A subcell based interface reconstruction method to deal with filaments

MULTIMAT 2011, Arcachon 1

A subcell based interface reconstruction method to deal with filaments

Christophe Fochesato1, Raphaël Loubère2,Renaud Motte1, Jean Ovadia3

1CEA, DAM, DIF, F-91297 Arpajon, France

2Institut de Mathématiques de Toulouse, CNRS, Université de Toulouse

3Retired fellow from CEA, CESTA, F-33114 Le Barp, France


I Introduction

– Context / Problem / Proposed solution / Example

II Presentation of the method

– Detection / Sub-zones / Volume distribution / Reconstruction

III Test cases

– Some static filaments / Mesh dependency

III Work in progress

– Defects to be corrected

– First advections

Conclusions / Perspectives

Outline


I Introduction


I - Context

• bi-fluid hydrodynamical flows with interfaces

• VoF interface reconstruction

• maximum possible resolution is not always sufficient

structure size < mesh cell size


I - Problem

• usual VoF methods use only one interface per mixed cell, typically a straight line (PLIC)

numerical surface tension

generation of flotsam reduces robustness

• Youngs’ normal can be irrelevant: ~0 because of almost symmetrical volume fractions on the stencil

• reconstruction is inaccurate although there is enough information to do better with the same 9-cells stencil


I – Proposed solution : a subgradients method

• work in two steps: improve static reconstruction / advection

the idea is to compute subgradients from a local stencil associated with each corner (2x2 cells for instance) in order to reconstruct up to 4 interfaces, one per subzone, with normals given by these subgradients

• method does not contain more physics

• another geometrical choice

with less numerical surface tension

avoiding to use irrelevant normal information

• localized algorithm in the code: no change in the numerical scheme


I - Example

our VoF implementation with Youngs’ normal

VoF / subgradients with PLIC per subzone


II Presentation of the method


II – Method summary

• detection of marked cells

• subgradients computation

• determination of subzones for reconstruction: 1, 2, 3 or 4

• distribution of fluid per subzone

• Youngs/PLIC reconstruction: one straight line per subzone


II – Detection of marked cells

• computation of a volume fraction gradient per cell

• the cell is marked

if normal is potentially not relevant: or

if the fluid potentially passes through the cell

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II – Computation of subgradients

• only for marked cells

• compute a gradient associated with each corner

on a 2x2 stencil

• confirmation that cell must be considered

if gradient is less relevantthan subgradients

orif the fluid really passes through the cell

or

if a filament endis found

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II – Determination of subzones

• keep only relevant subgradients

• with relevant subgradients, we associate subzones

4 relevant subgradients



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• use of a prescribed formula from the 9-cells stencil

• Correction if more volume of fluid than volume of the subzone

uniform scattering on other non full subzones

II – Distribution of the volume of fluid

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II – Reconstruction of interfaces

• PLIC per subzone

Youngs’ algorithm


III Test Cases


III – Implementation used for the tests

• cartesian grid

• gradients computation with Youngs’ Finite Difference formula

• subgradients computation with Finite Difference formula

• Lagrange + remap scheme with direction splitted remapping

interface reconstruction on 1D-stretched cells for each direction

exact intersection of transfered volume of the cell with reconstructed interface gives transfered volume for the fluid


III – Static filaments

• filaments to be reconstructed

- Lagrangian objects remapped on the grid



• with VoF / PLIC



• with subgradients
















III – Mesh dependency

• shifted by Δx / 4

• smallerfilament width


III – Mesh dependency

• shifted by Δx / 4

• rotated by 10o


IV Work in progress


IV – Defects to be corrected

• relative position in the cell is not known

the method tends to locate the fluid to the center of the cell

the idea is to extrapolate the location of the intersection point of the subdivision from the fluid presence in the 9-cells stencil

• connexity is not guaranteed

correction algorithm after reconstruction is possible


III – First advection cases


III – First advection cases


Conclusions, perspectives


Conclusions, perspectives

• a subgradient method to compute VoF/PLIC interfaces in subzones

• at given mesh, better representation of thin structures of fluid

• not a subgrid physical model: method as geometrical as original VoF with the same volume fraction field information

- tends to locate the fluid to the center of the cell

- connexity not guaranteed

- for advection, necessity of new information :

… natural extension to 3D

… natural extension to unstructured mesh

… no obvious extension to more than 2 fluids

summary

in progress

perspectives

Documents

A subcell based interface reconstruction method to deal with filaments