论文标题
具有自适应速度模具的可压缩晶格Boltzmann方法：无插值配方
Compressible lattice Boltzmann methods with adaptive velocity stencils: An interpolation-free formulation
论文作者
论文摘要
自适应晶格Boltzmann方法（LBMS）基于对局部宏观条件（例如速度和温度）进行自我调整的速度离散化。尽管此功能提高了LBM在较大速度和温度波动方面的准确性和稳定性，但由于空间插值而引起的算法的效率也强烈影响，这些算法插值需要在网格节点处获得种群。为了避免这种缺陷，目前的工作提出了自适应LBM的新公式，以模拟可压缩流，这些流程不再依赖于空间插值，因此，大大提高了其平行效率，以模拟高速可压缩流。为了实现这一目标，自适应阶段离散化仅限于符合有效的“碰撞和流”算法的特定状态，因此，它不需要其他插值步骤。使用网格传播的适当状态自适应求解器的开发对离散的模具施加了新的限制和挑战，即需要扩展的可操作性范围，从而可以在两个阶段离散之间过渡。实现离散多项式平衡的最小可操作性范围需要相当大的模板（例如D2Q81，D2Q121），因此对于可压缩流量模拟而言不具有竞争力。但是，如文章所示，使用D2Q21晶格以可接受的成本以可接受的成本提供数值平衡的使用可以在相邻离散偏移的可操作性范围内提供重叠。通过几个数值验证，目前的方法被证明允许有效地实现高粘度状态，即使在较低的粘度状态下，也可以有效地实现高马赫数流量的离散状态自适应LBM。
Adaptive lattice Boltzmann methods (LBMs) are based on velocity discretizations that self-adjust to local macroscopic conditions such as velocity and temperature. While this feature improves the accuracy and the stability of LBMs for large velocity and temperature fluctuations, it also strongly impacts the efficiency of the algorithm due to space interpolations that are required to get populations at grid nodes. To avoid this defect, the present work proposes new formulations of adaptive LBMs for the simulation of compressible flows which do not rely anymore on space interpolations, hence, drastically improving their parallel efficiency for the simulation of high-speed compressible flows. To reach this goal, the adaptive phase discretization is restricted to particular states that are compliant with the efficient "collide and stream" algorithm, and as a consequence it does not require additional interpolation steps. The development of proper state-adaptive solvers with on-grid propagation imposes new restrictions and challenges on the discrete stencils, namely the need for an extended operability range allowing for the transition between two phase discretizations. Achieving the minimum operability range for discrete polynomial equilibria requires rather large stencils (e.g. D2Q81, D2Q121) and is therefore not competitive for compressible flow simulations. However, as shown in the article, the use of numerical equilibria can provide for overlaps in the operability ranges of neighboring discrete shifts at acceptable cost using the D2Q21 lattice. Through several numerical validations, the present approach is shown to allow for an efficient realization of discrete state-adaptive LBMs for high Mach number flows even in the low viscosity regime.
