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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Embedded tetrahedral mesh: Karstic network

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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

Simulation time (seconds) 1104.62 21.73

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

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

PARDISO Parallel Direct Solver

Simulation time (seconds) 1104.62 21.73

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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