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1.
In this paper,Runge-Kutta Discontinuous Galerkin(RKDG) finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ?ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ?ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.  相似文献   

2.
The high-order accurate Runge–Kutta discontinuous Galerkin (RKDG) method is applied to the simulation of compressible multi-medium flow, generalizing the interface treating method given in Chertock et al. (2008) [9]. In mixed cells, where the interface is located, Riemann problems are solved to define the states on both sides of the interface. The input states to the Riemann problem are obtained by extrapolation to the cell boundary from solution polynomials in the neighbors of the mixed cell. The level set equation is solved by using a high-order accurate RKDG method for Hamilton–Jacobi equations, resulting in a unified DG solver for the coupled problem. The method is conservative if we include the states in the mixed cells, which are however not used in the updating of the numerical solution in other cells. The states in the mixed cells are plotted to better evaluate the conservation errors, manifested by overshoots/undershoots when compared with states in neighboring cells. These overshoots/undershoots in mixed cells are problem dependent and change with time. Numerical examples show that the results of our scheme compare well with other methods for one and two-dimensional problems. In particular, the algorithm can capture well complex flow features of the one-dimensional shock entropy wave interaction problem and two-dimensional shock–bubble interaction problem.  相似文献   

3.
多介质流动问题的求解一般是在结构网格上实现,而三角形网格对于复杂计算区域具有更好的适应性,本文结合rGFM方法,给出三角形网格上多介质流动问题界面处理方法.利用level-set方法跟踪界面,在界面处构造Riemann问题,得到界面处流体准确的流动状态.通过定义界面边界条件,将多介质流动问题转化为单介质流动问题,利用高精度RKDG方法求解.采用多个算例验证该方法的稳健性和有效性,结果表明该方法能准确捕捉界面和激波的位置,保持界面清晰.  相似文献   

4.
It has been claimed that the particular numerical flux used in Runge–Kutta Discontinuous Galerkin (RKDG) methods does not have a significant effect on the results of high-order simulations. We investigate this claim for the case of compressible ideal magnetohydrodynamics (MHD). We also address the role of limiting in RKDG methods.For smooth nonlinear solutions, we find that the use of a more accurate Riemann solver in third-order simulations results in lower errors and more rapid convergence. However, in the corresponding fourth-order simulations we find that varying the Riemann solver has a negligible effect on the solutions.In the vicinity of discontinuities, we find that high-order RKDG methods behave in a similar manner to the second-order method due to the use of a piecewise linear limiter. Thus, for solutions dominated by discontinuities, the choice of Riemann solver in a high-order method has similar significance to that in a second-order method. Our analysis of second-order methods indicates that the choice of Riemann solver is highly significant, with the more accurate Riemann solvers having the lowest computational effort required to obtain a given accuracy. This allows the error in fourth-order simulations of a discontinuous solution to be mitigated through the use of a more accurate Riemann solver.We demonstrate the minmod limiter is unsuitable for use in a high-order RKDG method. It tends to restrict the polynomial order of the trial space, and hence the order of accuracy of the method, even when this is not needed to maintain the TVD property of the scheme.  相似文献   

5.
构造Lagrange坐标系下二维可压缩气动方程组的RKDG(Runge-Kutta Discontinuous Galerkin)有限元方法.将流体力学方程组和几何守恒律统-求解,所有计算都在固定的网格上进行,计算过程中不需要网格节点的速度信息.对几个数值算例进行数值模拟,得到较好的数值模拟结果.  相似文献   

6.
7.
A numerical method for integrating the equations describing a dynamically coupled system made of a fluid and cosmic-rays is developed. In smooth flows the effect of CR pressure is accounted for by modification of the characteristic equations and the energy exchange between cosmic-rays and the fluid, due to diffusive processes in configuration and momentum space, is modeled with a flux conserving method. Provided the shock acceleration efficiency as a function of the upstream conditions and shock Mach number, we show that the Riemann solver can be modified to take into account the cosmic-ray mediation without having to resolve the cosmic-ray induced substructure. Shocks are advanced with Glimm’s method which preserves their discontinuous character without any smearing, thus allowing to maintain self-consistency in the shock solutions. In smooth flows either Glimm’s or a higher order Godunov’s method can be applied, with the latter producing better results when approximations are introduced in the Riemann solver.  相似文献   

8.
构造矩形网格下求解Lagrangian坐标系下气动方程组的单元中心型格式. 空间离散采用控制体积间断Petrov-Galerkin方法,时间离散采用二阶TVD Runge-Kutta方法. 利用限制器来抑制非物理震荡并保证RKCV算法的稳定性. 构造的算法可以保证物理量的局部守恒. 与Runge-Kutta间断Galerkin(RKDG)方法相比较,RKCV方法的计算公式少一项积分项使得计算较简单. 给出一些数值算例验证了算法的可靠性及效率.  相似文献   

9.
In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume (RKCV) discontinuous finite element method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discontinuous Galerkin (RKDG) method, the RKCV method is easier to implement. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm.  相似文献   

10.
刘志刚  邹晓兵  王新新 《强激光与粒子束》2022,34(7):075002-1-075002-11
基于拉格朗日描述,建立了水中金属丝电爆炸的单温磁流体动力学模型,并给出一种高阶混合有限元离散求解方法。拉氏可压缩流体方程组中,速度定义在H1连续有限元空间,内能定义在L2间断有限元空间实现物质界面的精确捕捉,存在激波的区域引入张量人工粘性抑制数值振荡。磁扩散方程仅考虑周向磁通量密度,简化为标量方程,使用H1连续有限元方法离散求解。焦耳热和洛伦兹力作为源项引入实现磁流体方程的耦合。数值算例表明:磁扩散求解器能够求解存在不同电导率的多介质磁扩散问题;拉氏流体求解器能够精确追踪物质界面,具有较好的激波分辨能力;耦合RLC电路的磁流体求解器能够复现水中金属丝电爆炸加热相变、冲击波的产生与传播、放电模式转变等物理过程。  相似文献   

11.
李诗尧  于明 《计算物理》2019,36(5):505-516
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   

12.
This paper presents a new high-order cell-centered Lagrangian scheme for two-dimensional compressible flow. The scheme uses a fully Lagrangian form of the gas dynamics equations, which is a weakly hyperbolic system of conservation laws. The system of equations is discretized in the Lagrangian space by discontinuous Galerkin method using a spectral basis. The vertex velocities and the numerical fluxes through the cell interfaces are computed consistently in the Eulerian space by virtue of an improved nodal solver. The nodal solver uses the HLLC approximate Riemann solver to compute the velocities of the vertex. The time marching is implemented by a class of TVD Runge–Kutta type methods. A new HWENO (Hermite WENO) reconstruction algorithm is developed and used as limiters for RKDG methods to maintain compactness of RKDG methods. The scheme is conservative for the mass, momentum and total energy. It can maintain high-order accuracy both in space and time, obey the geometrical conservation law, and achieve at least second order accuracy on quadrilateral meshes. Results of some numerical tests are presented to demonstrate the accuracy and the robustness of the scheme.  相似文献   

13.
胡立军  袁礼 《气体物理》2016,1(6):22-35
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   

14.
在动态网格上通过耦合求解流动控制方程和结构动力学方程, 发展了一种舵面控制下飞行器运动响应过程中气动弹性数值模拟研究方法.流动控制方程采用N-S方程, 结构动力学采用线性模态叠加方法, 其中流动控制方程空间离散采用基于非结构网格的有限体积方法, 对流通量采用计算HLLC格式, 非定常时间离散采用基于LU-SGS的双时间步长方法.模拟中, 气动运动和结构变形在双时间步长方法推进过程中采用改进松耦合方法, 气动网格与结构网格之间信息交换采用无限平板样条法实现, 飞行器的运动和变形采用基于重叠网格和Delaunay图映射变形网格相结合的方法进行处理.采用多个考核算例对发展的数值方法进行考核验证, 结果表明该方法可以高效精确模拟舵面开环控制下飞行器运动响应过程中的气动弹性特性.   相似文献   

15.
With the intermediate flow states predicted by local two phase Riemann problem,the modified ghost fluid method(MGFM)and its variant(r GFM)have been widely employed to resolve the interface condition in the simulation of compressible multi-medium flows.In this work,the drawback of the construction procedure of local two phase Riemann problem in r GFM was investigated in detail,and a refined version of the construction procedure was specially developed to make the simulation of underwater explosion bubbles more accurate and robust.Beside the refined r GFM,the fast and accurate particle level set method was also adopted to achieve a more effective and computationally efficient capture of the evolving multi-medium interfaces during the simulation.To demonstrate the improvement brought by current refinement,several typical numerical examples of underwater explosion bubbles were performed with original r GFM and refined r GFM,respectively.The results indicate that,when compared with original r GFM,numerical oscillations were effectively removed with the proposed refinement.Accordingly,with present refined treatment of interface condition,a more accurate and robust simulation of underwater explosion bubbles was accomplished in this work.  相似文献   

16.
 求解Riemann问题得到界面接触间断的流动状态,并以此构造带状区域的虚拟流体状态,对于多维问题设计了一种方便有效的算法。同时求解耦合的守恒形式欧拉方程组和非守恒界面捕捉方程,并用Level-Set函数捕捉界面,数值计算采用高分辨率MWENO格式。最后对可压缩多介质流动问题进行了数值模拟。  相似文献   

17.
吴迪  蔚喜军 《计算物理》2010,27(4):492-500
将龙格库塔间断有限元方法(RDDG)与自适应方法相结合,求解三维欧拉方程.区域剖分采用非结构四面体网格,依据数值解的变化采用自适应技术对网格进行局部加密或粗化,减少总体网格数目,提高计算效率.给出四种自适应策略并分析不同自适应策略的优缺点.数值算例表明方法的有效性.  相似文献   

18.
In this paper, we propose new Euler flux functions for use in a finite-volume Euler/Navier–Stokes code, which are very simple, carbuncle-free, yet have an excellent boundary-layer-resolving capability, by combining two different Riemann solvers into one based on a rotated Riemann solver approach. We show that very economical Euler flux functions can be devised by combining the Roe solver (a full-wave solver) and the Rusanov/HLL solver (a fewer-wave solver), based on a rotated Riemann solver approach: a fewer-wave solver automatically applied in the direction normal to shocks to suppress carbuncles and a full-wave solver applied, again automatically, across shear layers to avoid an excessive amount of dissipation. The resulting flux functions can be implemented in a very simple and economical manner, in the form of the Roe solver with modified wave speeds, so that converting an existing Roe flux code into the new fluxes is an extremely simple task. They require only 7–14% extra CPU time and no problem-dependent tuning parameters. These new rotated fluxes are not only robust for shock-capturing, but also accurate for resolving shear layers. This is demonstrated by an extensive series of numerical experiments with standard finite-volume Euler and Navier–Stokes codes, including various shock instability problems and also an unstructured grid case.  相似文献   

19.
虚拟流体方法为模拟具有清晰物质界面的多介质流动问题提供了一种简便途径.尤其基于多介质Riemann问题解的修正虚拟流体方法及其变体,能够真实考虑到界面附近非线性波的相互作用和物质性质的影响,可以有效解决各种界面强间断等挑战性难题,具有巨大的工程应用潜力.文章重点回顾了虚拟流体方法的发展历史,总结和对比了各种代表性版本在模拟可压缩多介质流时的界面条件定义方式和多维推广方式,并介绍了该方法的设计原则和精度分析方面的研究进展.文章还回顾了该方法在其他更广泛和更具挑战性典型科学问题中的最新应用进展,并对方法的优势和特点进行了总结.   相似文献   

20.
刘妍  茅德康 《计算物理》2020,37(2):140-152
基于可压缩多介质流动问题,分析AC(acoustic),MFCAV(multi fluid channel on averaged volume)和HLLC等近似Riemann解算器的优缺点,通过加权组合的方式设计一种自适应近似Riemann解算器ADRS(adaptive Riemann solver),详细介绍加权组合的自适应选取原则.将ADRS写成AC解算器的修正形式应用于健壮性好的相容中心型拉氏方法.给出Taylor Green vortex稳态流问题的误差分析等数值算例.  相似文献   

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