Then the naming and differentiation between time and spatial variables is basically a convention issue, the math behind does not really change
The first boundary load is added for the horizontal soil boundaries. In the COMSOL multiphysics user guide you can find a better explanation of how to use the general projection operator. For circular periodicity, a rotation matrix, not a linear shift, must be used in the destination map. This time in the x direction and using the second general extrusion operator in the u0 field. so we choose 0.6 to be on the safe side. Currently we are ISO 9001 certified. It can be used for a variety of different purposes, examples of which are presented here. Your internet explorer is in compatibility mode and may not be displaying the website correctly. In the course of building multiphysics models, we often encounter situations in which the solution to one physics is periodic or very nearly so while the solutions to other physics of interest are nonperiodic. In addition to simply copying known quantities, these operators can be used to create nonlocal couplings between unknown variables, as illustrated in our p-n junction example. Ivar. Click the player button again to view all the parameter values in succession. The variable Disp is individually defined within each of the three domains, as shown in the figure below. Your internet explorer is in compatibility mode and may not be displaying the website correctly. For meshing the model, sometimes an automatic mesh is sufficient, but we want to make our own for this model to improve convergence on the soil-wall boundary. However, if we want to use variables from a 2D axisymmetric component in the physics node of a 3D component (i.e., thermal expansion), we need to utilize General Extrusion operators. Disp is defined as one of three different scalars (0,1.5,3 mm) as per the fourth figure. Therefore, we can greatly reduce our model by solving only for the fluid flow within one unit cell and patterning this flow solution throughout the modeling domain for the convection-diffusion problem. The top and bottom surfaces are thermally insulated, and there are no heat sources. --
It can be used for a variety of different purposes, examples of which are presented here. In 4.0a, I can define a general extrusion coupling, and the source domain is applies to. This applies a varying species concentration over the inlet boundary. I have defined a general extrusion coupling operator to obtain the dependent variable (in my heat transfer case, the temperature "T") at a boundary. Create the ramp function for activating the struts. Mapping of data defined on a boundary (left) along the direction normal to the plane and into a volume (right). You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version Add a second distribution for the bottom boundary, and enter 2 for the number of elements. We want a depth ranging from 0 to -26 meters with a step size of two meters. When building the mapping, it is important to ask the following question: Given the coordinates of the destination point, how do we go to the source point? They appear in the Input faces list. A general extrusion operator can be evaluated at any point where the destination map expressions are defined. Lets begin by looking at a microfluidic device, as shown below. Schematic of a microfluidic mixer that depicts the repeated unit cell and the inlet and outlet zones. FIGURE 1. For the y-axis data, the expression is y, and for the x axis, the expression is u, with millimeters as units. We can then consider examples in which the General Extrusion operator must be used. But finally COMSOL basics is a PDE solver tool for a given subset of useful functions, of the type used for common physics (that fits in the global or coefficient form. Using source and destination maps to define implicit relations between source and destination coordinates in a General Extrusion operator. Now that the velocity field is defined throughout the modeling domain, the species concentration at the inlet is defined via the Inflow boundary condition. For example, to map data from a boundary around a centerline, introduce a cylindrical system, and use those coordinate system variables to define the source and destination map. This works and solution time is reduced to 118s so much more in line with the case without gaps! Take a look at the figure below. Given an expression defined on a plane, e.g., the xy-plane, it is desired to map this data along the z direction. The General Extrusion operator maps expressions defined on a source to an expression that can be evaluated on any destination geometry where the destination map expressions are valid. The final project, on the other hand, tasked us with designing a retaining wall to match certain specifications a tough and lengthy assignment. Settings used to revolve data about the azimuthal axis of a cylindrical coordinate system. Settings used to map data from a boundary parallel to the xy-plane along the z direction. One application of a General Extrusioncoupling is to mirror the solution on the x-axis. Sometimes, we may want to access an integral, average, maximum, or minimum over a source line, surface, or volume. General Extrusions specializes in providing secondary fabrication operations to transition an aluminum extrusion to a finished component. This variable should only exist on the . Settings used to revolve data about the azimuthal axis of a cylindrical coordinate system. Note that the source map needs to be one-to-one for the inverse to exist. Variable: comp1.Disp. For the final part of the physics set up, we are going to add five boundary loads to the model. If the nonlocal couplings you want to simulate are not included in the built-in features of COMSOL Multiphysics, you can use the strategies youve learned today to implement them. This worked perfectly for a point moving on a surface. The Linear Extrusion operator defines a linear extrusion that maps between geometric parts of the same dimension. To start a new discussion with a link back to this one, click here. For example, to map data from a boundary around a centerline, introduce a cylindrical system, and use those coordinate system variables to define the source and destination map. Note: This discussion is about an older version of the COMSOLMultiphysics software. Version 4.1 Note that a Linear Extrusion operator cannot be used here. The General Extrusion operator will map data from the boundary into the volume, along the z direction, as shown in the following screenshots. We want stress in the negative x-direction here. Next, let's take a look at the settings of the . Forming an assembly creates an identity pair between the wall soil and wall diaphragm boundaries. The player button feature allows you to see all the excavation depth results in one animation. We were the 1st North American Aluminum Extruder to achieve ISO 9002 Certification. Now we will use the operators in the physics nodes to implement the boundary conditions. Similarly, on side 2, we need access to the electric potential V_1 on the other side of the junction. Because the source entities are different, two operators are needed. Mapping of data defined on a cross section (left) around an axis of symmetry and into a volume (right). Now that the velocity field is defined throughout the modeling domain, the species concentration at the inlet is defined via the Inflow boundary condition. Example 1 In our earlier blog post on Linear Extrusion operators, we considered an affine mapping that pairs up points 1, 4, and 2 in the source domain to points 1, 5, and 3 in the destination domain. The same transforms can be implemented in three dimensions. An example of defining such a rotation matrix is detailed in this previous blog post. For the 2D model, I have computed the expression u(x,y). Right click the Boundary Load 3 node to rename it Strut_1. The velocity field is given by u and v, the fluid velocity in the x and y-directions, respectively. Select the faces that you want to extrude in the Graphics window. Ce consentement peut tre retir tout moment. The general extrusion operation applies a rotational transform. Is it possible to do this within GUI, or do i have to do it via MATLAB? Too simple. To implement, define a General Extrusion operator on a boundary parallel to the xy-plane, with the z-expression blank for both the Source Map and a Destination Map. the destination map, not sure what the source frame should be. Mapping of data between different components in the model to perform submodeling, Mapping between components to extract results on different geometries. The number of destination map expressions is the same as the space dimension of the intermediate mesh. I hope I have not missed it. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version We begin by adding the General Extrusion coupling operator from the definitions toolbar as shown in the screenshot below: Thus, every point in the original domain is mapped along the positive x-direction by the specified displacement. This problem can be solved by using a General Extrusion coupling operator to dynamically map the solution at a particular point (moving or stationary) onto a fixed source. Shu Heng Khor . Extrusion operators can be used to make couplings between points in the same component or different components. This approach helps avoid confusion if there is an extrusion or another operator also called genext1 or another variable called T in the second component. CNC Machining for Aluminum Extrusions. The two circles in the geometry have centers at the origin and radii of 1.0 and 1.5. General Extrusions makes simple and intricate aluminum shapes through both long and short production runs. For affine relations, General Extrusion operators can be used as an alternative to Linear Extrusion operators. The schematic diagram is shown in Figure 1. Your internet explorer is in compatibility mode and may not be displaying the website correctly. It also provides design assistance and engineering support. listed if standards is not an option). Given an expression defined on a plane, e.g., the xy-plane, it is desired to map this . If its a simple analysis may be u dont even want the two components. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version this defines if you should us a linear or general Extrusion or Projection
Mapping of data defined on a boundary (left) along the direction normal to the plane and into a volume (right). Instead, at every destination point, it first evaluates T_d(x_d,y_d) and carries out a mesh search operation to find the point on the source where this evaluation matches T_s(x_s,y_s). I defined a general extrusion operator, then defined variables such as T_sf = genext1(comp1.T), Y_sf = genext1(Y) and so. The parabola is the source. Using a General Extrusion operator to copy data from the 2D axisymmetric domain to the corresponding 3D domain. A 2D parabolic curve given by \frac{y}{d} =(\frac{ x}{d})^2 is in a square domain of side d. Our task is to build an operator that maps data from this curve (represented in blue in the figure below) to different parts of the square. Linear Extrusion operators are easier to build, but their utility is limited to affine transformations.General Extrusion operators are more general but take more work to define. In our earlier blog post on Linear Extrusion operators, we considered an affine mapping that pairs up points 1, 4, and 2 in the source domain to points 1, 5, and 3 in the destination domain. This is reasonable to do since it is assumed that the flow field is independent of the species concentration. The time varying coordinates of the point at which we want to evaluate the temperature can be entered as the coordinates of the destination map. This site is under development. To implement the normal current boundary condition on side 1, we need access to the electric potential V_2 on side 2. Considering a variable defined on the xy-plane within a unit square centered at the origin, as shown above, it is possible to implement a variety of transforms simply via different destination maps, and leaving the source map unchanged. Left: Temperature varies linearly from left to right. Sample data defined on the xy-plane, centered at the origin. The Graphics Window: Effective and Beautiful Postprocessing, Generating Microsoft PowerPoint Slideshows from Your Models, Combining Adaptive Mesh Refinement with Data Filtering. The companys manufacturing operations, which include a Youngstown, Ohio plant, comprise 220,000 square feet. Considering a variable defined on the xy-plane within a unit square centered at the origin, as shown above, it is possible to implement a variety of transforms simply via different destination maps, and leaving the source map unchanged. Gaining Understanding of Complex Phenomena with Virtual Laboratories, The Graphics Window: Effective and Beautiful Postprocessing, How to Use Maximum Likelihood for Parameter Estimation in COMSOL, Thank you for your Blog. Once a strut is activated, it will generate a force proportional to the struts stiffness and the horizontal displacement. We can tag the different sides as 1 and 2, as illustrated in the figure below. Settings used to map data from a boundary parallel to the xy-plane along the z direction. The periodic modeling domain and the fluid flow solution. Now that the velocity field is defined throughout the modeling domain, the species concentration at the inlet is defined via the Inflow boundary condition. Submit feedback about this page or contact support here. COMSOL Multiphysics will take care of T_s^{-1}(T_d(x_d,y_d)), a necessary step in identifying the source coordinates. Several cases are illustrated in the table below. I have the other model, where i would need this variable u, but this time, it is a 2D model, non time dependent. This consent may be withdrawn. To map the solution from one domain into the other domains that are offset by a known displacement along the x-axis, the destination map uses the expression x-Disp for the x-expression. I didn't mean to do integration, what i meant is something like: Thanks for replying. A retaining wall is used to hold back soil from a region you dont want it to move to, such as a lower level of the ground. Therefore, we have, Now we need to find the constants a,b,c,d,e, and f. Since source points (0, 0); (1.0, 0); and (0, 1.0) correspond respectively to destination points at (0, 0); (1.5, 0); and (0, 1.5), we get. It is also possible to define the mapping in terms of coordinate systems. 3 Replies, Please login with a confirmed email address before reporting spam. I have only one small question, if you dont mind, you could maybe write the expressions of the variable disp. Lets consider a point on the disk at a distance of 0.5 inches from the center of the disk located at (0,0). However, if we neglect the structure near the inlet and the outlet, we can reasonably assume that the flow within the channel bends will be identical between the unit cells. Right click again to duplicate it twice, since we want similar settings for the second and third struts. Now we will create a 1D plot and a line graph, with the wall diaphragm as the selection. All you need are the time-dependent coordinates of the point where you would like to evaluate the temperature. For example, if the intermediate mesh is in 2D space, there is no z-expression field. (For reference: the model is approx. This approach, as explained earlier, is limited to cases in which the source and destination are related by affine transformations. In this example, the operator is used by the Transport of Diluted Species interface to define the velocity field (illustrated below). To implement, define a General Extrusion operator on a boundary parallel to the xy-plane, with the z-expression blank for both the Source Map and a Destination Map. The video shown below uses the latter of the two strategies to model a 26-meter excavation. COMSOL Multiphysics includes built-in features pertaining to such physical effects. Mapping of data between different components in the model to perform submodeling, Mapping between components to extract results on different geometries, 2023 by COMSOL. If we know this ahead of time, it is possible to exploit the periodicity to reduce computational requirements. The results of the analysis, including the concentration and the mapped velocity field, are depicted below. These are the parameters we will be using later on, which represent in-situ stresses, properties of the metal struts, excavation steps, along with a couple other related parameters. For example, you can couple edges (boundaries) in 2D to edges in 3D; or couple 2D domains to 3D faces. In these first two examples, the Use source map check box in the Source section of the settings window has been left unchecked. Each side of the junction becomes a source entity in one of the extrusion operators, as depicted below. The ramp location is set to be -U_max. It is also possible to define the mapping in terms of coordinate systems. An Outlet boundary condition is applied at the other end. The components of this velocity field are now defined in all of the repeated domains via the General Extrusion operator: genext1(u) and genext1(v), respectively. Next, well look at how to use a General Extrusion operator to specify implicit relations. Take a look at the figure below. At any given time, the (x, y, z) coordinates of this point are given by: (0.5[in]*cos(t), 0.5[in]*sin(t), 2.75e-4[m]), where is the angular velocity of the rotating wafer disk. Settings used to map data from a boundary parallel to the xy-plane along the z direction. General Extrusion Variable. The same transforms can be implemented in three dimensions. Take a look at the figure below. Both cases involve mapping between points that share the same x-coordinate. Given an expression defined on a plane, e.g., the xy-plane, it is desired to map this data along the z direction. Note that for axisymmetric components, variables can be viewed in 3D with a Revolution 2D data set in the Results node. Extruding Data Along a Direction. Settings used to revolve data about the azimuthal axis of a cylindrical coordinate system. The corresponding normal current density for the Normal Current Density 2 node applied to edge 3 is -Js*(exp((V-genext1(V))/kTbyq)-1). A typical microfluidic device. The following types of Extrusion Coupling Operators are available: It is also possible to define the mapping in terms of coordinate systems. Right-click study 1 to compute the model. L(x,y) = \int_{o}^{x}\sqrt{1+(y\prime)^2}d\tau = \frac{x}{2}\sqrt{1+4(\frac{x}{d})^2}+\frac{d}{4}\ln(2\frac{x}{d}+\sqrt{1+4(\frac{x}{d})^2}). x_s = ax_d + by_d + e, \qquad y_s = cx_d + dy_d + f. r_s = \sqrt{x_d^2 + y_d^2}, \qquad z_s = z_d. Thank you for your time. For . Such devices feature small channels that are filled with fluids carrying different chemical species. Extrusion Model Coupling Operator takes a local concentration as an argument at the following boundary and evaluates it at the corresponding point at the leading boundary.
How to use the General Extrusion coupling operator to probe a solution at a moving point http://comsol.com/c/10mb Here is an interesting question: How can we easily probe the solution at a point that is moving in time, but associated with a stationary geometry?. How did you select the source in the general extrusion settings? The General Extrusion coupling's 'Mesh search method' is very important for model performance in largers models #resolventtip: Get the best performance out your 'General Extrusion'-coupling in Comsol The destination map here consists of the transient coordinates where we would like to evaluate temperature. Previously on the blog, we introduced you to Linear Extrusion operators and demonstrated their use in mapping variables between a source and a destination. But no possibility to define variables. General Extrusions, Inc. produces aluminum extrusions in compliance with RoHS (Restriction of Hazardous Substances) requirements. When it comes to general nonlinear mappings, General Extrusion operators are necessary. Email: support@comsol.com. Submit feedback about this page or contact support here. A linear mapping built using a General Extrusion operator. The model is solved in two steps first, the Laminar Flow physics interface is solved, and then the Transport of Diluted Species interface is solved. listed if standards is not an option). The General Extrusion operator will map data from the boundary into the volume, along the z direction, as shown in the following screenshots. Thank you. Extruding Data Along a Direction It contained both the high and low points for that academic semester; the lab portion was a lot of fun, learning about (read: playing with) the different soils and clays existing in the state of Georgia. Why are all the domains selected? Hello Oluwaseyi, This sounds like a case of a variable name used twice, but you may want to reach out to the support team for help. It is also possible to define the mapping in terms of coordinate systems. Good luck
The Copy Domain mesh feature can copy the mesh exactly, thereby avoiding any interpolation of the flow solution between meshes.
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