发表机构
University of Augsburg; HTW Berlin – University of Applied Sciences（奥格斯堡大学; 柏林应用科学大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出稳定的秩自适应步长截断有限体积法，求解分段线性边界区域带流入条件的Vlasov输运方程，低秩近似可处理大规模相空间离散，误差有界且继承稳定性，实验验证其有效性。
AI 中文摘要
我们基于低秩近似研究带流入边界条件的有界空间区域上线性Vlasov输运方程的数值解，将有限体积离散化与所得矩阵常微分方程的秩自适应步长截断格式相结合。空间和速度网格可采用非结构化形式，合适的数值通量可保留空间-速度分离表示。对于齐次流入情况，我们证明低秩格式继承了底层全有限体积前向欧拉法的L₂稳定性和CFL条件限制；此外，低秩近似误差可通过截断容差显式界定，避免了动态低秩近似中与切空间投影相关的建模误差。1d1v和2d2v数值实验验证了预测的误差行为：在2d2v场景中，该方法可处理带非零流入的非结构化空间网格，以及约5.8×10¹⁰个相空间单元的全张量积离散化，且数值秩最多为12。
英文摘要
We consider the numerical solution of the linear Vlasov transport equation on bounded spatial domains with inflow boundary conditions based on low-rank approximation. We combine a finite volume discretization with a rank-adaptive step-and-truncate scheme for the resulting matrix ODE. The spatial and velocity meshes may be unstructured, while suitable numerical fluxes retain a separated space-velocity representation. For homogeneous inflow, we show that the low-rank scheme inherits the $L_2$ stability and CFL restriction of the underlying full finite volume forward Euler method. In addition, the low-rank approximation error is bounded explicitly in terms of the truncation tolerances, avoiding the modeling error associated with tangent-space projections in dynamical low-rank approximation. Numerical experiments in 1d1v and 2d2v confirm the predicted error behavior. In 2d2v, the method handles an unstructured spatial mesh with nonzero inflow and a full tensor-product discretization of approximately $5.8\cdot10^{10}$ phase-space cells while the numerical rank is at most twelve.
