（様式 20）成果報告書

TSUBAME 共同利用 令和 2 年度 学術利用 成果報告書

利用課題名 液体金属流れ CFD 手法の開発及び核融合研究への応用
英文：Development of a High Order Flux Reconstruction Interface Capturing Method for Multiphase
Simulations
利用課題責任者 胡 長洪
Changhong Hu
所属 九州大学応用力学研究所
Research Institute for Applied Mechanics, Kyushu University
https://www.tj.kyushu-u.ac.jp/
邦文抄録（300 字程度）
高次精度の計算手法は従来の低次精度の解放と比較して，計算精度と計算性能などが優れている．しかし，高次精度方程式はギブズ現象の影響を受けやすく，シャープな界面を正確に扱うことが困難である．本研究では，高次精度 Flux Reconstruction 法（FR 法）を用いて，シャープな界面を捉える手法を提案する．局所的な人工粘性を課したレベルセット関数の前処理を利用することで，界面の法線ベクトルの計算精度を向上した．
英文抄録（100 words 程度）
High-order numerical methods can offer several advantages over conventional, low order methods for
fluid dynamics simulations such as higher accuracy and computational performance. A major
limitation of high-order methods is their susceptibility to the Gibbs phenomenon, preventing themfrom accurately resolving sharp interfaces. This work presents a method for capturing sharp interfaces
using the high-order Flux Reconstruction approach. The numerical accuracy of interface normalvectors is improved by utilizing a preconditioning procedure based on the level set method withlocalized artificial viscosity stabilization.

Keywords: Flux-reconstruction, High-order methods, Multiphase, Phase-field, GPU computing
背景と目的
Recent trends in CFD research indicate asteadily increasing interest in high-ordernumerical methods. The ability of such methods
to produce results with more accuracy on coarser
grids when compared to conventional low ordermethods resulted in a growing consensus among
CFD practitioners that high-order methods may
constitute the basis of next-generation CFD
research tools. Furthermore, high-order methods,
such as the flux-reconstruction and discontinuousGalerkin methods have compact stencils which
rendersthem
particularly
suitablefor
computation on modern hardware such as general
purpose graphical processing units (GPGPUs).
However, these methods have seen little use formultiphase simulations due to their susceptibility
to the Gibbs phenomenon; the appearance ofspurious oscillations in the vicinity ofdiscontinuities and steep gradients makes it
difficult to accurately resolve shocks or sharp
interfaces.
In order to address this issue in the context ofsharp interface capturing, a novel, preconditioned
and localized phase-field method is developed inthis work and hereafter referred to as the Flux

Reconstruction Preconditioned Phase Field
method (FR-PCPF). The numerical accuracy ofinterface normal vectors is improved by utilizinga preconditioning procedure based on the level set
method with localized artificial viscosity
stabilization. The developed method wasimplemented in the framework of themulti-platform Flux Reconstruction open-sourcecode PyFR [1]. Kinematic numerical tests in 2D
and 3D conducted on different mesh types showedthat the preconditioning procedure significantly
improves
accuracywithlittleadded
computational effort.
概要
This research aims to develop next generation
CFD techniques for solving incompressible, freesurface flows. Such phenomena are important ina variety of fields and applications such as
flooding and tsunami simulations, applications in
naval and marine engineering, and nuclear fusion
applications(flowofliquidmetalas
plasma-facing material). This development isbased on the high-order Flux Reconstruction
method, which allows obtaining more accurate
results while utilizing modern hardware more（様式 20）成果報告書

efficiently when compared to conventional CFD
techniques. The TSUBAME super-computer wasused to carry out simulations for testing andvalidation of GPU-accelerated, high-order CFD
code for solving free surface incompressible flows.
The simulations aimed to test the accuracy andcomputational efficiency and scaling of the codefor problems involving a large number of degreesof freedom.

multi-phase flows has been demonstrated bycoupling the interface capturing algorithm to theEntropically Damped Artificial Compressibility(EDAC) Navier-Stokes system of equations, andsimulations of the Rayleigh-Taylor instability (infigure 2) and bubble rise problems yielded good
matching with previously published results.

結果および考察Results from numerical benchmark tests thatwere carried out have shown that the FR-PCPF
method is able to produce results that arecomparable to some of the most accurate low andhigh order methods by using second orderpolynomial basis. Increasing the polynomial orderfurther
improves numerical accuracy. Figure 1
shows simulations of the Rider-Kothe vortex
benchmark case [2], where the black dashed lineis the initial state of the droplet, and the red line
shows the final state, which demonstrates thegood accuracy of the method.

Figure 1: Simulation of the Rayleigh-Taylor
instability using the FR-PCPF coupled with theEDAC formulation using different polynomialorders

Figure 2: Rider-Kothe simulation using theFR-PCPF method (red line is final state and blackline is initial state of droplet)
The FR-PCPF method is shown to be able toconserve mass and resolve challenging interface
features even with long time integration.
Increasing effective resolution (by either
increasing
thepolynomialorderpercomputational element or by increasing the meshresolution) was shown to produce consistentimprovements in global mass conservation,accuracy and the ability to resolve complicatedinterface features.
The FR-PCPF method’s applicability to

まとめ、今後の課題
In this report, progress on the development of ahigh-order method for interface capturing for use
in high-accuracy and large-scale simulations hasbeen summarized. Satisfactory results ofbenchmark tests were obtained. Future work
includes optimization of model parameters andextending the range of tractable density ratios tocover those needed in applications such as liquid
metal flow in low pressure environments.
References[1] Witherden FD, Farrington AM, Vincent PE. PyFR:
Anopensourceframework
forsolving
advection–diffusion type problems on streamingarchitectures using the flux reconstruction approach.
Computer Physics Communications. 2014 Nov
1;185(11):3028-40.
[2] Rider WJ, Kothe DB. Reconstructing volumetracking. Journal of computational physics. 1998 Apr
10;141(2):112-52.