This paper presents a simple and highly accurate method for capturing sharp interfaces moving in divergence-free velocity fields using the high-order Flux Reconstruction approach on unstructured grids. A well-known limitation of high-order methods is their susceptibility to the Gibbs phenomenon; the appearance of spurious oscillations in the vicinity of discontinuities and steep gradients makes it difficult to accurately resolve shocks or sharp interfaces. In order to address this issue in the context of sharp interface capturing, a novel, preconditioned and localized phase-field method is developed in this work. The numerical accuracy of interface normal vectors is improved by utilizing a preconditioning procedure based on the level set method with localized artificial viscosity stabilization. The developed method was implemented in the framework of the multi-platform Flux Reconstruction open-source code PyFR [1]. Kinematic numerical tests in 2D and 3D conducted on different mesh types showed that the preconditioning procedure significantly improves accuracy with little added computational effort. The results demonstrate the conservativeness of the proposed method and its ability to capture highly distorted interfaces with superior accuracy when compared to conventional and high-order VOF and level set methods. Dynamic interface capturing validation tests were also carried out by coupling the proposed method to the entropically damped artificial compressibility variant of the incompressible Navier-Stokes equations. The high accuracy and locality of the proposed method offer a promising route to carrying out massively-parallel, high accuracy simulations of multi-phase, incompressible phenomena.

本文提出了一种简单且高精度的方法，该方法使用非结构化网格上的高阶通量重构方法来捕获在无散度速度场中移动的尖锐界面。高阶方法的一个众所周知的局限性是它们对吉布斯现象的敏感性。在不连续点和陡峭的梯度附近会出现寄生振荡，因此很难准确地解决冲击或尖锐的界面。为了在清晰的界面捕获中解决这个问题，在这项工作中开发了一种新颖的，经过预处理的局部相场方法。界面法线向量的数值精度可通过利用基于水平集方法的局部预处理人工粘度稳定化的预处理程序来提高。所开发的方法是在多平台Flux Reconstruction开源代码PyFR [1]的框架中实现的。在不同的网格类型上进行的2D和3D运动学数值测试表明，预处理程序可以在不增加计算量的情况下显着提高准确性。结果表明，与传统方法和高阶VOF和水平集方法相比，该方法的保守性及其捕获具有高准确性的高度失真界面的能力。通过将提出的方法与不可压缩的Navier-Stokes方程的熵阻尼人工可压缩性变量耦合，还进行了动态接口捕获验证测试。所提出方法的高精度和局部性为进行大规模并行，