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.

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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*}

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

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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.

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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.

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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.

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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.

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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.

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