A high order flux reconstruction interface capturing method with a phase field preconditioning procedure

Abstract

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.