共查询到20条相似文献,搜索用时 156 毫秒
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根据两介质五方程简化模型的基本假设,发展了适用于任意多种介质的体积分数方程。为了捕捉多介质界面,将HLLC-HLLCM混合型数值通量的计算格式推广应用于二维平面和柱几何的多介质复杂流动问题,在高阶精度的数据重构过程中采用斜率修正型人工压缩方法ACM。通过一维、二维多介质黎曼问题算例测试,结果表明:发展的计算格式能够较好地分辨接触间断和激波,间断附近物理量无振荡;对于添加了初始扰动的激波问题,能够有效抑制激波数值不稳定性;使用二维柱球SOD问题和接触间断型黎曼问题检验计算格式对多介质复杂流动问题的适应性。 相似文献
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根据对流迎风分裂(AUSM)思想提出一种通量分裂方法,称为K-CUSP格式.它与传统H-CUSP和E-CUSP格式的最大差异在于总能量的分裂:K-CUSP格式将无粘守恒通量中所有的运动学量分裂到对流项,所有的热力学量分裂到压力项,即总能量被分裂成动能和静焓.对于压力项的数值通量,采用一种新的界面构造方法.数值测试表明:①K-CUSP格式继承了FVS格式的简单性和稳健性.在激波后不易出现压力过冲,在膨胀区域没有振荡,优于AUSM和WPS格式;②K-CUSP格式继承了FDS格式的分辨率.激波间断的分辨率和H-CUSP、E-CUSP格式基本相同,接触间断的分辨率高于FVS格式,低于Roe、AUSM和WPS格式.AUSM和WPS格式在计算运动接触间断时,速度存在很大振荡,而新格式不存在振荡. 相似文献
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文章通过对EFM(effective field modeling)模型进行简化, 消除了原模型的非守恒性项和非双曲性特性项, 发展了一种基于密度的气液两相流模拟方法: ρ-VOF方法.利用体积分数信息对控制单元内的自由界面进行重构, 得到了控制单元内流体的空间分布, 并采用AUSM+-up格式获得考虑气液流体接触间断信息的对流通量.新方法可统一处理激波间断和接触间断的相互作用, 保持自由界面的尖锐性, 并且其计算量与自由界面的空间复杂度无关.最后, 数值模拟了液体激波管气液激波管和气体激波跨二维液滴传播等问题, 并与文献结果进行对比, 验证了本方法在气液两相流模拟中的准确性. 相似文献
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提出一种数值模拟凝聚炸药爆轰问题的单元中心型Lagrange方法.利用有限体积离散爆轰反应流动方程组,基于双曲型偏微分方程组的特征理论获得离散网格节点的速度与压力,获得的网格节点速度与压力用于更新网格节点位置以及计算网格单元边的数值通量.以这种方式获得的网格节点解是一种"真正多维"的理论解,是一维Godunov格式在二维Riemann问题的推广.有限体积离散得到的爆轰反应流动的半离散系统使用一种显-隐Runge-Kutta格式来离散求解:显式格式处理对流项,隐式格式处理化学反应刚性源项.算例表明,提出的单元中心型Lagrange方法能够较好地模拟凝聚炸药的爆轰反应流动. 相似文献
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基于近似Riemann解的有限体积ALE方法 总被引:1,自引:0,他引:1
研究二维平面坐标系和二维轴对称坐标系中四边形网格上可压缩流体力学的有限体积ALE(Arbitrary Lagrangian Eulerian)方法.数值方法采用节点中心有限体积法,数值通量采用适用于任意状态方程的HLLC(Harten-Lax-Van Leer-Collela)通量.空间二阶精度通过用WENO(weighted essentially non-oscillatory)方法对原始变量进行重构获得,时间离散采用两步显式Runge-Kutta格式.数值例子显示,方法具有良好的激波分辨能力和高精度的数值逼近能力. 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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Time-Domain Numerical Solutions of Maxwell Interface Problems with Discontinuous Electromagnetic Waves 下载免费PDF全文
Ya Zhang Duc Duy Nguyen Kewei Du Jin Xu & Shan Zhao 《advances in applied mathematics and mechanics.》2016,8(3):353-385
This paper is devoted to time domain numerical solutions of two-dimensional
(2D) material interface problems governed by the transverse magnetic
(TM) and transverse electric (TE) Maxwell's equations with discontinuous electromagnetic
solutions. Due to the discontinuity in wave solutions across the interface, the
usual numerical methods will converge slowly or even fail to converge. This calls for
the development of advanced interface treatments for popular Maxwell solvers. We
will investigate such interface treatments by considering two typical Maxwell solvers
– one based on collocation formulation and the other based on Galerkin formulation. To
restore the accuracy reduction of the collocation finite-difference time-domain (FDTD)
algorithm near an interface, the physical jump conditions relating discontinuous wave
solutions on both sides of the interface must be rigorously enforced. For this purpose,
a novel matched interface and boundary (MIB) scheme is proposed in this work, in
which new jump conditions are derived so that the discontinuous and staggered features
of electric and magnetic field components can be accommodated. The resulting
MIB time-domain (MIBTD) scheme satisfies the jump conditions locally and suppresses
the staircase approximation errors completely over the Yee lattices. In the discontinuous
Galerkin time-domain (DGTD) algorithm – a popular Galerkin Maxwell solver, a
proper numerical flux can be designed to accurately capture the jumps in the electromagnetic
waves across the interface and automatically preserves the discontinuity in
the explicit time integration. The DGTD solution to Maxwell interface problems is explored
in this work, by considering a nodal based high order discontinuous Galerkin
method. In benchmark TM and TE tests with analytical solutions, both MIBTD and
DGTD schemes achieve the second order of accuracy in solving circular interfaces. In
comparison, the numerical convergence of the MIBTD method is slightly more uniform,
while the DGTD method is more flexible and robust. 相似文献
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Sung Don Kim Bok Jik Lee Hyoung Jin Lee In-Seuck Jeung 《Journal of computational physics》2009,228(20):7634-7642
Many researchers have reported failures of the approximate Riemann solvers in the presence of strong shock. This is believed to be due to perturbation transfer in the transverse direction of shock waves. We propose a simple and clear method to prevent such problems for the Harten–Lax–van Leer contact (HLLC) scheme. By defining a sensing function in the transverse direction of strong shock, the HLLC flux is switched to the Harten–Lax–van Leer (HLL) flux in that direction locally, and the magnitude of the additional dissipation is automatically determined using the HLL scheme. We combine the HLLC and HLL schemes in a single framework using a switching function. High-order accuracy is achieved using a weighted average flux (WAF) scheme, and a method for v-shear treatment is presented. The modified HLLC scheme is named HLLC–HLL. It is tested against a steady normal shock instability problem and Quirk’s test problems, and spurious solutions in the strong shock regions are successfully controlled. 相似文献
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We investigate the traditional kinetic flux vector splitting (KFVS) and BGK schemes for the compressible Euler equations. First, based on a careful study of the behavior of the discrete physical variables across the contact discontinuity, we analyze quantitatively the mechanism of inducing spurious oscillations of the velocity and pressure in the vicinity of the contact discontinuity for the first-order KFVS and BGK schemes. Then, with the help of this analysis, we propose a first-order modified KFVS (MKFVS) scheme which is oscillation-free in the vicinity of the contact discontinuity, provided certain consistent conditions are satisfied. Moreover, by using piecewise linear reconstruction and van Leer’s limiter, the first-order MKFVS scheme is extended to a second-order one, consequently, a nonoscillatory second-order MKFVS scheme is constructed. Finally, by combing the MKFVS schemes with the γ-model, we successfully extend the MKFVS schemes to multi-flows, and propose therefore a first- and second-order MKFVS schemes for multi-fluid computations, which are nonoscillatory across fluid interfaces. A number of numerical examples presented in this paper validate the theoretic analysis and demonstrate the good performance of the MKFVS schemes in simulation of contact discontinuities for both single- and multi-fluids. 相似文献
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磁场的存在使得磁流体力学特征波模不同于流体力学, 因此直接由流体力学HLLC黎曼算子导出的HLLC双中间态在交界的间断面会出现不守恒的问题。通常降级采用HLL单磁场中间态代替HLLC双磁场中间态以实现守恒和计算稳定, 代价是切向间断的模拟精度不足。本文对此进行改进, 在模拟切向间断时仍然保留原有的HLLC双磁场中间态, 同时各守恒量仍然能够满足Toro相容条件; 改进型HLLC算子在间断两侧的磁场分量存在差异, 因此能够更精确还原切向间断面。基于数值测试, 包括一维激波管和切向间断的时变模拟, 以及地球磁层三维数值模拟, 将模拟结果进行对比, 结果表明: 相比于已发展的HLLC算子, 改进型HLLC算子对切向间断具有更好的捕捉精度, 能够达到或接近耗时更多的HLLD算子的模拟精度。 相似文献
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A new high order finite-difference method utilizing the idea of Harten ENO subcell resolution method is proposed for chemical reactive flows and combustion. In reaction problems, when the reaction time scale is very small, e.g., orders of magnitude smaller than the fluid dynamics time scales, the governing equations will become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present proposed method is a modified fractional step method which solves the convection step and reaction step separately. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with the computed flow variables in the shock region modified by the Harten subcell resolution idea. For numerical experiments, a fifth-order finite-difference WENO scheme and its anti-diffusion WENO variant are considered. A wide range of 1D and 2D scalar and Euler system test cases are investigated. Studies indicate that for the considered test cases, the new method maintains high order accuracy in space for smooth flows, and for stiff source terms with discontinuities, it can capture the correct propagation speed of discontinuities in very coarse meshes with reasonable CFL numbers. 相似文献
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Matthew R. Smith K.-M. Lin C.-T. Hung Y.-S. Chen J.-S. Wu 《Journal of computational physics》2011,230(3):477-493
The integral form of the conventional HLL fluxes are presented by taking integrals around the control volume centred on each cell interface. These integrals are demonstrated to reduce to the conventional HLL flux through simplification by assuming spatially constant conserved properties. The integral flux expressions are then modified by permitting the analytical inclusion of spatially linearly varying conserved quantities. The newly obtained fluxes (which are named HLLG fluxes for clarification, where G stands for gradient inclusion) demonstrate that conventional reconstructions at cell interfaces are invalid and can produce unstable results when applied to conventional HLL schemes. The HLLG method is then applied to the solution of the Euler Equations and Shallow Water Equations for various common benchmark problems and finally applied to a 1D fluid modeling for an argon RF discharge at low pressure. Results show that the correct inclusion of flow gradients is shown to demonstrate superior transient behavior when compared to the existing HLL solver and conventional spatial reconstruction without significantly increasing computational expense. 相似文献