AI 中文总结
该研究提出一种加权逆风矢量动力学格子玻尔兹曼方法，通过新型逆风平衡分布函数提升了双曲守恒律求解的稳定性、降低误差并优化激波分辨率，可用于浅水、欧拉等双曲系统的数值模拟。
AI 中文摘要
矢量动力学格子玻尔兹曼（VKLB）方法近来成为求解双曲偏微分方程（PDE）系统的有前景的框架。VKLB利用离散的格子速度集离散化玻尔兹曼型方程，施加离散矩约束，并精心定义平衡分布函数。本研究引入由守恒变量和基于通量雅可比矩阵本征分解的连续通量分裂推导的数值通量构造的新型逆风平衡分布函数，该公式使加权逆风VKLB平衡可广泛应用于一般双曲系统。该方法在包含浅水、欧拉和理想磁流体动力学（MHD）方程的一系列具有挑战性的双曲系统上得到验证，在日益复杂的验证和基准问题中，所提方法展现出更好的稳定性、更小的误差范数以及更清晰的激波分辨率。
英文摘要
Vector kinetic lattice Boltzmann (VKLB) methods have recently emerged as a promising framework for solving hyperbolic partial differential equation (PDE) systems. VKLB discretizes Boltzmann-type equations using a discrete set of lattice velocities, enforces discrete moment constraints, and carefully defines equilibrium distribution functions. In this work, we introduce novel upwinded equilibrium distribution functions constructed from conservation variables and numerical fluxes derived via continuous flux vector splitting based on the eigendecomposition of the flux Jacobian. This formulation enables the weighted-upwind VKLB equilibrium to be applied broadly to general hyperbolic systems. The method is verified on a set of challenging hyperbolic systems that includes the shallow water, Euler and ideal magnetohydrodynamics (MHD) equations. The proposed method demonstrates improved stability, reduced error norms, and sharper shock resolution across increasingly complex verification and benchmark problems.
Comments24 pages, 17 figures
