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Choosing the Appropriate Mesh Type in Frost 3D Universal

When using numerical simulation software, the question “which mesh is the most suitable for object discretization?” often arises. The same geometry can actually be discretized with a coarse or fine grid mesh, which of course affects the accuracy and speed of numerical computation.


Experts in the field of numerical simulation have analyzed computational meshes created in Frost 3D Universal; a 1-km model of an oil pipeline on permafrost serving as the example. It should be noted that the pipeline geometry ‘bends’ through both the Z and Y planes and some pipeline sections penetrate ice layers. Dimensions of created 3D model: length – 1000 m, width – 50 m, depth – 55 m, diameter – 1.2 m. A thin ice layer under the pipeline at the end of a rectangular area is the main feature of our example. The computational domain was discretized with varying cell quantities in different versions of Frost 3D Universal, with the results shown below.

3D buried pipeline model on permafrost

3-dimensional pipeline model

Mesh discretization: 1.8 million nodes

Program version: 32-bit, single core CPU

Pipeline discretization with coarse mesh

Computational mesh: 1.8 million nodes

Program version: 32-bit, single core CPU

Zoom of ice layers

Zoom of ice layers in pipeline computer model


• Thin ice layer (in blue) under the pipeline was almost lost during computational mesh creation.

• The 4-m cell size is inappropriate for Stefan problem solving.

• The boundary between thawed and frozen ground was computed with a high degree of inaccuracy; for correct simulation, this model should be discretized with a fine mesh.

Computational mesh: 4.95 million nodes

Program version: 64-bit, single core CPU

Zoom of ice layers



• Insignificant mesh refinement (if compared with previous one).

• Low quality is noticeable in the thin ice layer mesh, most of which was lost.

Computational mesh: 19.2 million nodes

Program version: 64-bit, multicore CPU

Zoom of ice layers.

Increasing of cells quantity in mesh reduces discretization inaccuracy


• A 4x increase in the number of cells reduces the maximum cell size up to 1 meter and increases computational mesh accuracy.

• Such an increase reduces the inaccuracy of thin ice layer discretization.

• More accurate thermal field computation (near pipe bends in Y axes) is possible with significant mesh refinement.

Computational mesh: 54.7 million nodes

Program version: 64-bit, multicore GPU

Zoom of ice layers.

Small cell size reduces inaccuracy of simulation


• High-resolution of model discretization includes all object geometry (pipeline and thin ice layer).

• The small cell size allows accurate determination of the boundary of phase transition.

• Minimal cell sizes near areas with maximal temperature gradients allow rapid temperature change approximation.

• Negligible inaccuracy of numerical computation via discretization is achieved.

Hence, Frost 3D Universal multicore CPU and GPU versions are the most suitable for qualitative discretization of large computation areas with small elements. Our example involved a thin ice layer, but the same is true for thermal insulation of foundations, borehole thermocases, and similar design elements which significantly impact computation.

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Thermosyphon Technology for Ground Freezing
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Software package for simulation of heat processes in grounds with the account of:


  • Phase transitions
  • Filtration
  • Snow cover thickness
  • Operation of cooling devices
  • Heat impact of buildings and constructions
  • Complex ground structure

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