论文标题
基于稳定的L2最小化的基于气体动力学的玻尔兹曼方程
A Positive and Stable L2-minimization Based Moment Method for the Boltzmann Equation of Gas dynamics
论文作者
论文摘要
我们考虑了解决稀有气体动力学的玻尔兹曼方程的方法方法，从而导致以下瞬间问题。给定一组矩，找到潜在的概率密度函数。力矩关闭的问题具有无限的许多解决方案，并且需要一个额外的最佳标准来单击独特的解决方案。由于不连续的盖尔金速度离散化的动机，我们考虑了基于L2最小化的最佳标准。为了确保对瞬间问题的积极解决方案，我们对L2最小化的阳性限制进行了强制性限制。这会导致矩和阳性限制的二次优化问题。我们表明（Courant-Friedrichs-Lewy）CFL型条件可确保优化问题的可行性和矩近似的L2稳定性。数值实验展示了我们瞬间方法的准确性。
We consider the method-of-moments approach to solve the Boltzmann equation of rarefied gas dynamics, which results in the following moment-closure problem. Given a set of moments, find the underlying probability density function. The moment-closure problem has infinitely many solutions and requires an additional optimality criterion to single-out a unique solution. Motivated from a discontinuous Galerkin velocity discretization, we consider an optimality criterion based upon L2-minimization. To ensure a positive solution to the moment-closure problem, we enforce positivity constraints on L2-minimization. This results in a quadratic optimization problem with moments and positivity constraints. We show that a (Courant-Friedrichs-Lewy) CFL-type condition ensures both the feasibility of the optimization problem and the L2-stability of the moment approximation. Numerical experiments showcase the accuracy of our moment method.
