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Frost 3D meshes: model discretization with fine and coarse meshes

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; 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 quantity of cells in different versions of Frost 3D , with the results shown below.

3D buried pipeline model on permafrost

Pipeline model in 3D

Computational mesh: 1.8 million cells

Pipeline discretization with coarse mesh

Program version: 32-bit, single core CPU

Is no longer available

Zoom of ice layers in pipeline computer model

Zoom of ice layers

• 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 cells

Most ice layers are lost with 4.95 million cell discretization

Program version: 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 cells

Increasing of cells quantity in mesh reduces discretization inaccuracy

Program version: multi-core CPU. Zoom of ice layers

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

Small cell size reduces inaccuracy of simulation

Program version: multi-core GPU. Zoom of ice layers

• 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 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.