Skip to main content

Volume Mesh for Simulation

Volume meshes extend surface models into three-dimensional discretizations suitable for finite element analysis (FEA), computational fluid dynamics (CFD), and other simulation applications. This tutorial covers the workflow from segmentation to simulation-ready meshes.

Estimated time: 30 minutes

Prerequisites:

  • Completed surface generation tutorials
  • A clean, watertight surface model
  • Understanding of target simulation requirements

Understanding Volume Meshes​

While surface meshes represent only the boundary of objects, volume meshes fill the entire interior with volumetric elements—typically tetrahedra. This discretization enables simulation of:

A cross-section of a surface mesh, which is only the boundary, next to a volume mesh whose elements fill the interior

  • Structural mechanics (stress, strain, deformation)
  • Thermal analysis (heat transfer, temperature distribution)
  • Fluid dynamics (flow, pressure)
  • Electromagnetic fields

Element Types​

TypeNodesDescription
Linear (4-node)4Nodes at vertices only; linear interpolation
Quadratic (10-node)10Additional nodes at edge midpoints; higher accuracy

Linear elements are computationally efficient; quadratic elements capture curved boundaries and stress gradients more accurately.

A linear tetrahedron with four corner nodes next to a quadratic tetrahedron with the same four corners and six additional mid-edge nodes

Prerequisites for Volume Meshing​

Successful volume mesh generation requires clean input geometry.

Surface Requirements​

  • Watertight — No holes or gaps
  • Manifold — Each edge shared by exactly two triangles
  • Consistent normals — All triangles point outward
  • No self-intersections — Surface does not cross itself
  • Reasonable triangle quality — No extremely thin triangles

Preparing Your Surface​

Before meshing:

  1. Run Diagnostics and Fixes:

    • Navigate to Surface → Edit → Diagnostics and Fixes.
    • Identify and repair issues.
    • Fill holes, fix non-manifold edges, correct normals.

  2. Verify watertightness:

    • Check that hole count is zero.
    • Verify edge manifold status.

  3. Optimize triangle quality (optional):

    • Use Remesh for more uniform triangles.
    • Smooth away noise that might cause meshing issues.
Critical Step

Volume mesh generation will fail on surfaces with topological defects. Always run diagnostics before attempting tetrahedralization.

Creating Volume Meshes from Surfaces​

Step-by-Step Workflow​

  1. Select the surface in the Scene Tree.

  2. Access the tool:

    • Navigate to Surface → Convert → Surface to Volume Mesh.

  3. Choose the algorithm:

    MethodDescription
    Auto3DHigh-quality adaptive meshing
    Grid3DBackground grid-based approach

    Auto3D is recommended for most applications.

  4. Select element type:

    • Tetra 4-Node — Linear elements
    • Quadratic 10-Node — Higher-order elements

  5. Configure quality preset:

    PresetTriangle CountUse Case
    Very coarseMinimalQuick testing
    CoarseLowPreliminary analysis
    ModerateBalancedGeneral purpose
    FineHighAccurate analysis
    Very fineMaximumHigh-fidelity simulation
    CustomUser-definedSpecific requirements

  6. Click Apply.

  7. Review the result:

    • Volume mesh appears in the Scene Tree
    • Display in 3D view shows element structure

Custom Meshing Parameters​

For precise control, select Custom preset and configure:

ParameterDescriptionTypical Range
Max element sizeUpper limit on edge lengthDepends on geometry scale
Min element sizeLower limit on edge length0 for automatic
Growth rateSize transition rate (%)20-40% for gradual
Surface optimization stepsSurface mesh refinement1-5
Volume optimization stepsVolume mesh optimization1-5

Element Size Guidelines​

ApplicationRecommended Size
Initial testing5-10% of smallest feature
Standard analysis2-5% of smallest feature
High accuracy1-2% of smallest feature
Stress concentration regionsMuch smaller locally

Creating Volume Meshes from Masks​

Direct conversion from segmentation masks:

  1. Select the mask in the Scene Tree.

  2. Navigate to:

    • Segmentation → Convert → Mask To Volume Mesh.

  3. Configure parameters (similar to surface method).

  4. Click Apply.

This method internally generates a surface and then tetrahedralizes it, combining two steps.

Multi-Part Assemblies​

When meshing multiple surfaces that contact each other:

Maintaining Conformity​

Ensure nodes match at interfaces for proper load transfer:

  1. Select all surfaces to mesh together.
  2. In Surface to Volume Mesh, enable Maintain conformity.
  3. Run the mesh generation.
  4. Resulting meshes share nodes at contact surfaces.

Conforming meshes are required for:

  • Bonded assemblies
  • Contact analysis
  • Multi-material models

Non-Conforming Meshes​

When surfaces are independent:

  1. Disable conformity option.
  2. Mesh each surface separately or together without nodal matching.
  3. Use tie constraints in the solver to connect parts.

Volume Mesh Quality​

Quality Metrics​

MetricDescriptionTarget
Aspect ratioEdge length ratio< 10 (< 5 preferred)
Minimum angleSmallest dihedral angle> 10° (> 20° preferred)
JacobianElement distortion> 0.2

A regular, a stretched and a sliver tetrahedron with their edge ratio and smallest dihedral angle measured on the drawn elements

Checking Mesh Quality​

  1. Navigate to Measure → Analysis → Mesh Quality Analyzer.
  2. Select the volume mesh.
  3. View quality distribution:
    • Color-mapped visualization
    • Histogram of quality values
    • Statistics summary
  4. Identify problematic elements for potential refinement.

Improving Mesh Quality​

If quality is insufficient:

  1. Increase optimization steps in meshing parameters.
  2. Refine the source surface with Remesh or Smooth.
  3. Reduce maximum element size for finer mesh.
  4. Fix surface defects that may cause poor elements.

FEM Configuration​

Prepare the mesh for finite element analysis:

Configure FEM Model​

  1. Navigate to Volume Mesh → FEM → Export FEM Mesh.

  2. Define material properties:

    • Young's modulus
    • Poisson's ratio
    • Density
    • Other material parameters

  3. Define element sets:

    • Group elements for different materials
    • Create sets for output requests

Export FEM Mesh​

Export to solver-specific formats:

  1. Navigate to Volume Mesh → FEM → Export FEM Mesh.

  2. Select format:

    FormatSolver
    Abaqus (.inp)Abaqus
    Nastran (.bdf)Nastran
    LS-DYNA (.key)LS-DYNA
    OpenFOAM (.foam)OpenFOAM
    Fluent (.msh)Fluent
    Gmsh (.msh)Gmsh

  3. Configure export options.

  4. Click Export.

Practical Exercise: Complete FEA Workflow​

Scenario​

Create a volume mesh of a bone segment for stress analysis.

Part 1: Prepare the Surface​

  1. Load a bone segmentation mask.
  2. Generate a surface using Mask to Surface.
  3. Apply smoothing (Smart, 20 iterations).
  4. Run Diagnostics and Fixes.
  5. Fill any holes.
  6. Verify watertight status.

Part 2: Generate Volume Mesh​

  1. Select the bone surface.
  2. Navigate to Surface → Convert → Surface to Volume Mesh.
  3. Select Auto3D method.
  4. Choose Quadratic 10-Node elements (for stress analysis).
  5. Select Fine preset.
  6. Click Apply.

Part 3: Evaluate Mesh Quality​

  1. Navigate to Mesh Quality Analyzer.
  2. Select the volume mesh.
  3. Review:
    • Minimum angle distribution
    • Aspect ratio statistics
  4. Ensure most elements meet quality criteria.

Part 4: Export for FEA​

  1. Navigate to Configure FEM Model.
  2. Set bone material properties:
    • Young's modulus: 17 GPa (cortical bone)
    • Poisson's ratio: 0.3
  3. Navigate to Export FEM Mesh.
  4. Select Abaqus format.
  5. Export the mesh file.

Volume Mesh Transformation​

Apply geometric modifications to volume meshes:

Transform Operations​

Navigate to Volume Mesh → Transform for:

OperationDescription
TransformRotate, translate, scale numerically
Interactive TransformManipulate with 3D gizmo

Converting Back to Surface​

Extract the boundary surface:

  1. Navigate to Volume Mesh → Convert → Volume Mesh to Surface.
  2. The outer surface of the tetrahedral mesh is extracted.
  3. Useful for visualization or further surface processing.

Best Practices​

Mesh Generation​

  • Start with coarse mesh for initial testing
  • Refine only after verifying the workflow
  • Document meshing parameters for reproducibility

Quality Assurance​

  • Always check mesh quality before analysis
  • Address elements with very poor quality
  • Validate mesh convergence by comparing coarse vs. fine results

Solver Compatibility​

  • Verify element type compatibility with target solver
  • Check unit consistency (mm vs. m)
  • Validate material property formats

Troubleshooting​

Meshing fails completely​

  • Surface likely has defects
  • Run Diagnostics and Fixes
  • Check for self-intersections
  • Simplify complex regions

Poor element quality​

  • Increase optimization steps
  • Smooth the source surface
  • Reduce maximum element size
  • Address sharp features in the geometry

Mesh is too large​

  • Increase maximum element size
  • Use coarser preset
  • Consider adaptive meshing for local refinement

Solver import errors​

  • Verify format compatibility
  • Check element type support
  • Review node/element numbering

Next Steps​

Continue with advanced topics:

See Also​