论文标题
与一般碰撞模型的非线性空间均匀鲍尔茨曼方程的伴随DSMC
Adjoint DSMC for Nonlinear Spatially-Homogeneous Boltzmann Equation With a General Collision Model
论文作者
论文摘要
我们得出了一种直接模拟蒙特卡洛（DSMC）方法的伴随方法，用于具有一般碰撞定律的空间均匀玻尔兹曼方程。这将我们先前的结果概括为[Caflisch，R。，Silantyev，D。和Yang，Y.，2021年。计算物理学杂志，439，p.110404]，仅限于Maxwell Molecules的情况，其碰撞速率是恒定的。概括先前结果的主要困难是，在DSMC算法中需要一个拒绝采样步骤，以处理可变碰撞率。我们找到一个与伴随方程中所谓的分数函数相对应的新术语，以及一个新的伴随雅各布矩阵，捕获了碰撞参数对速度的依赖性。新公式适用于更通用的碰撞模型。
We derive an adjoint method for the Direct Simulation Monte Carlo (DSMC) method for the spatially homogeneous Boltzmann equation with a general collision law. This generalizes our previous results in [Caflisch, R., Silantyev, D. and Yang, Y., 2021. Journal of Computational Physics, 439, p.110404], which was restricted to the case of Maxwell molecules, for which the collision rate is constant. The main difficulty in generalizing the previous results is that a rejection sampling step is required in the DSMC algorithm in order to handle the variable collision rate. We find a new term corresponding to the so-called score function in the adjoint equation and a new adjoint Jacobian matrix capturing the dependence of the collision parameter on the velocities. The new formula works for a much more general class of collision models.
