基于Mie-Grüneisen状态方程的爆轰波运动数值模拟

依据C-J（Chapman-Jouguet）理论,对爆轰问题中的气态爆轰产物和未反应炸药分别考虑不同的参考状态,并根据参考状态选用特定的Mie-Grüneisen状态方程。忽略化学反应过程,爆轰产物厚度为零的前导激波面以界面的形式存在。数值模拟中,爆轰波的演化分为波面传播以及与未反应介质相互作用两个部分。传播过程中,爆轰波的传播速度即恒定的爆速,爆轰产物在传播过程中瞬间形成,而相互作用过程则是通过Mie-Grüneisen多介质混合模型来计算爆轰波的持续冲击作用。借助于Mie-Grüneisen状态方程以及Mie-Grüneisen多介质混合模型,可以很好地模拟爆轰波的运动过程。对比理论参数及文献的计算结果发现,模拟结果具备较好的准确度。     

基于非结构四边形网格的WENO格式

基于非结构四边形网格发展求解双曲守恒律的三阶加权基本无振荡（WENO）格式.针对任意非结构四边形网格选取重构模板，并给出基于线性多项式的三阶线性重构.但对于一般的非结构四边形网格，会出现非常大的线性权和负权，使得非线性重构的WENO格式对光滑问题也不稳定.本文给出一个处理非常大的线性权的优化重构方法，对优化后得到的负线性权采用分裂方法进行处理.对于非线性权，提出一种考虑局部网格和物理量间断的新光滑度量因子.采用优化重构方法和新的非线性权，当前的三阶WENO格式在质量很差的网格上也具有很好的稳定性.理论的三阶精度在数值精度测试算例中得到验证，同时一范数和无穷范数的误差绝对值不依赖于网格质量；具有强间断的数值结果证明了当前格式的有效性.     

一种适用于磁流体力学切向间断的HLLC黎曼算子

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。     

统一坐标系下二维气动方程组的Runge-Kutta间断Galerkin有限元方法

构造了统一坐标系下二维可压缩气动方程组的Runge-Kutta 间断Galerkin(RKDG)有限元格式. 文中将流体力学方程组和几何守恒律统一求解, 所有计算都在固定的网格上进行, 在计算过程中不需要网格节点的速度信息. 文中对几个数值算例进行了数值模拟, 得到了较好的数值模拟结果.     

基于移动网格的熵稳定格式

提出一种基于移动网格的熵稳定格式求解双曲型守恒律方程.该方法利用等分布原理得到新的网格分布,基于守恒型插值公式计算新的网格上的物理量,使用熵稳定数值通量和三阶强稳定Runge-Kutta时间推进方法得到下一时刻的数值解.数值算例表明该格式不仅能有效提高解在间断处的分辨率,而且能消除可能产生的伪振荡.     

多介质流体力学计算的高分辨率格式

将Ｈａｒｔｅｎ（１９８３）的高分辨率ＴＶＤ格式应用于一维Ｌａｇｒａｎｇｅ流体力学方程取得了成功，特别是按照传统的拉氏方法将热力学量ρ，ｐ，ｅ离散以后取在网格中心，速度则取在网格边界处，而将ＴＶＤ格式中的一些附加项看作人为粘性得到了满意的结果，得到一种计算多种介质的非守恒的高分辨率格式，给出了部分数值结果。     

一种基于AUSM分裂的真正多维HLL格式

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.      

一种高精度的修正Hermite-ENO格式

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.     

守恒律方程组的大时间步长叠波格式

大时间步长叠波格式最初思想为LeVeque提出的大时间步长Godunov格式,通过叠加间断分解发出的强波来构造数值格式.原方法只给出了间断强波的穿越叠加方法,文章对其进行了完善,并推广到多维.针对膨胀波提出了一种网格单元分解法可以自动满足熵条件,避免出现非物理解.给出了格式的具体计算公式,并用单个守恒律方程、一维/多维Euler方程组进行了数值计算.计算结果表明,新格式除了可以采用大时间步长的优点外,在一定范围内随CFL数增加其耗散反而更低,因而对激波接触间断膨胀波的分辨率更高.     

流体力学拉氏守恒滑移线算法设计

本文在Wilkins滑移线算法的基础上, 设计了从区网格边人工黏性对主点施加算法. 结合拉氏“相容性格式”, 通过定义“接触力”和“接触力做功”, 利用局部修正内能的方法设计了总能量守恒的流体力学拉氏格式. 该修正方法可保证对称性、守恒性; 提高数值模拟分辨率.     

Revisiting the thermostatistics of the Grüneisen parameters and applications to quasiharmonic solids

We present an integrated thermostatistical study of the Grüneisen parameter and its application to a quasiharmonic solid. This analysis comprises two parts. The first part considers the connections between different thermodynamic formulations of the Grüneisen parameter, including those arising from the Mie-Grüneisen formula and related equations of state. We also establish the most general consequences of the so-called Grüneisen׳s rule. In the second part, Grüneisen׳s rule is used to establish the thermostatistics of a solid that obeys the quasiharmonic approximation. Both cases are relevant to the application of fundamental microscopic models of the heat capacity of solids.     

A model for shock waves in solids and evidence for a thermal catastrophe

Shock-wave experiments and computer simulations yield a linear relation between shock velocity and particle velocity. We show that a Mie-Grüneisen equation of state combined with the Hugoniot relations matches the computer results and the experiments and leads to an explanation of the generality of the linear velocity dependence. At high shock velocities the onset of a thermal catastrophe, which results in a maximum shock compression, is predicted from our model.     

用冲击压缩数据计算物态方程的一种方法——Grüneisen系数最优化

 本文给出了一种用冲击压缩数据计算Grüneisen物态方程参数的方法。它使Grüneisen系数沿实验冲击绝热线的计算值与晶格振动理论的计算值达到最优拟合，给出了23种金属的冷能，冷压公式中的ρ_0K、Q和q以及Grüneisen系数的结果。用这些参数算得的冲击绝热线与实验冲击绝热线之间的平均相对偏差在1%以内。     

Thermodynamic response of Mie-Grüneisen materials at high pressures

Expressions are derived to give entropy and temperature in a material which obeys the Mie-Grüneisen equation, based on the assumption that both the Hugoniot pressure and the Grüneisen parameter may be expanded as infinite power series in strain. The resulting equations are used to obtain specific expressions for isothermal compression and for isentropic release from a Hugoniot state. A method is suggested for determining the Grüneisen parameter (as a function of strain) from isothermal compression data. Certain limitations involving possible phase transitions are pointed out.     

A hybrid,center-difference,limiter method for simulations of compressible multicomponent flows with Mie-Grüneisen equation of state

We develop an efficient spatially high-order, Cartesian-mesh, hybrid, center-difference, limiter methodology for numerical simulations of compressible multicomponent flows with isotropic Mie-Grüneisen equation of state. Effective switching between center-difference and limiter schemes is achieved by a set of robust tolerance and Lax-entropy based criterion [18]. Oscillations that could result from a mixed stencil scheme are minimized by requiring that the limiter method approaches the center-difference method in smooth regions. To achieve this the limiter is based on a norm of the deviation of WENO reconstruction weights from ideal. Results from a spatially 4th order version of the methodology are presented in one and two dimensions utilizing the California Institute of Technology’s VTF (Virtual Test Facility) AMROC [7] software.     

Second Hugoniot relationship for solids

The term second Hugoniot is used to describe a locus of states directly attainable by shock compression beginning with an initial state that has itself been achieved by shock compression. For many materials the principal Hugoniot is linear in the shock velocity-particle velocity [U_s — u_p] representation. A second Hugoniot for such materials is not linear in this representation, but the nonlinear effects can often be neglected if the compressions are not too great. These results are based on the Mie-Grüneisen equation of state and are more or less independent of the explicit functional dependence of the Grüneisen parameter. A criterion to evaluate the magnitude of nonlinear effects is posed and Mg and Pb are treated as examples. Calculated second Hugoniots are compared with experimental results for regular reflection in Mg, Pb and U. For these materials nonlinear effects are not important from a practical standpoint for final volumetric compressions to roughly two-thirds of the initial volume. Some future experimental work is also suggested.     

基于CE/SE方法的二维Euler型多物质流体弹塑性问题计算

将CE/SE方法推广到二维固体流体弹塑性问题的数值计算,同时结合杂交粒子水平集方法追踪物质界面和合适的边界条件,提出一套完整的二维Euler型流体弹塑性计算方案.通过长钨杆侵彻装甲钢实验的数值模拟,对方法的精度和有效性进行验证.     

Solid–fluid diffuse interface model in cases of extreme deformations

Diffuse interface methods have been recently proposed and successfully used for accurate compressible multi-fluid computations Abgrall [1]; Kapila et al. [20]; Saurel et al. [30]. These methods deal with extended systems of hyperbolic equations involving a non-conservative volume fraction equation and relaxation terms. Following the same theoretical frame, we derive here an Eulerian diffuse interface model for elastic solid-compressible fluid interactions in situations involving extreme deformations. Elastic effects are included following the Eulerian conservative formulation proposed in Godunov [16], Miller and Colella [23], Godunov and Romenskii [17], Plohr and Plohr [27] and Gavrilyuk et al. [14]. We apply first the Hamilton principle of stationary action to derive the conservative part of the model. The relaxation terms are then added which are compatible with the entropy inequality. In the limit of vanishing volume fractions the Euler equations of compressible fluids and a conservative hyperelastic model are recovered. It is solved by a unique hyperbolic solver valid at each mesh point (pure fluid, pure solid and mixture cell). Capabilities of the model and methods are illustrated on various tests of impacts of solids moving in an ambient compressible fluid.