共查询到20条相似文献,搜索用时 171 毫秒
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为解决熵守恒格式在激波附近出现数值振荡的问题,本文将熵相容格式与MUSCL格式相结合,提出一种既能适合于激波问题、又不依赖于传统人工黏性经验模型的高分辨率熵相容格式,通过对多个激波问题的数值计算,并对比二阶中心格式、熵守恒格式、熵相容格式和高分辨率熵相容格式的计算结果,发现:熵相容格式具有较好的激波捕捉能力,有效解决了熵守恒格式在激波附近的数值振荡问题;MUSCL重构格式进一步提高了熵相容格式的数值模拟能力,既能精确捕捉激波附近的流动细节,又在光滑区保持二阶精度;在对比的四种格式中,本文提出的高分辨率熵相容格式对激波问题的预测性能最佳。该项工作对发展激波湍流相互作用模型、提高跨/超音速叶轮机械流动预测精度具有理论价值和应用潜力。 相似文献
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多介质流的高分辨率Euler方法 总被引:2,自引:0,他引:2
在多介质流动问题中,不同介质有不同的状态方程。这使通量成为间断函数,从而没有通量的Jacobi矩阵。而用Euler坐标系描述的方程组的很多高分辨率格式都要用到Jacobi矩阵及其特征值和特征向量,即要求通量连续可微。因此必须重新处理整个守恒律方程组。对于γ气体问题将γ看作一个新未知量并增加一个守恒方程,从而使整个方程组的通量成为光滑函数,为高分辨率格式的构造铺平了道路。由于真实流动只遵守三个守恒律,多加的一个守恒律虽然对偏微分方程组没有影响,但对差分方程数值解有影响。这一点在数值实验中已有表现。提出了一个方案将这一影响尽量消除。所用格式可完全照搬单介质流动的任何现有格式。对一维多介质流动Euler方程组的激波管问题的数值实验表明这样处理所构造的格式具有同单介质流动问题同样的效果。 相似文献
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双曲型守恒律的一种高精度TVD差分格式 总被引:3,自引:0,他引:3
构造了一维双曲型守恒律方程的一个高精度高分辨率的守恒型TVD差分格式.其主要思想是:首先将计算区域划分为互不重叠的小单元,且每个小单元再根据希望的精度阶数分为细小单元;其次,根据流动方向将通量分裂为正、负通量,并通过小单元上的高阶插值逼近得到了细小单元边界上的正、负数值通量,为避免由高阶插值产生的数值振荡,进一步根据流向对其进行TVD校正;再利用高阶Runge KuttaTVD离散方法对时间进行离散,得到了高阶全离散方法.进一步推广到一维方程组情形.最后对一维欧拉方程组计算了几个算例. 相似文献
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利用双曲守恒律的Hamilton-Jacobi方程形式,应用Taylor公式与Galerkin有限元给出了求解双曲守恒律的计算方法。采用TVD差分格式的构造思想,对数值通量作修正,在等距网格情形下有限元方法得到的计算格式满足TVD性质,并给出了数值例子。 相似文献
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三维高超声速无粘定常绕流的数值模拟 总被引:13,自引:0,他引:13
本文采用一种简单有效的通量分裂结合一种二阶TVD格式的数值通量的方法,提出一种隐式的迎风有限体积格式,并利用这种格式,从气体动力学非定常Euler方程组出发,数值模拟了三维不对称物体的高超声速无粘定常绕流。数值结果表明此格式具有分辨率较高和收敛速度较快的优点。 相似文献
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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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Huajun Zhu Xiaogang Deng Meiliang Mao Huayong Liu & Guohua Tu 《advances in applied mathematics and mechanics.》2016,8(4):670-692
We compare in this paper the properties of Osher flux with O-variant and
P-variant (Osher-O flux and Osher-P flux) in finite volume methods for the two-dimensional
Euler equations and propose an entropy fix technique to improve their
robustness. We consider both first-order and second-order reconstructions. For inviscid
hypersonic flow past a circular cylinder, we observe different problems for different
schemes: a first-order Osher-O scheme on quadrangular grids yields a carbuncle
shock, while a first-order Osher-P scheme results in a dislocation shock for high Mach
number cases. In addition, a second-order Osher scheme can also yield a carbuncle
shock or be unstable. To improve the robustness of these schemes we propose an entropy
fix technique, and then present numerical results to show the effectiveness of
the proposed method. In addition, the influence of grid aspects ratio, relative shock
position to the grid and Mach number on shock stability are tested. Viscous heating
problem and double Mach reflection problem are simulated to test the influence of the
entropy fix on contact resolution and boundary layer resolution. 相似文献
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We present a high order kinetic flux-vector splitting (KFVS) scheme for the numerical solution of a conservative interface-capturing five-equation model of compressible two-fluid flows. This model was initially introduced by Wackers and Koren (2004) [21]. The flow equations are the bulk equations, combined with mass and energy equations for one of the two fluids. The latter equation contains a source term in order to account for the energy exchange. We numerically investigate both one- and two-dimensional flow models. The proposed numerical scheme is based on the direct splitting of macroscopic flux functions of the system of equations. In two space dimensions the scheme is derived in a usual dimensionally split manner. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge–Kutta time stepping method. For validation, the results of our scheme are compared with those from the high resolution central scheme of Nessyahu and Tadmor [14]. The accuracy, efficiency and simplicity of the KFVS scheme demonstrate its potential for modeling two-phase flows. 相似文献
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The proposed scheme, which is a conservative form of the interpolated differential operator scheme (IDO-CF), can provide high accurate solutions for both compressible and incompressible fluid equations. Spatial discretizations with fourth-order accuracy are derived from interpolation functions locally constructed by both cell-integrated values and point values. These values are coupled and time-integrated by solving fluid equations in the flux forms for the cell-integrated values and in the derivative forms for the point values. The IDO-CF scheme exactly conserves mass, momentum, and energy, retaining the high resolution more than the non-conservative form of the IDO scheme. A direct numerical simulation of turbulence is carried out with comparable accuracy to that of spectral methods. Benchmark tests of Riemann problems and lid-driven cavity flows show that the IDO-CF scheme is immensely promising in compressible and incompressible fluid dynamics studies. 相似文献
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A new numerical method-basic function method is proposed. This method can directly discrete differential operators on unstructured
grids. By using the expansion of basic function to approach the exact function, the central and upwind schemes of derivative
are constructed. By using the polynomial as basic function, applying the technique of flux splitting method and the combination
of central and upwind schemes, the non-physical fluctuation near the shock wave is suppressed. The first-order basic function
scheme of polynomial type for solving inviscid compressible flow numerically is constructed in this paper. Several numerical
results of many typical examples for one-, two- and three-dimensional inviscid compressible steady flow illustrate that it
is a new scheme with high accuracy and high resolution for shock wave. Especially, combining with the adaptive remeshing technique,
the satisfactory results can be obtained by these schemes. 相似文献