共查询到18条相似文献,搜索用时 46 毫秒
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一种新的LU型隐式格式及其应用 总被引:3,自引:2,他引:3
发展了一种新的LU型隐式格式。新格式除包含LU-SGS格式全部特色外,尽管采用了相似变换而不是近似处理来精确地构造通量矢量的迎风Jacobian矩阵,仍可避免块对角矩阵求逆.且左端项仍可保持矢量化处理。新格式显示出更快的收敛性和更高的稳定性且没有多余的数值耗散和自由参数,尤其适用于求解三维非定常流动问题。 相似文献
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针对使用可压缩流动数值方法求解不可压缩流动存在的刚性问题,基于虚拟压缩法思想,构造了一种以Mach数、速度、密度、温度等变量为元素的预处理矩阵,改变了控制方程组的特征根并使其量级更接近.通过理论推导与分析,证明新方法相比Weiss, Pletcher, Dailey和Choi的方法而言,不仅能降低方程组的刚性,提高了数值求解效率,而且拥有更好的稳定性,此外还能实现低速流动和高速流动之间的光滑过渡.采用有限差分格式进行离散,对流项的Roe格式作为基本加权无振荡(WENO)格式的求解器,黏性项则使用中心型紧致差分格式来计算,与预处理矩阵相结合展开数值实验,结果表明新预处理方法可以实现对无黏和有黏不可压缩流动问题的高精度模拟,且拥有比Weiss和Pletcher等提出的方法更好的收敛性和稳定性. 相似文献
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设计一种基于三单元具有六阶精度的修正Hermite-ENO格式(CHENO),求解一维双曲守恒律问题.CHENO格式利用有限体积法进行空间离散,在空间层上,使用ENO格式中的Newton差商法自适应选择模板.在重构半节点处的函数值及其一阶导数值时,利用Taylor展开给出修正Hermite插值使其提高到六阶精度,并设计了间断识别法与相应的处理方法以抑制间断处的虚假振荡;在时间层上采用三阶TVD Runge-Kutta法进行函数值及一阶导数值的推进.其主要优点是在达到高阶精度的同时具有紧致性.数值实验表明对一维双曲守恒律问题的求解达到了理论分析结果,是有效可行的. 相似文献
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对差分格式进行优化处理可以提高其谱精度。与高精度(指Taylor展开精度)格式相比,优化格式放大因子的误差随波数的变化不是单调的,而是必然会出现极值点,这样就存在临界距离Rcr,在此距离内优化格式描述的数值波的积累误差小于高精度格式,而超出此距离后优化格式的误差反而大,对于非定常流及气动声学计算来说,控制差分格式的临界距离是必要的。一般的优化目标函数以每个时间推进步的误差为基础(即放大因子法),Rcr不能在优化过程中确定。对此进行分析,指出积累误差的重要性并提出以此为基础的新的优化目标函数,这样在对格式进行优化时可以直接指定临界距离,从而为控制谱精度提供方便。 相似文献
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用改进的耦合型Level Set方法计算一维双介质可压缩流动 总被引:1,自引:1,他引:1
用带有虚拟流体(Ghost Fluid)修正的Level Set方法计算了一维可压缩双介质流动,把描述流动的Euler方程和描述流体界面运动的Level Set方程耦合起来,得到一个整体的守恒律系统,应用高分辨率差分格式求解;为了解决流体界面附近的数值跳动问题,在界面附近引入了虚拟流体方法的Isobaric修正,并给出了算例. 相似文献
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We present a BGK-type collision model which approximates, by a Chapman-Enskog expansion, the compressible Navier-Stokes equations with a Prandtl number that can be chosen arbitrarily between 0 and 1. This model has the basic properties of the Boltzmann equation, including theH-theorem, but contains an extra parameter in comparison with the standard BGK model. This parameter is introduced multiplying the collision operator by a nonlinear functional of the distribution function. It is adjusted to the Prandtl number. 相似文献
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A Discontinuous Galerkin Method Based on a BGK Scheme for the Navier-Stokes Equations on Arbitrary Grids 下载免费PDF全文
A discontinuous Galerkin Method based on a Bhatnagar-Gross-Krook
(BGK) formulation is presented for the solution of the compressible
Navier-Stokes equations on arbitrary grids. The idea behind this
approach is to combine the robustness of the BGK scheme with the
accuracy of the DG methods in an effort to develop a more accurate,
efficient, and robust method for numerical simulations of viscous
flows in a wide range of flow regimes. Unlike the traditional
discontinuous Galerkin methods, where a Local Discontinuous Galerkin
(LDG) formulation is usually used to discretize the viscous fluxes
in the Navier-Stokes equations, this DG method uses a BGK scheme to
compute the fluxes which not only couples the convective and
dissipative terms together, but also includes both discontinuous and
continuous representation in the flux evaluation at a cell interface
through a simple hybrid gas distribution function. The developed
method is used to compute a variety of viscous flow problems on
arbitrary grids. The numerical results obtained by this BGKDG method
are extremely promising and encouraging in terms of both accuracy
and robustness, indicating its ability and potential to become not
just a competitive but simply a superior approach than the current
available numerical methods. 相似文献
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One major problem in the development of hypersonic vehicles is severe aerodynamic heating; thus, the implementation of a thermal protection system is required. A numerical investigation on the reduction of aerodynamic heating using different thermal protection systems is conducted using a novel gas-kinetic BGK scheme. This method adopts a different solution strategy from the conventional computational fluid dynamics technique, and has shown a lot of benefits in the simulation of hypersonic flows. To be specific, it is established based on solving the Boltzmann equation, and the obtained gas distribution function is used to reconstruct the macroscopic solution of the flow field. Within the finite volume framework, the present BGK scheme is specially designed for the evaluation of numerical fluxes across the cell interface. Two typical thermal protection systems are investigated by using spikes and opposing jets, separately. Both their effectiveness and mechanisms to protect the body surface from heating are analyzed. The predicted distributions of pressure and heat flux, and the unique flow characteristics brought by spikes of different shapes or opposing jets of different total pressure ratios all verify the reliability and accuracy of the BGK scheme in the thermal protection system analysis. 相似文献
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During the past decade gas-kinetic methods based on the BGK simplification of the Boltzmann equation have been employed to compute fluid flow in a finite-difference or finite-volume context. Among the most successful formulations is the finite-volume scheme proposed by Xu [K. Xu, A gas-kinetic BGK scheme for the Navier–Stokes equations and its connection with artificial dissipation and Godunov method, J. Comput. Phys. 171 (48) (2001) 289–335]. In this paper we build on this theoretical framework mainly with the aim to improve the efficiency and convergence of the scheme, and extend the range of application to three-dimensional complex geometries using general unstructured meshes. To that end we propose a modified BGK finite-volume scheme, which significantly reduces the computational cost, and improves the behavior on stretched unstructured meshes. Furthermore, a modified data reconstruction procedure is presented to remove the known problem that the Chapman–Enskog expansion of the BGK equation fixes the Prandtl number at unity. The new Prandtl number correction operates at the level of the partial differential equations and is also significantly cheaper for general formulations than previously published methods. We address the issue of convergence acceleration by applying multigrid techniques to the kinetic discretization. The proposed modifications and convergence acceleration help make large-scale computations feasible at a cost competitive with conventional discretization techniques, while still exploiting the advantages of the gas-kinetic discretization, such as computing full viscous fluxes for finite volume schemes on a simple two-point stencil. 相似文献
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In this article, a discrete effect in the thermal Lattice BGK two-speed model is studied. These effects are due to the non-equilibrium state in the particle distribution function, and the non-equilibrium occurs near walls. The mechanism of the LBM counterpart of the thermal creep flow, which appears due to the temperature gradient of the boundary in rarefied gases, is clarified analytically and numerical calculations are performed for some cases. A technique for eliminating this effect is also shown. 相似文献
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Heat transfer in lattice BGK modeled fluid 总被引:1,自引:0,他引:1
The thermal lattice BGK model is a recently suggested numerical tool aiming at solving problems of thermohydrodynamics. The quality of the lattice BGK simulation is checked in this paper by calculating temperature profiles in the Couette flow under different Eckert and Mach numbers. A revised lower order model is proposed to improve the accuracy and the higher order model is proved to be advantageous in this respect, especially in the flow regime with a higher Mach number. 相似文献
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In view of making the best use of information coming from past observational data, a new difference scheme with multi-time levels (p>3) is suggested. Some mathematical characteristics of the scheme, which is called the retrospective scheme, are discussed. The numerical results of some examples show that the calculation accuracy of linear and nonlinear advection equations computed with the retrospective scheme is higher than that obtained via the leapfrog scheme. The scheme can be applied to many fields, such as meteorology, engineering physics, astronautics, environment and economy etc, where systematic observations are made normally. 相似文献
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A unified incompressible lattice BGK model and its application to three-dimensional lid-driven cavity flow 下载免费PDF全文
A unified lattice Bhatnagar-Gross-Krook (ILBGK) model iDdQq for the incompressible Navier-Stokes equation is presented. To test its efficiency, the lid-driven cavity flow in three-dimensional space for Reynolds number Re=3200 and span aspect ratio SAR=1, 2 and 3 is simulated in detail on a 48×48×(48×SAR) uniform lattice using the model. The test results agree well with those in previous experiments and numerical works and show the efficiency and strong numerical stability of the proposed ILBGK model. 相似文献