标题： 尼特罗流体动力学的高效单精度模拟 显示英文标题

标题： Efficient single-precision simulations of nematohydrodynamics

摘要： 在图形处理单元（GPU）上对向列流体动力学进行的模拟通常使用双精度，这确保了准确性，但显著增加了计算成本。 然而，消费级GPU针对单精度计算进行了优化，使得双精度模拟在广泛可用的硬件上效率低下。 在本工作中，我们证明单精度模拟可以达到与双精度方法相同的准确性，同时将计算速度提高了27倍。 为了实现这一点，我们引入了两个关键改进：(i) 在格子玻尔兹曼方法中的偏移分布函数，这可以减轻低速下的精度损失，以及(ii) 在有限差分求解器中使用更大的时间步长，这可以减少数值误差并提高整体准确性。 我们发现，与双精度不同，在单精度模拟中，准确性相对于有限差分时间步长呈非单调趋势，揭示了精确计算的最佳区域。 为了说明我们方法的有效性，我们模拟了泊肃叶流中单个和多个斯奎米昂管的动力学。 我们的结果证实，优化的单精度模拟能够实现复杂向列流体动力学系统的快速且准确的建模，在标准游戏GPU上实现了大规模模拟的可行性。 显示英文摘要

摘要： Simulations of nematohydrodynamics on graphics processing units (GPUs) are typically performed using double precision, which ensures accuracy but significantly increases computational cost. However, consumer-grade GPUs are optimized for single-precision calculations, making double-precision simulations inefficient on widely available hardware. In this work, we demonstrate that single-precision simulations can achieve the same accuracy as double-precision methods while delivering a 27-fold increase in computational speed. To achieve this, we introduce two key improvements: (i) the shifted distribution function in the lattice Boltzmann method, which mitigates precision loss at low velocities, and (ii) the use of larger time steps in the finite-difference solver, which reduces numerical errors and improves overall accuracy. We find that, unlike in double precision, accuracy in single-precision simulations follows a non-monotonic trend with respect to the finite-difference time step, revealing an optimal regime for precise computations. To illustrate the effectiveness of our approach, we simulate the dynamics of single and multiple skyrmionic tubes in Poiseuille flow. Our results confirm that optimized single-precision simulations enable fast and accurate modeling of complex nematohydrodynamic systems, making large-scale simulations feasible on standard gaming GPUs.