A Regularized Entropy-Based Moment Method for Kinetic Equations
A Regularized Entropy-Based Moment Method for Kinetic Equations
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DOI：
10.1137/18m1181201
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发表时间：
2018-04
期刊：
影响因子：
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通讯作者：
G. Alldredge;M. Frank;C. Hauck
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文献类型：
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作者：
G. Alldredge;M. Frank;C. Hauck
提出了一种新的基于熵的矩量法用于动力学方程的速度离散。这种方法是基于正则化的优化问题定义的原始基于熵的矩量法，这给了新的方法的优点，解决方案的矩向量不需要采取可实现的值。我们发现，这个方程仍然保留了许多原始方程的属性，包括双曲性，熵耗散法，旋转不变性。正则化的代价是解的矩向量与正则化优化问题返回的样本的矩向量之间的不匹配。然而，我们将展示如何使用定义正则化的参数来控制此错误。这表明，通过适当的正则化参数的选择，新的方法可以用来产生精确的解决方案，原来的基于熵的矩量法，我们证实了这一点与数值模拟。
We present a new entropy-based moment method for the velocity discretization of kinetic equations. This method is based on a regularization of the optimization problem defining the original entropy-based moment method, and this gives the new method the advantage that the moment vectors of the solution do not have to take on realizable values. We show that this equation still retains many of the properties of the original equations, including hyperbolicity, an entropy-dissipation law, and rotational invariance. The cost of the regularization is mismatch between the moment vector of the solution and that of the ansatz returned by the regularized optimization problem. However, we show how to control this error using the parameter defining the regularization. This suggests that with proper choice of the regularization parameter, the new method can be used to generate accurate solutions of the original entropy-based moment method, and we confirm this with numerical simulations.