Conservative, high-order particle–mesh scheme with applications to advection-dominated flows
Conservative, high-order particle–mesh scheme with applications to advection-dominated flows
复制标题
保守的高阶粒子网格方案及其在平流主导流中的应用
DOI：
10.1016/j.cma.2019.01.028
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发表时间：
2019
影响因子：
7.2
通讯作者：
D. Sulsky
中科院分区：
文献类型：
--
作者：
J. Maljaars;R. Labeur;Nathaniel Trask;D. Sulsky
通过结合细胞内粒子（PIC）和混合不连续伽辽金（HDG）方法的概念，我们提出了一种用于流动和传输问题的粒子网格方案，该方案允许无扩散平流，同时满足局部和全局质量和动量守恒，并扩展到高阶空间精度。这是通过引入一种新颖的粒子网格投影算子来实现的，该算子将粒子网格数据传输转换为偏微分方程约束的优化问题，从而允许从粒子轨迹推断单元边界处的平流通量泛函。该优化问题无缝地适合 HDG 框架，其中优化问题中的控制变量充当 HDG 方案中的平流通量。由此产生的代数问题可以使用静态凝聚有效地解决。通过线性平流扩散方程和不可压缩纳维-斯托克斯方程的数值例子证明了该方案的性能。结果证明了最佳的空间精度，并且当与 θ 时间积分方案结合时，显示了二阶时间精度。
By combining concepts from particle-in-cell (PIC) and hybridized discontinuous Galerkin (HDG) methods, we present a particle–mesh scheme for flow and transport problems which allows for diffusion-free advection while satisfying mass and momentum conservation–locally and globally–and extending to high-order spatial accuracy. This is achieved via the introduction of a novel particle–mesh projection operator which casts the particle–mesh data transfer as a PDE-constrained optimization problem, permitting advective flux functionals at cell boundaries to be inferred from particle trajectories. This optimization problem seamlessly fits in a HDG framework, whereby the control variables in the optimization problem serve as advective fluxes in the HDG scheme. The resulting algebraic problem can be solved efficiently using static condensation. The performance of the scheme is demonstrated by means of numerical examples for the linear advection–diffusion equation and the incompressible Navier–Stokes equations. The results demonstrate optimal spatial accuracy, and when combined with a θ time integration scheme, second-order temporal accuracy is shown.
影响因子：
4.1
作者：
Lind, S. J.;Stansby, P. K.
通讯作者：
Stansby, P. K.