物理系统中波动、传播等现象通常用双曲型守恒律方程的数学模型来描述,特别是在流体力学领域尤为重要。针对此类方程,我们考虑了Lax-Wendroff型中心间断伽辽金方法。该方法首先采用Lax-Wendroff型时间离散方法,也就是通过泰勒级数展开...物理系统中波动、传播等现象通常用双曲型守恒律方程的数学模型来描述,特别是在流体力学领域尤为重要。针对此类方程,我们考虑了Lax-Wendroff型中心间断伽辽金方法。该方法首先采用Lax-Wendroff型时间离散方法,也就是通过泰勒级数展开处理时间导数,然后在空间上运用中心间断伽辽金方法,从而避免了传统的多步时间积分方法。最后我们对多个双曲型守恒律方程开展数值实验,验证所提出方法在计算效率和精度上的有效性。In physical systems, phenomena like wave fluctuation and propagation are often described using hyperbolic conservation law equations, which play a crucial role in fluid mechanics. To solve these equations, we employ the Lax-Wendroff central discontinuous Galerkin method. This approach begins with the Lax-Wendroff time discretization, where time derivatives are managed through a Taylor series expansion. It then incorporates the central discontinuous Galerkin method for spatial discretization and effectively eliminates the need for traditional multi-step time integration schemes. Finally, numerical experiments on various hyperbolic conservation law equations are constructed to validate the effectiveness of our method in terms of both computational efficiency and accuracy.展开更多
本文构造了基于Lax-Wendroff时间离散的有限差分HWENO (Hermite加权本质非振荡)格式,用于求解非线性退化抛物方程。与传统的Runge-Kutta时间离散方法相比,Lax-Wendroff方法在提高计算效率的同时,能够在解的光滑区域实现时空一致的高阶...本文构造了基于Lax-Wendroff时间离散的有限差分HWENO (Hermite加权本质非振荡)格式,用于求解非线性退化抛物方程。与传统的Runge-Kutta时间离散方法相比,Lax-Wendroff方法在提高计算效率的同时,能够在解的光滑区域实现时空一致的高阶精度。通过数值算例,验证了该方法的有效性。This paper constructs a finite difference HWENO (Hermite Weighted Essentially Non-Oscillatory) scheme based on Lax-Wendroff time discretization for solving nonlinear degenerate parabolic equations. Compared to traditional Runge-Kutta time discretization methods, the Lax-Wendroff method improves computational efficiency while achieving high-order accuracy in both space and time in smooth regions of the solution. The effectiveness of the method is validated through numerical examples.展开更多
Y2000-62202-2737 0014036超音速飞行器的 H<sub>2</sub>/H<sub>∞</sub>最优控制的统一方法=Uni-fied approach to H<sub>2</sub> and H-infinity optimal control of hy-personic vehicles[会,英...Y2000-62202-2737 0014036超音速飞行器的 H<sub>2</sub>/H<sub>∞</sub>最优控制的统一方法=Uni-fied approach to H<sub>2</sub> and H-infinity optimal control of hy-personic vehicles[会,英]/Naidu,D.S.& Banda,S.S.//1999 IEEE Proceedings of American Control Con-ference,Vol.4 of 6.—2737～2741（NiD）本文提出了一种能够克服设计系统在单位圆内根过分集中以及传统 Z 变换方法发生数值困难的统一方法,并将其应用于超音速飞行器的控制器设计。设计方法采用了包含系统输出的二次型 H<sub>2</sub>/H 无穷指标,适用于连续与离散时间系统的控制器设计。展开更多
文摘物理系统中波动、传播等现象通常用双曲型守恒律方程的数学模型来描述,特别是在流体力学领域尤为重要。针对此类方程,我们考虑了Lax-Wendroff型中心间断伽辽金方法。该方法首先采用Lax-Wendroff型时间离散方法,也就是通过泰勒级数展开处理时间导数,然后在空间上运用中心间断伽辽金方法,从而避免了传统的多步时间积分方法。最后我们对多个双曲型守恒律方程开展数值实验,验证所提出方法在计算效率和精度上的有效性。In physical systems, phenomena like wave fluctuation and propagation are often described using hyperbolic conservation law equations, which play a crucial role in fluid mechanics. To solve these equations, we employ the Lax-Wendroff central discontinuous Galerkin method. This approach begins with the Lax-Wendroff time discretization, where time derivatives are managed through a Taylor series expansion. It then incorporates the central discontinuous Galerkin method for spatial discretization and effectively eliminates the need for traditional multi-step time integration schemes. Finally, numerical experiments on various hyperbolic conservation law equations are constructed to validate the effectiveness of our method in terms of both computational efficiency and accuracy.
文摘本文构造了基于Lax-Wendroff时间离散的有限差分HWENO (Hermite加权本质非振荡)格式,用于求解非线性退化抛物方程。与传统的Runge-Kutta时间离散方法相比,Lax-Wendroff方法在提高计算效率的同时,能够在解的光滑区域实现时空一致的高阶精度。通过数值算例,验证了该方法的有效性。This paper constructs a finite difference HWENO (Hermite Weighted Essentially Non-Oscillatory) scheme based on Lax-Wendroff time discretization for solving nonlinear degenerate parabolic equations. Compared to traditional Runge-Kutta time discretization methods, the Lax-Wendroff method improves computational efficiency while achieving high-order accuracy in both space and time in smooth regions of the solution. The effectiveness of the method is validated through numerical examples.
文摘Y2000-62202-2737 0014036超音速飞行器的 H<sub>2</sub>/H<sub>∞</sub>最优控制的统一方法=Uni-fied approach to H<sub>2</sub> and H-infinity optimal control of hy-personic vehicles[会,英]/Naidu,D.S.& Banda,S.S.//1999 IEEE Proceedings of American Control Con-ference,Vol.4 of 6.—2737～2741（NiD）本文提出了一种能够克服设计系统在单位圆内根过分集中以及传统 Z 变换方法发生数值困难的统一方法,并将其应用于超音速飞行器的控制器设计。设计方法采用了包含系统输出的二次型 H<sub>2</sub>/H 无穷指标,适用于连续与离散时间系统的控制器设计。
