论文标题
一阶粘性流动的双曲线模型与表面张力的一阶双曲线模型
An exactly curl-free staggered semi-implicit finite volume scheme for a first order hyperbolic model of viscous flow with surface tension
论文作者
论文摘要
在本文中，我们提出了一个半图形的数值求解器，用于具有表面张力和粘度的两相流量的一阶双曲公式。数值方法解决了PDE系统提出的几个复杂性：（i）管理方程中卷曲类型的存在限制需要明确强制执行某些矢量字段的零curl属性（界面场和失真场）；通过在交错的网格上采用一组兼容的卷曲和梯度离散的差分运算符，完全消除了问题，从而可以准确地保留Schwartz的身份。 （ii）演变方程具有高度非线性刚性代数术语，用于描述粘性相互作用，作为在刚性应变弛豫极限中的弹性塑料固体的紧急行为；此类源项可与有效的半分析技术可靠地集成。 （iii）在低模数制度中，标准明确的戈多诺夫型计划失去了效率和准确性；该问题是通过简单的半密码，基于压力的，对声波和非声波的分裂处理来解决的，再次使用交错的网格通过交错的网格，通过一系列可以通过对称阳性的线性系统来恢复单个标量场（压力）的隐式解决方案，这些系统可以通过合并渐变方法有效地溶解。
In this paper, we present a semi-implicit numerical solver for a first order hyperbolic formulation of two-phase flow with surface tension and viscosity. The numerical method addresses several complexities presented by the PDE system in consideration: (i) The presence of involution constraints of curl type in the governing equations requires explicit enforcement of the zero-curl property of certain vector fields (an interface field and a distortion field); the problem is eliminated entirely by adopting a set of compatible curl and gradient discrete differential operators on a staggered grid, allowing to preserve the Schwartz identity of cross-derivatives exactly. (ii) The evolution equations feature highly nonlinear stiff algebraic source terms which are used for the description of viscous interactions as emergent behaviour of an elasto-plastic solid in the stiff strain relaxation limit; such source terms are reliably integrated with an efficient semi-analytical technique. (iii) In the low-Mach number regime, standard explicit Godunov-type schemes lose efficiency and accuracy; the issue is addressed by means of a simple semi-implicit, pressure-based, split treatment of acoustic and non-acoustic waves, again using staggered grids that recover the implicit solution for a single scalar field (the pressure) through a sequence of symmetric-positive definite linear systems that can be efficiently solved via the conjugate gradient method.
