Following the release of the article “Thermal analysis of a lengthy section of a gas pipeline on permafrost”, we received lots of questions from users.
In this post, we cover the more frequently asked questions concerning the functionality of the updated version of Frost 3D Universal software. Firstly, however, we would like to remind readers that the new version of the software was released in May, 2014. Here, we implemented new technologies in the architecture of the software and its main components, which enables the calculation of computational meshes as large as 100 million nodes on a PC. To demonstrate the extraordinary performance of the newest version of Frost 3D Universal, we conducted the thermal analysis of a long section of pipeline lying on permafrost, with a mesh consisting of 58.5 million nodes.
Question: Why do we need such large computational meshes?
Answer: The necessity for such large quantities of computational mesh nodes derives from the following factors:
1) The computation of extensive regions and long or massive objects often involves many elements for discretization in the computational domain.
2) There are often relatively small elements in the computational domain; there could, for example, be a thin layer of heat insulation, or ground strata. A significant increase in mesh refinement is required to discretize these relatively miniscule elements.
3) Areas with significant temperature gradients (near heat insulators, heat sources, cooling devices, etc.) require increased computational mesh density, consequently significantly increasing the total amount of nodes in the computational domain.
Note that even with the use of a non-uniform cell size (at irregular computational mesh), for example, we still need a lot of nodes. The increase in the cell size in irregular computational meshes needs to be very smooth; otherwise, the numerical method returns significantly less accurate results.
Ground water flow rates predefine largely predetermine the construction methods and materials used for footings, basement walls, underground constructions and many other in-ground works. The stability of beds and banks of water reservoirs and channels also depends on the filtration in coastal terrain. Factoring the flow of ground water improves the modeling accuracy of othe rphysical processes in the ground. When distribution of thermal fields takes place in the ground, the convective heat transfer is caused by groundwater flow.
Water is able to flow through the ground because of the presence of pores, which are voids of various diameters and shapes that appear due to the fact that structural elements produced during terrain formation don’t fit flush with each other. The approach for modeling water flow processes differ according to the degree of water porosity and the velocity of water in pores: if the pores are in a saturated condition, the groundwater flow process is simulated based on the Darcy differential equation; water flow in unsaturated ground is described by Richard’s or Brinkman’s equation.
Numerical solution of the problem was implemented in Frost 3D Universal software, with a computational mesh of 58.5 million nodes, to predict ground thaw under the influence of the pipeline. A 2-year simulation of the ground thaw around the pipeline was performed. The computation in Frost 3D Universal software on a quad-core CPU took approximately 70 hours and used 17 GB of RAM. We had already simulated this model before with less detailed discretization: the mesh consisted of 22.3 million nodes and this wasn’t enough to enable us to factor in small elements such as thin heat insulators. Using an NVIDIA Titan graphics accelerator, the prediction of ground thaw over a 20-year period took about 7 hours.
The model of a lengthy section of a gas pipeline
The specific nature of the current problem – simulation of the ground thaw formation along a 500-meter section of the oil pipeline, 1.2 meters in diameter – rendered a large computational mesh necessary. This section is characterized by a complex geological-lithological structure of grounds, which also includes layers of ice deposits. A total of 21 ground typologies with various thermophysical properties were revealed in this section alone. Altitude differences in the daylight surface of 35 meters were also taken into account.
The first benchmark tests on the heat problem with phase transition (Stefan problem) calculation were executed for a sphere with a radius of 10 meters for 364 days. The summary table below gives the computational time taken by the corresponding graphics accelerator.
In the range of applied problems for various industries, for example, architecture, fine arts, animation (movies), meshes of complex configuration may be of great demand. Let us show, how it is possible to describe a configurationally complex computational mesh, consisted of voxels (bubble shaped), which are located on a sheet and twisted into cylinder.
Let us describe a mathematical model used at the design of algorithms of cylinder shaped voxel meshes.
INITIAL DATA FOR CREATING VOXEL MESH
There is a sheet with voxels (bubbles of cylinder shape) located on its surface. Then, it is assumed that voxels are situated on the sheet according to the template, demonstrated in the picture 1.
Many software packages for numerical computations allow users to use a static adaptive (hereby referred to as adaptive) step in the construction of an orthogonal hexahedral structured computational mesh. This means that informed users can employ their experience to get a more accurate computation without significantly increasing the computation time by specifying the areas of the computational domain in which, in their opinion, it is necessary to apply more detailed partitioning (use a smaller spatial step) as compared to the rest of the computational domain.
When properly used, adaptive partitioning of the computational domain is a powerful tool in numerical computations to increase accuracy. However, when the above option is overused, the computational time can increase dramatically without necessarily altering the accuracy of the computation to any significant degree. In this article, we describe the theoretical advantages and disadvantages of using adaptive partitioning of the computational domain, and also give two examples for numerical computations of thermal fields in ground. In the first example, application of the adaptive step is appropriate; this is not the case, however, in the second.