Tutorial 5.01

HYDRUS Tutorial 5.01 - Domain Types

HYDRUS (version 2.x and later) can handle both two- and three-dimensional domains of arbitrary shapes. Domains that do not have any limitations with respect of their complexity are called 2D-General and 3D-General domains. Apart from these complex domains, for many practical problems one can use much simpler domains that are easier to define and modify. HYDRUS supports three such simpler types of domains: 2D-Simple, 3D-Simple, and 3D-Layered. Simple Domains represent simple blocks, which are defined using parameters defining their dimensions and slopes. The 3D-Layered Domains enable definitions of considerably more complex three-dimensional domains, but even here there are still significant geometrical limitations.

Users may ask the question: why does HYDRUS support multiple domain types, when obviously the two most general types, i.e., 2D-General and 3D-General, would be sufficient. There are two reasons for that:

A) Historical Development. Already with the first version of HYDRUS-2D (in 1996), users could decide whether it is sufficient to define their projects using Simple Domains, or they need to purchase an additional module Meshgen-2D to generate general two-dimensional domains and FE meshes. Even though the capabilities of HYDRUS have gradually increased, a similar system of licensing is used today. Differences between different HYDRUS editions, i.e., 2D-Lite, 2D-Standard, 3D-Lite, 3D-Standard, and 3D-Professional, that are now available, are in supporting different types of geometric domains. The 3D-Professional Edition supports all types of geometric domains.

B) Work Efficiency. The choice of a simpler type of domains delivers faster and easier work with a geometric model. This can be seen, for example, when working with the 3D-Layered domain when one can create a necessary geometric model using few operations much faster than when working with the 3D-General Domain. On the other hand, when working in the 3D-General mode, one can perform more complex operations with the geometric model. Deciding on the type of domain is one of the first questions when setting up a new project and a right choice here is worthwhile.

A certain disadvantage is that work with the various types of geometries is quite different and there are three different concepts in defining computational domains: Simple, General, and 3D-Layred.

The user should familiarize himself with the different types of domains that can be used and then use the simplest type of domain needed for his/her particular project (a Simple domain needs the minimum information).

The following slides provide an introduction to these three concepts.

Figure 1 - Transport Domains

This figure demonstrates the five different types of transport domains that are currently supported by HYDRUS. The simplest transport domains are rectangular, two-dimensional domains, while the most complex transport domains are general three-dimensional domains. HYDRUS divides these transport domains as follows: 2D - Simple 2D - General 3D - Simple 3D - Layered 3D - General These different types of domains are supported by different HYDRUS Levels: 2D - Lite (A) (i.e., supports domains of the type (2D - Simple) 2D - Standard (A+B) 3D - Lite (A+C) 3D - Standard (A+B+C+D) 3D - Professional (All)

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Figure 2 - Simple Domain 2D/3D

The transport domain may be defined using relatively simple two-dimensional rectangular or three-dimensional hexahedral objects. In such cases, dimensions and other parameters of the transport domain are specified numerically using either the Rectangular or Hexahedral Domain Definition dialog windows. In both of these cases the transport domain is discretized into a structured finite element mesh. In the Rectangular or Hexahedral Domain Definition dialog windows, users need to specify the vertical and horizontal dimensions of the transport domain, as well as a possible slope of the base of the domain in different directions. Nodes along the upper boundary may have variable z-coordinates. However, the lower boundary must always be horizontal (or have a specified slope), while the left and right boundary lines (sides) must be vertical.

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Figure 3 - 2D-General Domain

General Two-Dimensional Domains can be formed using one or more Surfaces that can touch each other, but cannot overlap. Each of the Surfaces is defined by a set of Boundary Curves that enclose the transport domain. All surfaces must lie in the same plane. Surfaces can contain openings, internal points, or internal curves. It is also possible to create an opening in a surface and then enter another surface into it. An unstructured Finite Element Mesh is used to discretized 2D-General Domains. The very flexible unstructured finite element generator (MeshGen2D) can be used for virtually any type of complicated domain. The generator attempts to generate finite elements with the size defined using the parameter Targeted FE Size. This FE size can be further modified in different parts of the domain using various tools, such as Stretching in different directions to make the mesh anisotropic, specifying the Maximum and Minimum Numbers of Nodes on a Boundary Curve, or using Finite Element Mesh Refinement, that can be defined around Points, and for Lines and Surfaces.

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Figure 4 - 3D-Layered Domain

3D-Layered Domains are defined using a Base Surface (a General Two-Dimensional Domain, see the text above for Figure 3) and one or more Thickness Vectors. Thickness vectors do not have to be perpendicular to the Base Surface. The Domain can be divided into one or more Layers, which subdivide the domain into multiple, usually horizontal, Subdomains. These Layers can be used, for example, to keep constant thicknesses of selected horizons or constant discretization close to the soil surface. Relatively general three-dimensional domains, fulfilling the needs of most HYDRUS users, can be defined using the 3D-Layered Domains. However, 3D-Layered Domains still have certain limitations. For example, Layers have to be continuous and some shapes cannot be directly considered (e.g., spheres). All these limitations are overcome in the most general option (Level) of HYDRUS, i.e., in 3D-General Domains (3D-Professional).

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Figure 5 - FE-Mesh in 3D-Layered Domain

The Base Surface of the 3D-Layered Domains is discretized first using, as above for 2D-General Domains, the unstructured finite element mesh generator MeshGen2D. The same options as for 2D-General Domains, i.e., Targeted FE Size, Stretching, FE-Mesh Refinement (see the text with Figure 3 above), can be used when discretizing the Base Surface as well. Discretization in the vertical (perpendicular to the Base Surface) direction follows Layers defined at Thickness Vectors. Users can specify the number of horizontal FE-Layers to discretize the Domain in the vertical direction. Users have high flexibility in defining the vertical spacing of FE-Layers, by specifying, for example, the relative sizes of elements at the top and the bottom, with element sizes then proportionally distributed.

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Figure 6 - 3D-General Domain

In the 3D-Professional version, the 3D General Domains (general three-dimensional domains) can be formed from three-dimensional objects (Solids) of general shapes. Three-dimensional objects (Solids) are formed using Boundary Surfaces, which can be either Planar Surfaces or Curved Surfaces (Quadrangle, Rotary, Pipe, B-Spline). Boundary Surfaces of a Solid must enclose a closed space and cannot intersect each other. In more complicated cases it is also possible to use Intersections of Surfaces and Solids to create, in this way, openings in solids or to carry out with Solids various logical operations. Internal Solids, Cavities, and Integrated Objects can be defined as well.

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Figure 7 - FE-Mesh in 3D-General Domain

The mesh generator Genex/T3D is used to generate three-dimensional FE meshes for the 3D-General Domains. The generated unstructured FE-Mesh is composed from either only tetrahedrals or from elements of different shapes (e.g., tetrahedrals, triangular prisms, and others). Similar options as in MeshGen2D, i.e., FE-Mesh Refinements at Points, on Curves, Surfaces, and Solids, and FE-Mesh Stretching, are available in Genex/T3D as well.

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Figure 8 - 3D-Professional - Example 1

This figure shows a complex three-dimensional domain (3D-General) with Discontinuous 3D Layers. This is an example of a problem that could not be developed using 3D-Layered Domains (available in the 3D-Standard Level).

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Figure 9 - 3D-Professional - Example 2

This figure shows a complex three-dimensional domain (3D-General) with a complex drainage system. Unlike the version 3D-Standard, the version 3D-Professional allows you to create comfortably inside of the transport domain a complex system of internal holes or objects. Examples could be, for example, Tutorial 5.12 or Tutorial 5.15.

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Figure 10 - 3D-Professional - Example 3

This is another example, for which we recommend using the 3D-Professional version. The reason being the markedly variable thickness of the transport domain that requires variable spatial discretization (FE Mesh) in the vertical direction at different locations (XY) of the domain. The disadvantage of the 3D-Layered domain is the fact that the number of finite elements must be the same in the vertical direction for the whole region (or for the whole Base Surface).

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Figure 11 - 3D-Professional - Example 4

This figure shows a model of a more complex landscape with a Tunnel through curved geological layers, created using an Intersection of multiple Curved Surfaces. The Hillside is defined using three major geological layers: the bottom layer (dark blue), the intermediate layer (light blue), and the surface layer (green), each defined using curved surfaces.

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Figure 12 - 3D-Professional - Example 5

The picture shows an example of the test of defining internal objects. Internal objects can be points, curves, surfaces, internal solids, and/or holes/cavities. The displayed domain contains several Internal objects of spherical shape filled with various materials.

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Figure 13 - 3D-Professional - Geometry Import

Version 2.x extends options to import geometric data and/or auxiliary/supporting objects. An already existing import of data from text files has been extended by an import of points and curves in the DXF format and, further, of triangular meshes in the STL and TIN formats. You can also import bitmaps (BMP), place them arbitrarily in the 3D space, and use them as a template when graphically entering spatial data.

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Figure 14 - Import of Surface Meshes

This figure, together with the previous Figure 13, demonstrates the wide range of usability of the import of triangular meshes. Using surface-area meshes, one can import virtually any shape. However, the current version 2.01 uses such triangular surfaces only as so-called background layers, i.e., auxiliary layers which facilitate graphical entry of spatial data. We're planning to implement (in future versions) the import of surface triangular meshes as fully functioning Surfaces, useful for specifying objects of the transport domain.

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