共查询到20条相似文献,搜索用时 31 毫秒
1.
A class of generalized high order finite compact difference schemes is proposed for shock/vortex, shock/boundary layer interaction problems. The finite compact difference scheme takes the region between two shocks as a compact stencil. The high order WENO fluxes on shock stencils are used as the internal boundary fluxes for the compact scheme. A lemma based on the property of smoothness estimators on a 5-points stencil is given to detect the shock position. There is no free parameter introduced to switch the compact scheme and the WENO scheme. Some numerical experiments are given and they demonstrate that the present scheme has low dissipation due to the compact central differencing scheme used in the smooth regions. 相似文献
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提出了一种基于二阶波动方程的(2M,4)高阶时域有限差分(FDTD)方法,通过使用辛积分传播子(SIP)在时域上获得4阶精度,使用离散奇异卷积(DSC)方法在空域上达到2M阶精度。与已有的(2M,4) 阶FDTD方法相比,虽然两者都采用SIP和DSC方法,但是此二者的不同点在于:第一,新方法基于二阶波动方程;第二,在离散计算空间时使用单一网格而不是传统的Yee网格;第三,单独计算某一场分量从而节约内存并减少计算量。数值计算结果表明,与传统高阶算法相比,基于波动方程的高阶FDTD方法耗费的机时只有它的50%,内存消耗下降10%, 而两者的计算结果之间相对误差小于5‰。 相似文献
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Jingtao Xin Chunqing Gao Zheng Wang Qian Zhang Zhengyong Wang 《Optics Communications》2012,285(18):3688-3691
A novel beam combination scheme was proposed to generate high order linearly polarized axially symmetric beam (LPASB) by superposing two Laguerre–Gaussian (LG) beams with opposite azimuthal quantum numbers. An amplitude computer-generated hologram (CGH) was not only used to generate two LG beams but also used in the combination scheme. Amplitude CGH was also used to detect the order of the LPASB. 相似文献
4.
Wei Gao Yang Liu Bin Cao & Hong Li 《advances in applied mathematics and mechanics.》2012,4(5):617-635
A bounded high order upwind scheme is presented for the modified Burgers' equation by using the normalized-variable formulation in the finite volume framework. The characteristic line of the present scheme in the normalized-variable diagram is designed on the Hermite polynomial interpolation. In order to suppress unphysical oscillations, the present scheme respects both the TVD (total variational diminishing) constraint and CBC (convection boundedness criterion) condition. Numerical results demonstrate the present scheme possesses good robustness and high resolution for the modified Burgers' equation. 相似文献
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常微分方程边值问题的高阶三对角OCI差分法 总被引:1,自引:0,他引:1
本文给出了二阶线性常微分方程两点边值问题(ODETPBVP)的高阶差分格式构造的基本思想,推导出六阶三对角OCI差分格式,并对端点有奇异性的方程进行了极限值处理,消去了奇异性,对边界层问题采用了非均匀网格上的六阶三对角OCI差分格式。通过大量的数值比较实验表明,这种高阶三对角OCI差分格式能很好地求解奇异性问题,固有不稳定性问题,奇异摄动问题,对生不稳定性问题和振荡性问题。 相似文献
6.
多介质流体力学计算的守恒型高分辨率格式 总被引:2,自引:0,他引:2
应用Lagrange坐标系下的守恒型格式计算多介质流体力学问题,在物质交界面附近采用一阶格式的数值通量,而在其余部分采用高分辨率格式的数值通量,不仅保持了高分辨率的良好性质,而且消除了一般的守恒型格式在界面附近所产生的震荡. 相似文献
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We report a new long-term interferometric stabilization scheme for a delay line to be used for pump–probe spectroscopy on
the attosecond time scale. A separate interferometer with a He–Ne laser beam is used to stabilize the delay line with respect
to a slow drift in the optical delay induced mainly by ambient temperature changes in the laboratory. The power of the stabilization
scheme is demonstrated with the characterization of an attosecond pulse train in the extreme ultraviolet formed through high
order harmonic generation of Ti:sapphire laser radiation. We use the RABBITT technique for the attosecond pulse-train characterization
in a reaction microscope employed here for photoelectron–photoion-coincidence spectroscopy.
PACS 42.65.Ky; 42.65.Re; 07.60.Ly; 07.81.+a; 32.80.Fb 相似文献
9.
从迎风紧致逼进[1]出发,提出求解流体力学双曲型守恒律的一种高精度的数值方法,同时采用群速度控制方法捕捉激波。该方法在光滑区具有三阶精度。 相似文献
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In this paper, a multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids, which has been proposed by Kalita et al. [J.C. Kalita, A.K. Dass, D.C. Dalal, A transformation-free HOC scheme for steady convection–diffusion on non-uniform grids, Int. J. Numer. Methods Fluids 44 (2004) 33–53], is proposed to solve the two-dimensional (2D) convection diffusion equation. The HOC scheme is not involved in any grid transformation to map the nonuniform grids to uniform grids, consequently, the multigrid method is brand-new for solving the discrete system arising from the difference equation on nonuniform grids. The corresponding multigrid projection and interpolation operators are constructed by the area ratio. Some boundary layer and local singularity problems are used to demonstrate the superiority of the present method. Numerical results show that the multigrid method with the HOC scheme on nonuniform grids almost gets as equally efficient convergence rate as on uniform grids and the computed solution on nonuniform grids retains fourth order accuracy while on uniform grids just gets very poor solution for very steep boundary layer or high local singularity problems. The present method is also applied to solve the 2D incompressible Navier–Stokes equations using the stream function–vorticity formulation and the numerical solutions of the lid-driven cavity flow problem are obtained and compared with solutions available in the literature. 相似文献
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Assessing the Performance of a Three Dimensional Hybrid Central-WENO Finite Difference Scheme with Computation of a Sonic Injector in Supersonic Cross Flow
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Wai-Sun Don Antonio de Gregorio Jean-Piero Suarez & Gustaaf B. Jacobs 《advances in applied mathematics and mechanics.》2012,4(6):719-736
A hybridization of a high order WENO-Z finite difference scheme and a high order
central finite difference method for computation of the two-dimensional Euler
equations first presented in [B. Costa and W. S. Don, J. Comput. Appl. Math., 204(2) (2007)]
is extended to three-dimensions and for parallel computation. The Hybrid scheme
switches dynamically from a WENO-Z scheme to a central scheme at any grid location
and time instance if the flow is sufficiently smooth and vice versa if the flow is
exhibiting sharp shock-type phenomena. The smoothness of the flow is determined by
a high order multi-resolution analysis. The method is tested on a benchmark sonic
flow injection in supersonic cross flow. Increase of the order of the method reduces
the numerical dissipation of the underlying schemes, which is shown to improve the
resolution of small dynamic vortical scales. Shocks are captured sharply in an
essentially non-oscillatory manner via the high order shock-capturing WENO-Z scheme.
Computations of the injector flow with a WENO-Z scheme only and with the Hybrid
scheme are in very close agreement. Thirty percent of grid points require a
computationally expensive WENO-Z scheme for high-resolution capturing of shocks,
whereas the remainder of grid points may be solved with the computationally more
affordable central scheme. The computational cost of the Hybrid scheme can be up
to a factor of one and a half lower as compared to computations with a WENO-Z scheme
only for the sonic injector benchmark. 相似文献
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气相爆轰高阶中心差分-WENO组合格式自适应网格方法 总被引:1,自引:0,他引:1
研究一种高阶中心差分-WENO组合格式,并采用自适应网格方法进行二维和三维气相爆轰波的数值模拟.采用ZND爆轰模型的控制方程为包含化学反应源项的Euler方程组.组合格式在大梯度区采用WENO格式捕捉间断,在光滑区采用高阶中心差分格式提高计算效率.采用一种基于流场结构特征的自适应网格.计算结果,表明这种方法同时具有高精度、高分辨率和高效率的特点. 相似文献
16.
A novel pulse stretching-compression system suitable for kHz-rate chirped-pulse amplification of ≈10 fs pulses in Ti:sapphire systems is demonstrated. The material dispersion of the system components used for pulse selection and isolation broadens the wide-band seed pulses by a factor of ≈300, allowing amplification up to the submillijoule energy range. The compressor consists of a pair of prisms and newly-developed chirped multilayer dielectric mirrors for compensating high order dispersion. Using this simple scheme a recompression of unamplified pulses down to 15 fs with a throughput as high as 80% is demonstrated. 相似文献
17.
文章给出了一种真正多维的HLL Riemann解算器.采用AUSM分裂将通量分解成为对流通量和压力通量, 其中对流通量的计算采用迎风格式, 压力通量的计算采用HLL格式, 且将HLL格式的耗散项中的密度差用压力差代替, 从而使得格式能够分辨接触间断.为了实现数值格式真正多维的特性, 分别计算了网格界面中点和角点上的数值通量, 并且采用Simpson公式加权组合中点和角点上的数值通量得到网格界面的数值通量.为了减少重构角点处状态时的模板宽度, 计算中采用基于SDWLS梯度的线性重构获得2阶空间精度, 而时间离散采用2阶保强稳Runge-Kutta方法.数值实验表明, 相比于传统的一维HLL格式, 文章的真正多维HLL格式具有能够分辨接触间断, 以及更大的时间步长等优点.与其他能够分辨接触间断的格式(例如HLLC格式)不同, 真正多维的HLL格式在计算二维问题时不会出现激波不稳定现象. 相似文献
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考虑一类广义的高阶非线性Schrodinger方程组,给出蛙跳格式及混合Crank-Nicolson蛙跳格式,并证明其稳定性与收敛性。最后,数值例子表明数值结果与理论分析相一致。 相似文献
19.
Kenji Imadera Yasuaki Kishimoto Daisuke Saito Jiquan Li Takayuki Utsumi 《Journal of computational physics》2009,228(23):8919-8943
We have applied the conservative form of the Interpolated Differential Operator (IDO-CF) scheme in order to solve the Vlasov–Poisson equation, which is one of the multi-moment schemes. Through numerical tests of the nonlinear Landau damping and two-stream instability, we compared the present scheme with other schemes such as the Spline and CIP ones. We mainly investigated the conservation property of the L1-norm, energy, entropy and phase space area for each scheme, and demonstrated that the IDO-CF scheme is capable of performing stable long time scale simulation while maintaining high accuracy. The scheme is based on an Eulerian approach, and it can thus be directly used for Fokker–Planck, high dimensional Vlasov–Poisson and also guiding-center drift simulations, aiming at particular problems of plasma physics. The benchmark tests for such simulations have shown that the IDO-CF scheme is superior in keeping the conservation properties without causing serious phase error. 相似文献
20.
In this paper, we propose a novel Vlasov solver based on a semi-Lagrangian method which combines Strang splitting in time with high order WENO (weighted essentially non-oscillatory) reconstruction in space. A key insight in this work is that the spatial interpolation matrices, used in the reconstruction process of a semi-Lagrangian approach to linear hyperbolic equations, can be factored into right and left flux matrices. It is the factoring of the interpolation matrices which makes it possible to apply the WENO methodology in the reconstruction used in the semi-Lagrangian update. The spatial WENO reconstruction developed for this method is conservative and updates point values of the solution. While the third, fifth, seventh and ninth order reconstructions are presented in this paper, the scheme can be extended to arbitrarily high order. WENO reconstruction is able to achieve high order accuracy in smooth parts of the solution while being able to capture sharp interfaces without introducing oscillations. Moreover, the CFL time step restriction of a regular finite difference or finite volume WENO scheme is removed in a semi-Lagrangian framework, allowing for a cheaper and more flexible numerical realization. The quality of the proposed method is demonstrated by applying the approach to basic test problems, such as linear advection and rigid body rotation, and to classical plasma problems, such as Landau damping and the two-stream instability. Even though the method is only second order accurate in time, our numerical results suggest the use of high order reconstruction is advantageous when considering the Vlasov–Poisson system. 相似文献