbolic conservation laws based on a new minmod-type slope limiter.Firstly,we identify the numerical entropy production,a third-order differential term deduced from the previous work of Ismail and Roe[11].The corresponding dissipation term is added to the original Roe flux to achieve entropy consistency.The new,resultant entropy-consistent(EC)flux has a general and explicit analytical form without any corrective factor,making it easy to compute and a less-expensive method.The inequality constraints are imposed on the standard piece-wise quadratic reconstruction to enforce the pointwise values of bounded-type numerical solutions.We design the new minmod slope limiter as combining two separate limiters for left and right states.We propose the EC-Limited flux by adding this reconstruction data method to the primitive variables rather than to the conservative variables of the EC flux to preserve the equilibrium of the primitive variables.These resulting fluxes are easily applied to general hyperbolic conservation laws while having attractive features:entropy-stable,robust,and non-oscillatory.To illustrate the potential of these proposed fluxes,we show the applications to the Burgers equation and the Euler equations.展开更多
基金supported by the NSFC Grant No.11872210 and Grant No.MCMS-I-0120G01Chi-Wang Shu:Research is supported by the AFOSR Grant FA9550-20-1-0055 and the NSF Grant DMS-2010107Jianxian Qiu:Research is supported by the NSFC Grant No.12071392.
文摘In this paper, we design high-order Runge-Kutta discontinuous Galerkin (RKDG) methods with multi-resolution weighted essentially non-oscillatory (multi-resolution WENO) limiters to compute compressible steady-state problems on triangular meshes. A troubled cell indicator extended from structured meshes to unstructured meshes is constructed to identify triangular cells in which the application of the limiting procedures is required. In such troubled cells, the multi-resolution WENO limiting methods are used to the hierarchical L^(2) projection polynomial sequence of the DG solution. Through using the RKDG methods with multi-resolution WENO limiters, the optimal high-order accuracy can be gradually reduced to first-order in the triangular troubled cells, so that the shock wave oscillations can be well suppressed. In steady-state simulations on triangular meshes, the numerical residual converges to near machine zero. The proposed spatial reconstruction methods enhance the robustness of classical DG methods on triangular meshes. The good results of these RKDG methods with multi-resolution WENO limiters are verified by a series of two-dimensional steady-state problems.
基金Research was supported in part by the ONR Grant N00014-2112773.
文摘Slope limiters play an essential role in maintaining the non-oscillatory behavior of high-resolution methods for nonlinear conservation laws.The family of minmod limiters serves as the prototype example.Here,we revisit the question of non-oscillatory behavior of high-resolution central schemes in terms of the slope limiter proposed by van Albada et al.(Astron Astrophys 108:76–84,1982).The van Albada(vA)limiter is smoother near extrema,and consequently,in many cases,it outperforms the results obtained using the standard minmod limiter.In particular,we prove that the vA limiter ensures the one-dimensional Total-Variation Diminishing(TVD)stability and demonstrate that it yields noticeable improvement in computation of one-and two-dimensional systems.
文摘为改善风火打捆系统的暂态稳定性,提出将具有串补功能的复合型故障限流器(Fault Current Limiter,FCL)接入到风火打捆系统中。将双馈风电机组(Doubly-Fed Induction Generator,DFIG)对系统的影响用等效外特性参数表示,在分析DFIG接入系统对暂态稳定的影响和复合型FCL工作原理的基础上,分析带复合型FCL的风火打捆系统的功率特性方程,通过分析在不同运行状态下复合型FCL对功率特性方程中输入阻抗、转移阻抗的影响,确定其对传输功率极限的作用,分析其提高暂态稳定性的机理。制定了故障发生前、中、后不同阶段,复合型FCL提高风火打捆系统暂态稳定性的控制策略。正常运行及故障切除后发挥复合型FCL的串补功能;故障状态下通过确定目标功率差与触发角之间的关系,通过控制限流电抗,发挥FCL限制短路电流、提高母线电压的作用,达到提高功率输送能力,改善暂态稳定性的目的。仿真分析表明机理分析和所提控制策略的有效性。
文摘Recent works have shown that neural networks are promising parameter-free limiters for a variety of numerical schemes(Morgan et al.in A machine learning approach for detect-ing shocks with high-order hydrodynamic methods.et al.in J Comput Phys 367:166-191.,2018;Veiga et al.in European Conference on Computational Mechanics andⅦEuropean Conference on Computational Fluid Dynamics,vol.1,pp.2525-2550.ECCM.,2018).Following this trend,we train a neural network to serve as a shock-indicator function using simulation data from a Runge-Kutta discontinuous Galer-kin(RKDG)method and a modal high-order limiter(Krivodonova in J Comput Phys 226:879-896.,2007).With this methodology,we obtain one-and two-dimensional black-box shock-indicators which are then coupled to a standard limiter.Furthermore,we describe a strategy to transfer the shock-indicator to a residual distribution(RD)scheme without the need for a full training cycle and large data-set,by finding a mapping between the solution feature spaces from an RD scheme to an RKDG scheme,both in one-and two-dimensional problems,and on Cartesian and unstruc-tured meshes.We report on the quality of the numerical solutions when using the neural network shock-indicator coupled to a limiter,comparing its performance to traditional lim-iters,for both RKDG and RD schemes.
基金supported by National Natural Science Foundation of China(No.52177131)the Interdisciplinary Program of Wuhan National High Magnetic Field Center(No.WHMFC202130)Huazhong University of Science and Technology。
文摘Due to its significant attributes,the liquid metal current limiter(LMCL)is considered a new strategy for limiting short-circuit current in the power grid.A resistive wall liquid metal current limiter(RWLMCL)is designed to advance the starting current-limiting time.Experiments are performed to investigate the dynamic behaviors of liquid metal,and the influence of different currents on the liquid metal self-shrinkage effect is compared and analyzed.Furthermore,the liquid metal self-shrinkage effect is mathematically modeled,and the reason for the formation of arc plasma is obtained by simulation.The laws of arc plasma formation and the current transfer in the cavity are revealed,and the motion mechanisms are explained by physical principles.The simulations are in accordance with the test data.It is demonstrated that the sudden change of the current density at both ends of the wall causes the liquid metal to shrink and depress under the electromagnetic force,and the current starts to transfer from the liquid metal path to the wall resistance path.The RWLMCL can effectively advance the starting current-limiting time.
基金the National Natural Science Found Project of China through project number 11971075.
文摘This paper proposes a new version of the high-resolution entropy-consistent(EC-Limited)flux for hyperbolic conservation laws based on a new minmod-type slope limiter.Firstly,we identify the numerical entropy production,a third-order differential term deduced from the previous work of Ismail and Roe[11].The corresponding dissipation term is added to the original Roe flux to achieve entropy consistency.The new,resultant entropy-consistent(EC)flux has a general and explicit analytical form without any corrective factor,making it easy to compute and a less-expensive method.The inequality constraints are imposed on the standard piece-wise quadratic reconstruction to enforce the pointwise values of bounded-type numerical solutions.We design the new minmod slope limiter as combining two separate limiters for left and right states.We propose the EC-Limited flux by adding this reconstruction data method to the primitive variables rather than to the conservative variables of the EC flux to preserve the equilibrium of the primitive variables.These resulting fluxes are easily applied to general hyperbolic conservation laws while having attractive features:entropy-stable,robust,and non-oscillatory.To illustrate the potential of these proposed fluxes,we show the applications to the Burgers equation and the Euler equations.
