In this example, a 26-meter excavation is modeled by means of a parametric sweep, with a step size of 2 meters. 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. Your internet explorer is in compatibility mode and may not be displaying the website correctly. Extrusion operators can be used to make couplings between points in the same component or different components. Add a distribution for the wall diaphragm and enter 60 for the number of elements. As in Example 1, we enter the expression on the right-hand side in the destination map. These indices are, in a sense, coordinates of an intermediate mesh, and a General Extrusion operator matches source and destination points that have the same intermediate coordinates. You can find it at page 348: . I am trying to implement the Periodic Boundary condition in a 3D model by following your post but I have some questions. Examples of the General Extrusion Operator - COMSOL General Extrusions, Inc. continues its tradition as a leading manufacturer of aluminum extrusions where quality always comes first. Extrude - COMSOL Multiphysics The periodic modeling domain and the fluid flow solution. COMSOL Multiphysics will take care of T_s^{-1}(T_d(x_d,y_d)), a necessary step in identifying the source coordinates. 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. Online Support Center: https://www.comsol.com/support Click plot to view the displacement at the different excavation depths. Simulation Organogenesis in COMSOL: Deforming and Interacting Domains For . For the y-axis data, the expression is y, and for the x axis, the expression is u, with millimeters as units. We are then looking at the problem of evaluating the temperature at a point that follows the rotating wafer material. I deplore the glaring oversight of COMSOL: Considering how frequently one encounters problems that include a combination of Rotationally-Symmetric and Cartesian components, that COMSOL has not seen fit to provide a specific operator for this case! the destination map, not sure what the source frame should be. A circular micro-electrode array with three phases is designed and prototyped using PolyMUMPs process for AC electro-osmotic flow pumping. Shu Heng Khor . This site is under development. The same transforms can be implemented in three dimensions. We have discussed how the General Extrusion component coupling can be used to set up a linear pattern of a periodic solution as part of a multiphysics analysis. The parts can exist in geometries of different space dimensions. The Copy Domain mesh feature can copy the mesh exactly, thereby avoiding any interpolation of the flow solution between meshes. The reason is that x^i and y^i are indices for the first and second pairs of expressions used to define the source-destination relationship implicitly. Take a look at the figure below. Mapping of data defined on a boundary (left) along the direction normal to the plane and into a volume (right). The General Extrusion feature is available in the model tree under Component > Definitions > Component Coupling. This will allow you to compare different cross-sectional data and evaluate measures such as maximum, minimum, and average over several cross sections. The two circles in the geometry have centers at the origin and radii of 1.0 and 1.5. The relationship between the source and destination points is therefore, If we want an explicit source-destination mapping of the form. 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. We can simply enter the time varying coordinates in the x, y, and z-expressions of the destination map. Currently we are ISO 9001 certified. Sample data defined on the xy-plane, centered at the origin. The flow solution on this unit cell is also plotted, as shown below. The boundary condition at the top side is illustrated below. We need to provide T_d and T_s, such that. Ce consentement peut tre retir tout moment. Discussion Closed This discussion was created more than 6 months ago and has been closed. 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. indeed I do not believe I really understand what you intend to do. 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}). Here, the p-n junction in a diode is represented by a thin gap in the geometry. 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. L=\frac{x_s}{2}\sqrt{1+4(\frac{x_s}{d})^2}+\frac{d}{4}\ln(2\frac{x_s}{d}+\sqrt{1+4(\frac{x_s}{d})^2}), we introduced you to Linear Extrusion operators, earlier blog post on Linear Extrusion operators, Using the General Extrusion Coupling Operator in COMSOL: Dynamic Probe, Using General Extrusion Operators to Model Rotation, Using General Extrusion Operators to Model Periodic Structures, Submodeling: How to Analyze Local Effects in Large Models, Postprocessing Local Data Using Component Coupling, Multiscale Modeling in High-Frequency Electromagnetics. Accessing Nonlocal Variables with Linear Extrusion Operators - COMSOL Tutti i diritti sono riservati. Therefore we want stress in the y-direction. Click the player button again to view all the parameter values in succession. Take a look at the figure below. #resolventtip: Get the best performance out your 'General Extrusion This is why i need to convert u(x,t) back to its original form, u(x,y). I have defined a general extrusion coupling operator to obtain the dependent variable (in my heat transfer case, the temperature "T") at a boundary. To add a General Extrusion operator, we go to Definitions > Component Couplings > General Extrusion. To explore the use of General Extrusion operators in other types of situations, consult the following blog posts: By providing your email address, you consent to receive emails from COMSOL AB and its affiliates about the COMSOL Blog, and agree that COMSOL may process your information according to its Privacy Policy. The same transforms can be implemented in three dimensions. Mapping of data between different components in the model to perform submodeling, Mapping between components to extract results on different geometries, 2023 by COMSOL. Create the ramp function for activating the struts. The electric potential on one side of the gap is accessed from the other side by using an extrusion operator in order to compute the current density flowing across the gap. Several cases are illustrated in the table below. Unknown function or operator. It can be used for a variety of different purposes, examples of which are presented here. One option involves a sweep of the geometry, removing the geometry (excavation) one step at a time. Extrusion operators are used to construct pointwise relations between source and destination points. As the excavation deepens, three struts are activated using a ramp function, and boolean expressions. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version In the Work plane list, select the work plane to extrude from. For example, if the intermediate mesh is in 2D space, there is no z-expression field. There are some models. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version For clarity, we did not use this trick here. Thank you! In general, the destination map accepts scalar values that may be space- or time-dependent expressions. It is also possible to define the mapping in terms of coordinate systems. 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. Note that while COMSOL employees may participate in the discussion forum, COMSOL software users who are on-subscription should submit their questions via the Support Center for a more comprehensive response from the Technical Support team. Note that the source map needs to be one-to-one for the inverse to exist. The species concentration (shown in color) is solved in all three repeating domains. Mapping of data between different components in the model to perform submodeling, Mapping between components to extract results on different geometries. This works and solution time is reduced to 118s so much more in line with the case without gaps! If the structural boundary conditions are not axisymmetric, we can save time by performing an axisymmetric thermal analysis in one component, and then mapping the temperature from the 2D axisymmetric domain to the 3D domain for structural analysis in another component. FIGURE 1. Next, well look at how to use a General Extrusion operator to specify implicit relations. A linear mapping built using a General Extrusion operator. Because the source entities are different, two operators are needed. For circular periodicity, a rotation matrix, not a linear shift, must be used in the destination map. Ivar. Now that the velocity field is defined throughout the modeling domain, the species concentration at the inlet is defined via the Inflow boundary condition. Modeling an Excavation in COMSOL. Now we will create a 1D plot and a line graph, with the wall diaphragm as the selection. 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. Thanks in advance. In this example, since the x, y, and z-coordinates of the destination map are explicitly specified without any association with the coordinates of a geometric entity, it doesnt matter where we evaluate the General Extrusion coupling operator. Thanks for replying. Several cases are illustrated in the table below. listed if standards is not an option). listed if standards is not an option). Thus, two extrusion operators are required. Alternatively, from the Extrude from list, select Work plane to extrude objects from a work plane. General Extrusions is owned and run by the Schuler family.Read More. Such devices feature small channels that are filled with fluids carrying different chemical species. listed if standards is not an option). With the General Extrusion operator defined, we can now use it throughout the model. It is also possible to define the mapping in terms of coordinate systems. The video shown below uses the latter of the two strategies to model a 26-meter excavation. We can choose a prescribed displacement to make sure the soil at boundary 4 only moves in the y direction. Several cases are illustrated in the table below. Once a strut is activated, it will generate a force proportional to the struts stiffness and the horizontal displacement. Next, lets take a look at the settings of the General Extrusion coupling operator. Within their design, a common goal is to achieve optimal mixing within a small surface area, hence the serpentine channel. First a mapped mesh for the retaining wall domain. Good luck It can be used for a variety of different purposes, examples of which are presented here. Submit feedback about this page or contact support here. The working fluid is water with properties defined at room temperature and pressure. unfortunately, I get the following error. Thank you Walter for a wonderful discussion. In the results, how is Point 2 related to the general extrusion? Your internet explorer is in compatibility mode and may not be displaying the website correctly. The schematic diagram is shown in Figure 1. In this blog post, we will take a look at how to use the General Extrusion coupling operator to probe a solution at a point in your geometry, and illustrate how to implement a dynamic probe using an example model. Editing and Repairing Imported Meshes in COMSOL Multiphysics, Exploiting Hardware Parallelism with COMSOL Batch Sweeps, The Graphics Window: Effective and Beautiful Postprocessing, Thank you so much for this article, I was in need of something that shows the mathematical operations of the extrusion coupling. 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. We can then consider examples in which the General Extrusion operator must be used. The Micromixer tutorial, available in our Application Gallery, is an example of such a model. Lets begin by looking at a microfluidic device, as shown below. Why are all the domains selected? First, did you only the repeating unit in your graphics window before using the General Extrusion and Periodic Boundary conditions node or was it the entire geometry? Additional settings are shown below. 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. So lets revisit the Advanced settings and switch back Mesh search method to Use Tolerance the defaults is 0.3 which we have seen to fail in this case we have to search across a 0.1m gap, and we have meshed with 0.2m mesh-elements, thus we need, tol=search_distance/element_size=0.1[m]/0.2[m]=0.5. General Extrusion Variable. 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?. Any affine transformation can be expressed as the sum of a linear transformation and a translation operation. The incident heat flux from the laser is modeled as spatially varying, with time varying coordinates for the location of the incident heat flux. Settings used to map data from a boundary parallel to the xy-plane along the z direction. It is also possible to define the mapping in terms of coordinate systems. The corresponding normal current density for the Normal Current Density 2 node applied to edge 3 is -Js*(exp((V-genext1(V))/kTbyq)-1). Submit feedback about this page or contact support here. listed if standards is not an option). COMSOL provides Model Coupling Operators to implement such a mapping. We want stress in the negative x-direction here. A one-to-one source map makes the search return, at most, one source point for a given destination point. The Shockley diode equation for the current-voltage (I-V) relation is used at the junction. The results of the analysis, including the concentration and the mapped velocity field, are depicted below. Now, add a free triangular for the remaining geometry. To begin, lets focus on how to replicate a Linear Extrusion operator with a General Extrusion operator. The plot below shows the temperature evaluated at the focal point of the moving laser: this defines if you should us a linear or general Extrusion or Projection 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. so we choose 0.6 to be on the safe side. listed if standards is not an option). A little calculus gives us the arc length of the parabola between the origin and the source point (x,y). I am trying to use the same for droplet evaporation. To start a new discussion with a link back to this one, click here. Thus, the latter quantity from a source point P_s needs to be copied to the destination entity. Add a second distribution for the bottom boundary, and enter 2 for the number of elements. Your internet explorer is in compatibility mode and may not be displaying the website correctly. The operator genext1 is not known inside the 3D component comp2; neither is T. If we want to use the temperature from the 2D axisymmetric component as an input in the 3D component, we have to use comp1.genext1(comp1.T). How did you select the source in the general extrusion settings? This can be either an explicit definition of the source point P_s as a function of P_d or an implicit relation between P_d and P_s. General Extrusions is engaged in fabrication, anodizing, and powder coating, as well as aluminum finishing and machining. at an interface. The default plot shows the von Mises stress. 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. This graph shows the wall deflection or horizontal displacement as a function of depth for different excavation steps. Take a look at the figure below. Temperature evaluated at a point on the rotating wafer. Enter in the equation shown which is the ramp function of the wall deflection, with an added term limiting the expression to occur only when the depth is below the strut. Phone: (330) 783 0270 Fax: (330) 788 1250 Email: sales@genext.com P.O. Extruding Data Along a Direction Image by IX-factory STK Own work, via Wikimedia Commons. In this example, the operator is used by the Transport of Diluted Species interface to define the velocity field (illustrated below). Now, if desired, it is possible to model the entire device shown above. When expanded it provides a list of search options that will switch the search inputs to match the current selection. Rename the third strut to finish off the physics set up. Settings used to revolve data about the azimuthal axis of a cylindrical coordinate system. As you can see, they are in the same location but are different boundaries. First add a size node to make sure the mesh is finer. The applied heat load is described via a user-defined function, hf (x,y,t), that describes how the laser heat load moves back and forth along the x -axis in the global coordinate system. This worked perfectly for a point moving on a surface. To add a General Extrusion operator, we go to Definitions > Component Couplings > General Extrusion. Extruding Data Along a Direction Lets now explore how to use a General Extrusion operator to copy data from a 2D axisymmetric component to a 3D component, such that the source and destination points correspond to the same point in space. We were the first North American aluminum extruder to achieve ISO 9002 Certification. The focus of this blog post is on the transformation T : x_d \rightarrow x_s.. COMSOL Multiphysics offers two coupling operators to specify this mapping: Linear Extrusion operators and General Extrusion operators. How to Extrude, Revolve, and Sweep 2D Geometries in COMSOL - YouTube