用于冻结局部和非局部水动力模型的能量稳定多网格方法
Energy Stable Multigrid Method for Local and Non-local Hydrodynamic Models for Freezing
AI总结：
本文提出了一种能量稳定且质量守恒的隐式有限差分方法，用于求解由时间依赖密度泛函理论冻结产生的水动力模型，适用于局部和非局部自由能功能的计算。
摘要：
本文介绍了一种用于由时间依赖密度泛函理论冻结产生的水动力模型的数值方法。这些模型以可压缩纳维-斯托克斯方程的形式出现，其压力由自由能的变分导数决定，而自由能是一个密度场的泛函。我们为这些模型提出了无条件能量稳定且质量守恒的隐式有限差分方法。这些方法基于自由能的凸分解，确保了对于任意的时间和空间步长，离散能量都是非递增的。这些方法适用于广泛的模型类别，包括局部和非局部自由能泛函。数值方法的理论基础在一般背景下进行了阐述。该方法应用于使用两种特定自由能泛函的问题：一个局部泛函和一个非局部泛函。非线性多网格方法用于求解数值方法，该方法在隐式时间步中是非线性的。非局部泛函，即卷积算子，通过离散傅里叶变换进行近似。展示了验证数值方法稳定性和准确性的数值模拟。
英文摘要：
In this paper we present a numerical method for hydrodynamic models that arise from time dependent density functional theories of freezing. The models take the form of compressible Navier-Stokes equations whose pressure is determined by the variational derivative of a free energy, which is a functional of the density field. We present unconditionally energy stable and mass conserving implicit finite difference methods for the models. The methods are based on a convex splitting of the free energy and that ensures that a discrete energy is non-increasing for any choice of time and space step. The methods are applicable to a large class of models, including both local and non-local free energy functionals. The theoretical basis for the numerical method is presented in a general context. The method is applied to problems using two specific free energy functionals: one local and one non-local functional. A nonlinear multigrid method is used to solve the numerical method, which is nonlinear at the implicit time step. The non-local functional, which is a convolution operator, is approximated using the Discrete Fourier Transform. Numerical simulations that confirm the stability and accuracy of the numerical method are presented.
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。
