Using Global Equations: Modeling Room Air Temperature in a House, Using Global Equations to Introduce Fully Coupled Goal Seeking. So using this equation, we dont need to solve for fluid flow at all, but we do need to know the air temperature inside the house. Chapter 12: Global Equations and ODEs Lets draw a simplified engineering sketch of how this can be modeled: Here, the house walls are modeled explicitly via the finite element method; the true wall dimensions are used and appropriate material properties are applied. Through the Model Builder toolbar, you can open the menu for showing more options, and then select the check box next to Equation View and click OK. construct the domain first and give you physical parameters then choose the numerical scheme for your model. Your internet explorer is in compatibility mode and may not be displaying the website correctly. Dear Walter: Once we solve for this fixed value of V_applied, the solution to this problem can be used as the initial value once we switch back to using our original Global Equation. That will lead to a matrix form representation of equations. The field being solved for is the temperature of the walls and we are assuming steady state conditions. In the second step, the opposite settings are applied. And the problem is that for give postion (x,y) (or (r,theta)) in certain domain, (rp,thetap) should be calculated and then the Jacobian
http://www.comsol.com/blogs/solving-multiphysics-problems/ This second step does require an adjustment to the default solver settings. There are two ways to introduce a nonzero gradient in the electric potential. It is suggested to start with the first approach and try the second if the memory requirements are too high. Suggested Products Use the Global Equations node for ODEs, differential algebraic equations, purely algebraic equations and conditions, and transcendental equations, or to add degrees of freedom to a model using the introduced states. COMSOL ACCESS AND TECHNICAL SUPPORT To receive technical support from COMSOL for the COMSOL products, please contact your local COMSOL representative or send your questions to support@comsol.com. r\left( V,T,V_{applied}\right) = \left (\frac{1}{3W}\int\sigma(T)\nabla V \cdot \nabla V d\Omega-1 \right), \frac{\partial r}{\partial V_{applied}} = 0. An interesting question came up the other day that I felt would make an excellent blog post since it allows us to discuss one of the very powerful, and often underutilized, features of COMSOL Multiphysics: the Global Equation. Use a segregated solver, but combine the global equations and the electric potential equations into one step, which is solved to convergence using the automatic Newton approach and a direct solver. I cant find a reason for it. A more elegant approach is to introduce a variation of our Global Equation for V_applied that solves the equation: This equation simply sets V_applied equal to 1[V], and the software will then solve the system of equations and compute a consistent electric potential field. The first time derivative of u is written ut, and the second time derivative of u is utt. In addition, the derivatives shown above have to be nonzero at the initial conditions, otherwise the entire row of the Jacobian would be zero. This is shown in the screenshot below. Accessing the Equations and Variables Equation View You can access the equations and variables used internally by COMSOL Multiphysics by enabling the Equation View nodes to display in the model tree. Global equations are a way of adding an additional equation to a model. This is shown in the screenshot below. Introducing an initial value into the Electric Currents physics that will lead to a nonzero gradient on the electric potential field.
By examination, we can we see that: whereas the other two derivatives with respect to the electric potential, \partial r / \partial V, and the temperature fields, \partial r / \partial T, will be nonzero. Posted 21 sept. 2014, 05:14 UTC+2 Version 4.4 0 Replies . To do so, we add a Global Equation feature within the Electric Currents physics. These terms tell the nonlinear solver how to update V_applied such that our global equation will equal zero. V is the volume of the inner hemisphere and Vt, Vtt are its 1st and 2nd time derivative respectively. Since we have four equations for four variables, you can choose Number of dependent variables 4. It may be less obvious that you can also solve algebraic and even . Thanks for your reply. In the Select Physics tree, select Mathematics>ODE and DAE interfaces>Global ODEs and DAEs (ge . are parameters defined in 'global expressions'. Using Heat Transfer in solids, choose Stationary and the geometry is 1m*1m square , 2. 4. The approach shown here assumes that the thermal mass of the air is negligible, but if we wanted to model this as a transient problem, we could include the time-derivative of the air temperature and the total mass and specific heat of air in the global equation as well. Well also assume that the ground underneath is at a constant temperature. Customize COMSOL Multiphysics to meet your simulation needs with application-specific modules.
Along with the unknown, we need to know what equation this variable must satisfy. The electric and thermal conductivities of the material are nonlinear with temperature. I had a simulation with AC/DC which simulates Three-phase electric power and it wokrd. http://bit.ly/fGRVIa Your internet explorer is in compatibility mode and may not be displaying the website correctly. This consent may be withdrawn. --
The temperature solution can still be solved in a segregated fashion using an iterative solver. 5. Add a boundary heat source at one boundary and the heat rate is Q_0, the other three boundary is nature . 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. Tingyu Su . Magnus Ringh, COMSOL, Hi
listed if standards is not an option). Particular functionality may be common to several products. Please login with a confirmed email address before reporting spam Hi all, I am using weak-form PDE interface to do multi-variable physics modeling. The problem here is that global equations and variables cannot depend on space coordinates such as x and y. Recently I read a blog about Comsol using skills, and there is a example about how to using global equation to limit the max temperature at a probe. The average person at rest dissipates about 75 W of heat. The purpose of this notebook is to show you how you can create a simple, state-of-the-art time series classification model using the great fastai-v1 library in 4 steps : 1. A global equation can be used to describe a load, constraint, material property, or anything else in the model that has a uniquely definable solution. Good luck
Your internet explorer is in compatibility mode and may not be displaying the website correctly. I modified the simlation so that i inserted an electrical circuit which replaces the 3 voltage sources for the 3 phase and after this it dosent work anymore.. Since this is a steady state problem, it doesn't matter what initial conditions we give for this variable. r=f(rp,thetap,theta)
Global equation as follows 0.5*real (emw.iomega*epsilon0_const* (2.5^2+i*im_eps ilon))*int1 (emw.normE^2)- 2.3e-5 [W] (just to show that equation is not coordinate dependent) It solves for im_epsilon ( this variable included in epsilonr of CdS). The problem here is that global equations and variables cannot depend on space coordinates such as x and y. Note: This discussion is about an older version of the COMSOLMultiphysics software. To start Comsol Multiphysics 5.0 open the Terminal and enter comsol -ckl Model Wizard. ?theta/?rp ?theta/?thetap
The Global Equation interface, as well as the appropriate solver settings. There are two choices: The global equation and the electric potential must be solved simultaneously and using a direct solver. In this case, the choice is clear: we want to ensure that the sum of all the heat going in and out of the volume of air equals zero. f and g are known nonlinear functions. Prodotti consigliati To do so, we add a Global Equation feature within the Electric Currents physics. I am using a parametric segregated solver to solve. Posted Sep 12, 2021, 6:21 a.m. GMT+1 or
It is these additional terms that are the really interesting and useful contribution. Since this is a steady state problem, it doesnt matter what initial conditions we give for this variable. Although this approach is very computationally efficient, due to the use of the segregated solver, it relies on an ad hoc update equation that needs to be constructed with some knowledge of the underlying physics of the problem. Thank you for your reply. 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 short answer is that a Global Equation cannot contain terms that are spatially-dependent. By combining the above, the information contained in Maxwell's equations for electrostatics can be encoded in just one equation: (5) The usefulness of this equation in engineering applications is limited due to its inability to represent dielectric materials. --
Low-Frequency Electromagnetics, Parameters, Variables, & Functions, Studies & Solvers, COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH), How to Model Generalized Plane Strain with COMSOL Multiphysics, Part 2: Model a Linear Electromagnetic Plunger with a Blocker, Control Current and Voltage Sources with the AC/DC Module. Hello Carl,
When you are solving a problem with global equations, you will want to use a Fully Coupled Stationary Solver with a Direct Linear System Solver. But we do not know the air temperature inside the room, T_{air}. We still need to introduce a Global Equation for the applied potential, V_applied, but now we need an equation that is satisfied and solved for at the same time as the equations for the electric potential. This turns out to be a bit nontrivial in this case, in that there must be a nonzero gradient in the electric potential at the specified initial values. However, recall that in the former case, this extra equation updates the applied potential using an ad hoc scaling within a separate segregated solver iteration. Rearranging, this is equivalent to: This can be read as: Compute the value of V_applied such that the losses in the inclusion equal 3 watts. This approach requires more changes to the settings, but will require less memory to solve. Other approaches for solving this class of problems, discussed in our previous post, are: The significant advantage of the approach shown here, despite its higher memory requirements, is that it converges quickly and robustly. In this example, a structural mechanics model of a spring is augmented by a global equation which solves for the load to achieve a desired spring displacement. Today, we will introduce a goal-seeking equation into a model in the COMSOL Multiphysics software that is used in combination with a fully coupled approach to solving a nonlinear problem. Many of our users are well aware of the fact that COMSOL Multiphysics can be used to solve partial differential equations (PDEs) as well as ordinary differential equations (ODEs) and initial value problems. This additional degree of freedom will represent something we do not want to model explicitly. COMSOL does not always flag when you use and redefine an internal variable, bacause its "allowed" and required if you are tweaking the equations, you are supposed to be the "master" and to know it's just that there are som many things to "know" when you mix up all these physics so nicely
To start a new discussion with a link back to this one, click here. View the specification chart to find your ideal combination. u/p2 in the right hand side previously lacked the factor 1/p2 , where p is the porosity. Introducing a Global Equation within a physics interface. I am amature in using COMSOL. Best,
A global equation can be used to describe a load, constraint, material property, or anything else in the model that has a uniquely definable solution. Lets modify our previous example to demonstrate. The objective of our model is to adjust the potential difference between the top electrode and the ground electrode such that 3 watts are dissipated within the inclusion. Global equations are a way of adding an additional equation to a model. Global Constraint: Global Equations: Pointwise Constraint: Weak Constraint: Weak Contribution: Weak Contribution on Mesh Boundaries: Coordinate Systems : Base Vector System: Boundary System: This consent may be withdrawn. Thanks for the update Walter, indeed I have been using Global equations in COMSOL for now a couple of decencies, but never really got into he details of the solvers, and as I read you, there are several subtle options to improve convergence, and probably precision. Best regards,
January 14, 2014. Is there any way to use an app for a 2D model ? In the field defining the equation, we will use an Integration Coupling Operator named intop to integrate the normal total energy heat flux variable, ht.nteflux, across all of the wall boundaries. You seem to have the same question as in this older thread and the same solution that Magnus provided in that thread should work for you as well. Let us consider a small house with a person inside, as shown below. Posted 31 aot 2022, 22:59 UTC+2 Electromagnetics, Structural & Acoustics 0 Replies . But I might be wrong, it's just my first guess ;)
You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version The equations is actually a transformation from (rp,thetap) to (r,theta). Adding a Global equation to a PDE in COMSOL Multiphysics, Accumulation of Heat example. This can be achieved via the Modify model configuration for study step check box and then enabling/disabling the two different Global Equations within the two study steps. Your internet explorer is in compatibility mode and may not be displaying the website correctly. If you still need help with COMSOL and have an on-subscription license, please visit our Support Center for help. In this post, we will look at using global equations to introduce an additional degree of freedom to a model. To remedy this problem, the theory is extended with the effects of induced polarization. In this example, a structural mechanics model of a spring is augmented by a global equation which solves for the load to . The information provided may be out of date. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version If I add a Gloal Equation as separate physic, can I use a segregated stationary solver / iterative linear solver? : Hi
Indeed, I should solve the nonlinear equations like
The approach shown here is one of several approaches that can be used to address goal-seeking problems within the GUI without having to resort to any programming. When setting this up, make sure to turn on the Advanced Physics Options in the Model Builder so that you can add global equations to a physics interface. Matlab-based Automation Controlling with Comsol Global Equations Reverse Engineering of Transient Problems 3 Dr. Thomas Frommelt - T&I Modeling Summary and Outlook Iron and Steel Non-Ferrous Metal Semiconductor SGL Group Best Solutions for our Customers 4 Dr. Thomas Frommelt - T&I Modeling Carbon and graphite cathodes in customized designs If you would like to see an example that walks through all of the steps of setting up a global equation in your model, please see this example of Using Global Equations to Satisfy Constraints. The trick for COMSOL to adapt your equation to their models, i.e. Ivar, Hi,
Just like in our previous blog post, this can be achieved via a Global Equation, although this time, we add the Global Equation within the physics that it affects. where xp=rp*cos(thetap) and yp=rp*sin(thetap), respectively. Dear Walter, So the air temperature is the one additional unknown that we need to add to this finite element model. Yes, you can click "Equation View" to edit equation. I have: the state u: [0,T] for the system , the adjoint state : [T,0 . (How can I import a table into COMSOL). You can define rho using a domain variable (in version 4) or a subdomain expression variable (in version 3.5) without any equation. If you try to solve it by hand, the issue will become immediately apparent. great information you provide in this blog! Furthermore, this example may also be defined and modeled using components from the following product combinations: The combination of COMSOL products required to model your application depends on several factors and may include boundary conditions, material properties, physics interfaces, and part libraries. There is, however, a cost to these additional terms. Good luck
It is simpler to keep the scalar form of representation, and to keep the default value 1 in the window. I have couple of questions: 1.
Although I still have a question on .., you will want to use a Fully Coupled Stationary Solver with a Direct Linear System Solver. It seems that you define u = rho, where rho is a function of x and y. Several equations can be added and the equation can be coupled. Optimizing Solar Cell Designs with a Simulation App, Creating Schlieren-Type Visualizations in COMSOL Multiphysics, How to Inspect Your Mesh in COMSOL Multiphysics. If you still need help with COMSOL and have an on-subscription license, please visit our Support Center for help. You can define rho using a domain variable (in version 4) or a subdomain expression variable (in version 3.5) without any equation. The boundaries conditions you are applying here are not *interior* to the modeling domain. listed if standards is not an option). Dear Enzo, Posted Dec 9, 2010, 3:27 p.m. GMT+1 This approach can be much more robust and general, but does come with a computational cost. Jeff. There is a fan circulating air, mixing it thoroughly, so we can assume the inside air temperature is constant. Basically, you cannot solve one equation without the other. . How can I use TMY3 temperature data instead of ASHRAE ?
listed if standards is not an option). The problem here is that global equations and variables cannot depend on space coordinates such as x and y. In general, there are 3 main ways to classify time series, based on the input to the neural network: raw data. Now, if we wanted to be very accurate, we could build a conjugate heat transfer model of this, and solve for the temperature field and the fluid flow inside of and around the house. Global Equations. a) a naming conflict, or b) from the definitions provided in the Global Equation, as you need to give valid derivatives too to have the system to extract the Jacobian correctly (if I'm not fully wrong), and the corrrect Jacobian is needed to get a valid results, (one step at the time we get our way to the final solution.) More for me to play with in the coming days . )=0, where u is the unknown solved by the module itself, f is defined in 'global expressions' and a~d. Why is that? How can I define a TEC app for a heat sink or a hot surface? How to contact COMSOL: Benelux COMSOL BV Rntgenlaan 19 2719 DX Zoetermeer The Netherlands Phone: +31 (0) 79 363 4230 Fax: +31 (0) 79 361 4212 info@comsol.nl www.comsol.nl Denmark COMSOL A/S Diplomvej 376 2800 Kgs. For general product information, contact COMSOL at info@comsol.com. Here, we will use an equation that contributes terms to the Jacobian matrix when solved simultaneously with the affected physics. That is, the software figures out the update to V_applied automatically. A global equation can be used to describe a load, constraint, material property, or anything else in the model that has a uniquely definable solution. Train model. This robust and rapid convergence is a consequence of the additional terms within the Jacobian matrix and highlights another one the strengths of COMSOL Multiphysics for solving highly nonlinear coupled multiphysics problems. The same as what is done in the video: https://www.comsol.com/video/simulate-thermoelectric-devices-tecs. I can help with COMSOL. Global equation or constraint . Hi, I'm trying to define an equation in global equations and it is corresponded with the coordinates x and y (or certain global variable), e.g. How to Convert Point Cloud Data to Surfaces and Solids, How to Customize Your Model Builder Workflow Using Add-Ins, Hi Walter,
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