有序流体的动力学理论方法：直接模拟蒙特卡洛方法
A Kinetic Theory Approach To Ordered Fluids: Direct Simulation Monte Carlo Methods
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中文总结 AI 辅助
本文提出一种用于有序流体动力学理论的直接模拟蒙特卡洛方法，通过Strang分裂耦合碰撞与平均场Vlasov输运，数值验证了麦克斯韦弛豫及Onsager势下的各向同性-向列相变。
中文摘要 AI 辅助
我们提出了一种直接模拟蒙特卡洛（DSMC）方法，用于作者近期引入的有序流体的动力学理论。这些流体的微观组分携带属于某个流形的序参量。该方法采用Strang分裂，将二元碰撞的蒙特卡洛处理与序参量流形上平均场Vlasov输运的辛积分耦合起来。对于麦克斯韦碰撞核，我们使用Nanbu-Babovsky方法；对于一般碰撞核，则使用Bird的接受-拒绝方法。平均场Vlasov力在每个时间步从粒子系综中重构。我们还引入了Bhatnagar-Gross-Krook（BGK）/Andersen热浴来控制系统温度。我们针对一般的序参量流形制定了该方法，并将其专门应用于二维棒状（杆状）分子。数值测试验证了该方法的有效性。我们确认了由H定理预测的麦克斯韦分布的弛豫，并模拟了由二次、Kuramoto和Onsager相互作用势驱动的平均场取向。使用Onsager势时，我们成功地在正确的临界温度下捕获了各向同性-向列相变。
英文摘要
We present a direct simulation Monte Carlo (DSMC) method for the kinetic theory of ordered fluids recently introduced by the authors. The microscopic constituents of these fluids carry an order parameter belonging to a manifold. The method applies Strang splitting to couple a Monte Carlo treatment of the binary collisions with a symplectic integration of the mean-field Vlasov transport on the order-parameter manifold. We use the Nanbu-Babovsky approach for Maxwellian collision kernels, and Bird's acceptance-rejection method for general ones. The mean-field Vlasov force is reconstructed from the particle ensemble at each time step. We also include a Bhatnagar-Gross-Krook (BGK) / Andersen thermostat to control the system temperature. We formulate the method for a generic order-parameter manifold, and specialize it to two-dimensional calamitic (rod-like) molecules. Numerical tests validate the method. We confirm the relaxation to the Maxwellian distribution predicted by the H-theorem, and simulate the mean-field alignment driven by quadratic, Kuramoto, and Onsager interaction potentials. With the Onsager potential we successfully capture the isotropic-nematic phase transition at the correct critical temperature.
发表机构
- University of Oxford（牛津大学）
- Charles University（查理大学）
- University of Ferrara（费拉拉大学）
- Simula Research Laboratory（西穆拉研究实验室）
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