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首页> 外文期刊>Journal of Computational Physics >A high-order WENO-Z finite difference based particle-source-in-cell method for computation of particle-laden flows with shocks
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A high-order WENO-Z finite difference based particle-source-in-cell method for computation of particle-laden flows with shocks

机译：基于高阶WENO-Z有限差分的单元内粒子源方法，计算带冲击的含粒子流

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A high-order particle-source-in-cell (PSIC) algorithm is presented for the computation of the interaction between shocks, small scale structures, and liquid and/or solid particles in high-speed engineering applications. The improved high-order finite difference weighted essentially non-oscillatory (WENO-Z) method for solution of the hyperbolic conservation laws that govern the shocked carrier gas flow, lies at the heart of the algorithm. Finite sized particles are modeled as points and are traced in the Lagrangian frame. The physical coupling of particles in the Lagrangian frame and the gas in the Eulerian frame through momentum and energy exchange, is numerically treated through high-order interpolation and weighing. The centered high-order interpolation of the fluid properties to the particle location is shown to lead to numerical instability in shocked flow. An essentially non-oscillatory interpolation (ENO) scheme is devised for the coupling that improves stability. The ENO based algorithm is shown to be numerically stable and to accurately capture shocks, small flow features and particle dispersion. Both the carrier gas and the particles are updated in time without splitting with a third-order Runge-Kutta TVD method. One and two-dimensional computations of a shock moving into a particle cloud demonstrates the characteristics of the WENO-Z based PSIC method (PSIC/WENO-Z). The PSIC/WENO-Z computations are not only in excellent agreement with the numerical simulations with a third-order Rusanov based PSIC and physical experiments in [V. Boiko, V.P. Kiselev, S.P. Kiselev, A. Papyrin, S. Poplavsky, V. Fornin, Shock wave interaction with a cloud of particles, Shock Waves, 7 (1997) 275-285], but also show a significant improvement in the resolution of small scale structures. In two-dimensional simulations of the Mach 3 shock moving into forty thousand bronze particles arranged in the shape of a rectangle, the long time accuracy of the high-order method is demonstrated. The fifth-order PSIC/WENO-Z method with the fifth-order ENO interpolation scheme improves the small scale structure resolution over the third-order PSIC/WENO-Z method with a second-order central interpolation scheme. Preliminary analysis of the particle interaction with the flow structures shows that sharp particle material arms form on the side of the rectangular shape. The arms initially shield the particles from the accelerated flow behind the shock. A reflected compression wave, however, reshocks the particle arm from the shielded area and mixes the particles. (c) 2008 Elsevier Inc. All rights reserved.
机译：提出了一种高阶单元格粒子源算法（PSIC），用于计算高速工程应用中的冲击，小规模结构以及液体和/或固体粒子之间的相互作用。该算法的核心是改进的高阶有限差分加权基本非振荡（WENO-Z）方法，该方法可解决控制冲击载气流的双曲守恒定律。将有限大小的粒子建模为点，并在拉格朗日框架中进行追踪。拉格朗日框架中的粒子与欧拉框架中的气体通过动量和能量交换的物理耦合，通过高阶插值和加权进行了数值处理。流体属性到粒子位置的居中高阶插值被显示为导致冲击流中的数值不稳定。设计了一种本质上非振荡的插值（ENO）方案用于提高稳定性的耦合。基于ENO的算法显示出数值上的稳定性，并且可以准确地捕获冲击，小流量特征和颗粒扩散。载气和颗粒都可以及时更新，而无需使用三阶Runge-Kutta TVD方法进行拆分。冲击运动进入粒子云的一维和二维计算证明了基于WENO-Z的PSIC方法（PSIC / WENO-Z）的特性。 PSIC / WENO-Z计算不仅与基于Rusanov的三阶PSIC进行的数值模拟以及在[V. Boiko，副总裁Kiselev，SP Kiselev，A。Papyrin，S。Poplavsky，V。Fornin，与粒子云的冲击波相互作用，Shock Waves，7（1997）275-285]，但也显示了小规模分辨率的显着改善结构。在将Mach 3冲击运动成矩形排列的4万个青铜颗粒的二维模拟中，证明了高阶方法的长时间精度。具有五阶ENO插值方案的五阶PSIC / WENO-Z方法比具有二阶中央插值方案的三阶PSIC / WENO-Z方法提高了小规模结构分辨率。对颗粒与流动结构的相互作用的初步分析表明，在矩形的侧面上形成了尖锐的颗粒材料臂。手臂最初将微粒从震动后的加速流中屏蔽掉。但是，反射的压缩波将粒子臂从屏蔽区域中重新撞击并混合粒子。 （c）2008 Elsevier Inc.保留所有权利。

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