Clausnitzer at al comparing meshing approaches

Comparing meshing approaches for groundwater modeling at a geometrically challenging mine siteVolker Clausnitzer, Fabien Cornaton, Peter SchätzlDHI-WASY

Robin DufourDHI Peru

Motivation

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Legacy layered meshing

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18 geological formations

85 numerical layers

10 million elements

5 million nodes

• 18 geological formations

• 85 numerical layers –

continuous, following the

faults

• 10 million elements

• 5 million nodes

Mesh Flexibility in 3D

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• Layered prism-based FE meshes

Excellent flexibility in 2D

Extruded to 3D

Vertical join faces restrict flexibility but simplify interactive model set-up once

mesh has been created

• Unstructured tetrahedral FE meshes

Excellent flexibility in 3D

Difficult to handle in interactive work

3D element types

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Layered meshes

Penta- or hexahedrons with vertical quadrilateral join faces

3D element types

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Unstructured meshes / mesh parts

Tetrahedrons

3D element types

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Combined meshes

Pyramids connect layered and unstructured mesh portions

TetGen

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• Mesh generator for tetrahedral meshing of any 3D polyhedral domain

• Author: Hang Si (Weierstrass Institute for Applied Analysis and Stochastics,

WIAS Berlin)

tetgen.org

Tetrahedral meshing embedded in a layered

mesh

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Embedded tetrahedral mesh

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• Strategy: Combine mesh types

Where possible, mesh with layered prisms

Where necessary, embed unstructured tetrahedral meshes

(artificial underground structures, inclined faults

karstic networks, pinch-outs, …)

Embedded tetrahedral mesh: Karstic network

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Fully unstructured tetrahedral meshing

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Legacy Approach

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3D GeoModeller geologic model

Layered-mesh FEFLOW model

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Steady-state solution

22 layers; 5,380,760 pentahedral elements; 2,816,304 nodes

Fully unstructured (tetrahedral) meshing

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• Takes spatial distribution of geologic units, 3D geometric description

of unit interfaces from dedicated geologic modelers

• 3D GeoModeller, GOCAD, (Leapfrog, MineSight, …)

• Geometric constraints passed to TetGen

• GUI-supported parameter assignment based on geologic spatial

information

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Interfaces of geologic units

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Interfaces and geologic units

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Interfaces and geologic units

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Tet-meshed geologic units

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Clipped tetrahedrons

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Full tetrahedral mesh

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Steady-state solution

861,685 tetrahedral elements; 195,628 nodes

Performance

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6 cores

Performance Comparison

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Layered Mesh Tetrahedral Mesh

Number of nodes

(Size of equation system)

2,816,304 195,628

SAMG Algebraic Multigrid Solver

Simulation time (seconds) 654.67 18.95

PARDISO Parallel Direct Solver


Performance Comparison

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Layered Mesh Tetrahedral Mesh

Number of nodes

(Size of equation system)

2,816,304 195,628

SAMG Algebraic Multigrid Solver


Relative mass-balance error 2.0e-6 2.8e-8

PARDISO Parallel Direct Solver


Relative mass-balance error 1.6e-13 4.2e-14

Summary

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• Unstructured tetrahedral meshing can be

− combined with layered meshes or

− used for the entire domain

• Substantial reduction in mesh size for the same level of geologic

detail

• Direct solvers become applicable to new class of problems

Thank you

…and perhaps see you at FEFLOW 2015, September 21–25 in Berlin, Germany!

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Software

Clausnitzer at al comparing meshing approaches