随机Landau-Lifshitz Navier-Stokes方程的数值方法
Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations
AI总结：
本文研究随机Landau-Lifshitz Navier-Stokes方程的显式欧拉离散化，提出一种守恒中心格式结合三阶Runge-Kutta时间积分器以准确再现密度涨落，并通过多种数值测试与理论及DSMC模拟比较。
摘要：
Landau-Lifshitz Navier-Stokes (LLNS) 方程通过使用随机通量将热涨落纳入宏观流体动力学。本文研究了完整LLNS方程的显式欧拉离散化。考虑了几种CFD方法（包括MacCormack两步Lax-Wendroff格式和分段抛物方法），发现这些方法在动量和能量涨落的方差上给出了良好的结果（约10%误差）。然而，这两种格式都不能准确再现密度涨落。我们引入了一种守恒中心格式，结合三阶Runge-Kutta时间积分器，该格式能够准确产生密度涨落。考虑了多种数值测试，包括驻立激波的随机游走，并将随机LLNS PDE求解器的结果与理论（当可用时）以及使用直接模拟蒙特卡洛（DSMC）算法的分子模拟进行了比较。
英文摘要：
The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several CFD approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the Piecewise Parabolic Method) and are found to give good results (about 10% error) for the variances of momentum and energy fluctuations. However, neither of these schemes accurately reproduces the density fluctuations. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce density fluctuations. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS PDE solver are compared with theory, when available, and with molecular simulations using a Direct Simulation Monte Carlo (DSMC) algorithm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
