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首页> 外文期刊>Journal of Computational Physics >Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid-structure interaction, and free surface flow: Part II
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Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid-structure interaction, and free surface flow: Part II

机译：隐式网状不连续的Galerkin方法和界面仪表，用于高阶准确的界面动态，具有表面张力动力学，刚体流体结构相互作用和自由表面流动：第二部分

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In this two-part paper, a high-order accurate implicit mesh discontinuous Galerkin (dG) framework is developed for fluid interface dynamics, facilitating precise computation of interfacial fluid flow in evolving geometries. The framework uses implicitly defined meshes-wherein a reference quadtree or octree grid is combined with an implicit representation of evolving interfaces and moving domain boundaries-and allows physically prescribed interfacial jump conditions to be imposed or captured with high-order accuracy. Part one discusses the design of the framework, including: (i) high-order quadrature for implicitly defined elements and faces; (ii) high-order accurate discretisation of scalar and vector-valued elliptic partial differential equations with interfacial jumps in ellipticity coefficient, leading to optimal-order accuracy in the maximum norm and discrete linear systems that are symmetric positive (semi)definite; (iii) the design of incompressible fluid flow projection operators, which except for the influence of small penalty parameters, are discretely idempotent; and (iv) the design of geometric multigrid methods for elliptic interface problems on implicitly defined meshes and their use as preconditioners for the conjugate gradient method. Also discussed is a variety of aspects relating to moving interfaces, including: (v) dG discretisations of the level set method on implicitly defined meshes; (vi) transferring state between evolving implicit meshes; (vii) preserving mesh topology to accurately compute temporal derivatives; (viii) high-order accurate reinitialisation of level set functions; and (ix) the integration of adaptive mesh refinement.
机译：在这篇两篇纸张中，为流体接口动态开发了一份高阶准确的隐式网状物不连续的Galerkin（DG）框架，促进了在演化几何形状中的界面流体流动的精确计算。该框架使用了隐式定义的网格 - 其中参考Quadtree或OctREE网格与不断变化的接口和移动域边界的隐式表示 - 并且允许以高阶精度施加或捕获物理规定的界面跳转条件。第一部分讨论了框架的设计，包括：（i）隐式定义元素和面部的高阶正交; （ii）具有椭圆形系数的界面跳跃的标量和矢量值椭圆部分微分方程的高阶准确自由态，导致对称阳性（半）确定的最大规范和离散线性系统中的最佳精度。 （iii）不可压缩的流体流量投影算子的设计，除了小额惩罚参数的影响之外是谨慎的幂等的; （iv）在隐式定义网格上的椭圆接口问题的几何多重资源方法的设计及其用作共轭梯度法的预处理器。还讨论了与移动接口有关的各种方面，包括：（v）在隐式定义的网格上的级别集方法的DG离散模式; （vi）在不断的隐式网格之间传输状态; （vii）保持网状拓扑，以准确计算时间衍生物; （viii）高阶准确重新安装水平集功能; （ix）自适应网格细化的集成。

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