矢量格子玻尔兹曼方法的保守局部网格细化
Conservative local grid refinement for the vectorial lattice Boltzmann method
- ETH Zürich（苏黎世联邦理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出矢量格子玻尔兹曼方法的保守局部网格细化耦合，通过时间重构与回流实现质量、动量、能量精确守恒，并扩展自适应细化，在二维算例中验证了精度提升。
AI中文摘要：
我们提出了一种用于矢量格子玻尔兹曼方法（VLBM）的保守局部网格细化耦合。VLBM是一种用于双曲守恒律的动力学类型格式，其中每个守恒场由其自身的分布函数承载，而非通过麦克斯韦分布的矩截断获得。粗网格和细网格区域共享相同的链接速度，并以不同的时间步长推进，按固定比率进行子循环；时间上的均值保持重构提供了缺失的粗到细边界数据，而匹配的Berger-Colella风格回流将细到粗数据返回，共同精确守恒质量、动量和能量，与状态方程、局部松弛参数或时间步长无关。此外，我们通过一对保守的拆分和合并算子提出了自适应网格细化扩展，无需修改底层耦合。该方法在一系列难度递增的二维案例上得到验证，每个案例均恢复了精确守恒，并相对于等效均匀网格获得了预期的精度提升。
英文摘要：
We present a conservative local grid-refinement coupling for the vectorial lattice Boltzmann method (VLBM), a kinetic-type scheme for hyperbolic conservation laws in which each conserved field is carried by its own population rather than by moment truncation of a Maxwellian. Coarse and fine regions share a common link speed and are advanced with different time steps, sub-cycled at a fixed ratio; a mean-preserving reconstruction in time supplies the missing coarse-to-fine boundary data, and a matched, Berger--Colella-style reflux returns the fine-to-coarse data, together conserving mass, momentum, and energy exactly, independent of the equation of state, the local relaxation parameter, or the time step. In addition, we propose an adaptive mesh refinement extension through a conservative pair of splitting and merging operators that require no modification to the underlying coupling. The approach is validated on a sequence of increasingly demanding two-dimensional cases, in every case recovering exact conservation and the expected accuracy gains over an equivalent uniform grid.
