On Spatial Interpolation of Ground Temperature from Temperature Logs of Monitoring Wells


Non-asymptotic numerical simulation of transient heat transfer requires knowledge of initial conditions. If the heat transfer medium is ground, they typically use temperature logs (depth-temperature tables) of monitoring wells for the initial time point. Then one may either use scattered-data interpolation [1] or solve a steady heat transfer problem with Dirichlet boundary conditions at temperature measurement points. If you choose the second way and the problem is nonlinear, there might be some convergence issues.
Ground Temperature Interpolation Based on Temperature Measurement Points

Figure 1: Ground Temperature Interpolation in Frost 3D Universal

Continue reading

Convective Term in the Douglas-Rachford ADI Scheme

1. Introduction

For the mathematical simulation of thermal field distribution in the ground, it is necessary to account for convective heat transfer (heat transfer by means of mass transfer). Convective heat transfer is caused by the filtration of water into the ground resulting, for example, from precipitation. The temperature distribution is described by the partial differential equation of heat conduction where, in the case of convection, there is a so-called convective term. Since the computational domain is arbitrary, the heat equation is solved numerically by using finite-difference methods (FDM). The Douglas – Rachford ADI scheme is one of these methods. In this paper, we focus on modification of the scheme to account for convection in the computational domain.

Continue reading

Analysis of Foundation Deformation

1. Introduction

It is well known that the foundations of buildings are subject to loads which can result in deformation and subsidence. Hence, the analysis of foundation deformation must be conducted at the design stage. This article describes the computer simulation of foundation deformation. We propose an approach based on numerical solution of the stationary differential equation in partial derivatives. This equation describes the transversal deflection of a thin plate (foundation slab), taking elasticity into account, due to an external orthogonal force.

2. Plate Deflection Equation

Let the Cartesian coordinate system (x,y) be the plate plane.By \Omega we define the domain of the plate in this plane. Let \Gamma=\partial {\Omega} be the boundary of the \Omega domain. The function for plate deflection is given by u(x,y):\Omega\to R. At small transversal (vertical) deflections, the function u(x,y) satisfies the following equation [1]:

(1)   \begin{equation*}  D(x,y)\times ( \frac{\partial^4{u(x,y)}}{\partial^4{x}} +2\frac{\partial^4{u(x,y)}}{\partial^2{x}\partial^2{y}}+\frac{\partial^4{u(x,y)}}{\partial^4{y}})= \end{equation*}

    \[ = f(x,y) + r(x,y,u), (x,y)\in \Omega \]

Continue reading

Implementation of the Douglas - Rachford Scheme with Cuda Technology


This article describes the performance of calculations on video cards (using CUDA) for modeling physical processes and phenomena based on the solution of the three-dimensional heat equation via the Douglas-Rachford scheme (ADI method). A comparative analysis of the calculation speeds of the central (CPU) and graphics (GPU) processors was conducted.


For the mathematical simulation of heat distribution, accounting for filtration and phase transition, the following heat equation is applied:

(1)   \begin{equation*}  C_{ev}\frac{\partial T}{\partial t}+\bigtriangledown{(-k\bigtriangledown{T})}+C_w\vec{v}\bigtriangledown{T}-Q=0 \end{equation*}

A description of the coefficients is given in Table 1.

Continue reading

Parallel Computations Efficiency: Abaqus, Ansys and Simmakers

Hardware that is based on parallel computing architecture has recently been gaining increasing popularity in high performance computing.

The efficiency of parallel processing hardware in engineering problem solving such as the computer simulation of physical processes is not directly dependent on the number of processors: four CPU cores do not in fact provide a fourfold speed increase in solving complex engineering problems over one CPU core. Similarly, the transfer of computation to graphics cards with hundreds of cores cannot provide a hundredfold increase in speed.

First of all, parallel computation acceleration is limited by computational algorithms; running algorithms with a low degree of parallelization on supercomputers and high-performance workstations is irrational. The notion of "efficiency of parallelization" is explained by Amdahl's law, according to which if at least 1/10 of the program is executed sequentially, then the acceleration cannot be increased beyond 10 times the original speed regardless the number of cores employed.

Telling examples of the limited effectiveness of algorithm parallelization for solving engineering problems are provided in the relatively weak results of worldwide leaders in computer-aided engineering (CAE) software - Abaqus and Ansys.

Continue reading

Calculation of Base Settlement on Permafrost Ground According to SNIP 2.02.04-88

The article is devoted to methods of base settlement on permafrost calculation with detailed description according to SNIP 2.02.04-88.


The calculation of bases in permafrost regions is quite a complicated and specialized process, heavily influenced by thermal field and thawing phenomena. Thermal field causes permafrost thawing and decreases its load bearing capacity while increasing ground base deformation, which is usually evidenced in the form of base settlement. In fact, to determine the deformations during building maintenance, it is necessary to solve for the stress-strain state of the base, which is described by differential equations of equilibrium and the laws of elastic-plastic deformation.

Continue reading

Automatic Geological Structure Reconstruction


In this article, a new geological structure reconstruction method is described, based on information regarding the occurrence of geological horizons obtained by exploration.

A number of terms used in the description of the technique need to be determined. Under the wells in this note seem geotechnical boreholes that determine the physical and mechanical properties of soils. A borehole provides information on the vertical distribution of layers through the soil depth. The layers of materials around the drilling wells are shown by the segments in Figure 1.

Reconstruction of borehole

Fig. 1: Layers of materials revealed by boreholes

When creating the geological models in specialized software packages, some additional steps are required in most cases. For example, when reconstructing geological layers using borehole data, the grouping of layer segments is performed manually. This can be a very complicated process for sites with a large number of boreholes and layers.

Continue reading

FAQ for the Updated Version of Frost 3D Universal Software

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.

Continue reading

Application of ANSYS Software for Thermal Analysis of Permafrost Ground. Advantages of Frost 3D Universal Software.

An engineering company has recently asked Simmakers to comment on the possibility of applying the finite-element package of ANSYS to the problems of ground thawing and thermal stabilization, and to explain the advantages of Frost 3D Universal software when solving such problems.

Note that this issue has also been addressed by various specialists in dedicated forums and conferences.

Claims by the ANSYS distributor:

ANSYS with finite-element method analysis is used for ground thawing analysis. ANSYS is a longstanding universal software system for finite-element analysis. It is popular with specialists in the field of computer engineering (CAE, Computer-Aided Engineering) and finite-element solutions for linear and non-linear, stationary and non-stationary spatial problems of rigid body mechanics and construction mechanics (including non-stationary geometrically and physically non-linear problems of contact interaction of construction elements), problems of liquid and gas mechanics, heat exchange and heat transfer, electrodynamics, acoustics, and also mechanics of coupled fields.

Continue reading

Simulation of Groundwater Flow in Saturated Ground

Applicability in construction engineering

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.

Continue reading