debris flows & mud slides: a lagrangian method for two- phase flow simulation matthias preisig...
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DEBRIS FLOWS & MUD SLIDES: A Lagrangian method for two-
phase flow simulation
Matthias Preisig and Thomas Zimmermann, Swiss Federal Institute of Technology
Lausanne, Switzerland
Funded by the Swiss National Science Foundation
Goal: Modeling debris flows
Large displacements
Free surface flow
Two-phase material(soil-water)
La Conchita, CA, January 2005 © by AP
Initiation of flow
Transport
Deposition
Being able to: Predict flow path (danger zone) Obtain design parameters for protection
devices (depth, quantity, energy)
Why model debris flows?
WSL WSL
Outline
Governing equations of 2-phase flow
Computation of volume fractions
Lagrangian update and remapping
Numerical examples
Two-Phase Flow
Flow of two viscous fluids (solid phase is regarded as fluid)
Phases occupy same control volume in space (no phase interfaces)
Momentum exchange via drag force
Fluid phase: Cf
Solid phase: Cs
Concentrations:
Cf = 1
Cs = 1Cf = 1
Cf + Cs = 1
Remesh:Remesh:
Lagrangian update algorithmSolve for vsn+1, vfn+1 and pn+1Solve for vsn+1, vfn+1 and pn+1
Find free surfaceFind free surface
Update nodesUpdate nodes
Solve for Csn+1 and Cf
n+1Solve for Cs
n+1 and Cfn+1
Remesh inside boundary → n+1Remesh inside boundary → n+1
Map vsn+1, vfn+1, pn+1,Csn+1 and Cf
n+1 on n+1Map vsn+1, vfn+1, pn+1,Csn+1
and Cfn+1 on n+1
n
dsn+1
dfn+1
Numerical method
Meshless (NEM – natural neighbor based, Sukumar et al.) Unique interpolation for a given nodal
distribution Less sensitive to uneven nodal distribution than
FEM
u = 1u = 0
support of shape function
NEM – FEM: Automatic Remeshing
FEM: nodal connectivity using Delaunay triangulation
NEM: connectivity depends only on point location
Dam break
Releasing horizontal BC’s on right side
Automatic remeshing prevents excessive element distortion
Triangles in above picture represent integration domains, no elemental connectivity!
Drop of heavy fluid in light fluid
C1 = 0.9
C1 = 0.1
Density: 1 = 2 2
High momentum exchange coefficient Kdrag
( )
Free surface
Drop of heavy fluid in light fluid
C1 = 0.9
C1 = 0.1
Density: 1 = 10 2
Low momentum exchange coefficient Kdrag
( )
NEM – FEM: Pro’s and Con’s
NEM FEM (lin. triangles)
Irregular point distribution
++ --
Regular grid + -
Locking Stabilization required
Numerical integration
- +
Implementation - +
Incompressible Elasticity (Stokes)
(i)
(iia)
(iib)
Find u, p such that:
Stabilization (Laplacian Pressure Operator Scheme) after Brezzi & Pitkäranta (1984)
Conclusions
Updated Lagrangian algorithm for two-phase flow Only material domain is modeled Definition of free surface straightforward No stabilization of convective terms required
Most general continuum model for two-phase flows