r=f(rp,thetap,theta) This approach, albeit more computationally expensive than the segregated approach we introduced previously, has some interesting advantages in terms of robustness and highlights one of the core strengths of the COMSOL software. For general product information, contact COMSOL at info@comsol.com. January 14, 2014. 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. Ivar, Hi, This affects the kind of linear system solver that we will have to use within the nonlinear iterations. The field being solved for is the temperature of the walls and we are assuming steady state conditions. 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. Your internet explorer is in compatibility mode and may not be displaying the website correctly. We will see later that there are some advantages to the nondimensionalization of this equation. |?x/?xp ?x/?yp| -- 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. How can I use TMY3 temperature data instead of ASHRAE ? However, solving for the fluid flow is going to be computationally demanding, as compared to just solving a heat transfer problem. 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. Modifying the model configuration for the first study step, where the Global Equation for the initial value is solved. ?r/?rp ?r/?thetap That will lead to a matrix form representation of equations. 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. Here, we will look at the same example we considered before, of a Joule heating problem of two electrodes applied to a medium with an inclusion. Dear Enzo, Introducing a Global Equation within a physics interface. Note that we are entering a residual equation that must equal zero at the solution point. It is these additional terms that are the really interesting and useful contribution. 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 Thank you for your reply. 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. The Global Equation interface, as well as the appropriate solver settings. Posted Sep 12, 2021, 6:21 a.m. GMT+1 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. Good luck listed if standards is not an option). Particular functionality may be common to several products. Since this is a steady state problem, it doesn't matter what initial conditions we give for this variable. Introducing an additional Global Equation to find an initial value. In the Select Physics tree, select Mathematics>ODE and DAE interfaces>Global ODEs and DAEs (ge . In the approach presented, a hydrostatic pressure load is applied to a Named Selection of exterior nodes that are located below a liquid surface. There is, however, a cost to these additional terms. great information you provide in this blog! 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. If I add a Gloal Equation as separate physic, can I use a segregated stationary solver / iterative linear solver? Using Ansys Workbench Mechanical to simulate buoyancy loads on a floating body has been illustrated. 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. . To start a new discussion with a link back to this one, click here. This is simple to do, at least in this case, but might not always work, since we do introduce a nonphysical initial value. The problem here is that global equations and variables cannot depend on space coordinates such as x and y. To provide this flexibility, COMSOL Multiphysics uses a built-in interpreter that interprets equations, expressions, and other mathematical descriptions before producing a model. 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. The equation that we enter is: Where intop() is an integration operator defined over the inclusion. With more than 30 add-on products to choose from, you can further expand the simulation Well also assume that the ground underneath is at a constant temperature. A transient structural simulation is run by looping through many load step solves, with the surface. 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. How to Convert Point Cloud Data to Surfaces and Solids, How to Customize Your Model Builder Workflow Using Add-Ins, Hi Walter, As discussed in a previous blog post on introducing goal seeking into the segregated solver, one can augment a multiphysics model with an additional global equation within which we define how to update an input to a model such that a particular output is achieved. The information provided may be out of date. listed if standards is not an option). Note: This discussion is about an older version of the COMSOLMultiphysics software. Send Private Message Flag post as spam. This second step does require an adjustment to the default solver settings. 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. 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. I can help with COMSOL. 3. There is a fan circulating air, mixing it thoroughly, so we can assume the inside air temperature is constant. 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. To start a new discussion with a link back to this one, click here. 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. In the second step, the opposite settings are applied. 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. Hello Chin Neng Leong . The problem here is that global equations and variables cannot depend on space coordinates such as x and y. To remedy this problem, the theory is extended with the effects of induced polarization. You can define rho using a domain variable (in version 4) or a subdomain expression variable (in version 3.5) without any equation. Tingyu Su . Add a boundary heat source at one boundary and the heat rate is Q_0, the other three boundary is nature . At the same time, I apply pressure at the inner surface whose value is determined from an ODE (P+R*C*Pt+ (R+R_c)*Vt+R*R_c*C*Vtt=0). http://www.comsol.com/blogs/solving-multiphysics-problems/ The COMSOL Sales and Support teams are available for answering any questions you may have regarding this. Is there any way to use an app for a 2D model ? Discussion Closed This discussion was created more than 6 months ago and has been closed. V is the volume of the inner hemisphere and Vt, Vtt are its 1st and 2nd time derivative respectively. Solving Algebraic Field Equations. 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. Please login with a confirmed email address before reporting spam Hi, I'm having a problem in defining an ODE by using Global Equations. This technique, along with the ones discussed previously, are great tools for an analyst to have in their toolbelt. Posted 21 sept. 2014, 05:14 UTC+2 Version 4.4 0 Replies . Since we have four equations for four variables, you can choose Number of dependent variables 4. 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. We have simplified the problem by assuming that the air has a uniform temperature, and thus simplified the modeling, via the usage of the Global Equation. Note that we are entering a residual equation that must equal zero at the solution point. There's a comsol model with 1 module with unknown u and there's another unknown v satisfying an equation f(u,v,a,b,c,d,)=0, where u is the unknown solved by the module itself, f is defined in 'global expressions' and a~d are parameters defined in 'global expressions'. |?y/?xp ?y/?yp| 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. Dear Walter, This is shown in the screenshot below. u/p2 in the right hand side previously lacked the factor 1/p2 , where p is the porosity. To start Comsol Multiphysics 5.0 open the Terminal and enter comsol -ckl Model Wizard. In addition, the derivatives shown above have to be nonzero at the initial conditions, otherwise the entire row of the Jacobian would be zero. The reason why you would want to use a fully coupled solver are described here: I have couple of questions: 1. Indeed, I should solve the nonlinear equations like The main default node is Global Equations, which you use to define the global equations, including the names of the variables (states), the required initial values, and an optional description. The same as what is done in the video: https://www.comsol.com/video/simulate-thermoelectric-devices-tecs. f and g are known nonlinear functions. Since this is a steady state problem, it doesn't matter what initial conditions we give for this variable. 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. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version 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. This consent may be withdrawn. Dear Walter: Along with the unknown, we need to know what equation this variable must satisfy. More for me to play with in the coming days . It may be less obvious that you can also solve algebraic and even . I cant find a reason for it. Here, we will use an equation that contributes terms to the Jacobian matrix when solved simultaneously with the affected physics. The short answer is that a Global Equation cannot contain terms that are spatially-dependent. This additional degree of freedom will represent something we do not want to model explicitly. (How can I import a table into COMSOL). 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. . Use a fully coupled approach for the entire problem, and use a direct solver. There are two ways to introduce a nonzero gradient in the electric potential. You seem to have the same question as in [this older thread](https://www.comsol.com/forum/thread/18590/a-gloabl-equation-problem?last=2011-05-23T20:35:26Z) and the same solution that Magnus provided in that thread should work for you as well. The equation that we enter is: intop (ec.Qrh)/3 [W] - 1 Where intop () is an integration operator defined over the inclusion. You can define rho using a domain variable (in version 4) or a subdomain expression variable (in version 3.5) without any equation. After we solve this model, well be able to visualize the temperature distribution on all of the interior walls, and evaluate the air temperature via Results > Derived Values > Global Evaluation. This requires the least changes to the solver settings, but solving a large system of equations with a direct solver is going to require a lot of memory. Global equations are a way of adding an additional equation to a model. Adding a Global equation to a PDE in COMSOL Multiphysics, Accumulation of Heat example. Now it works good, but it seems like equation from Global ODEs and DAEs module is solved on . It seems that you define u = rho, where rho is a function of x and y. The equation is entered in the global equations box as follows, what am I missing? The first time derivative of u is written ut, and the second time derivative of u is utt. There are two choices: The global equation and the electric potential must be solved simultaneously and using a direct solver. are parameters defined in 'global expressions'. listed if standards is not an option). To do so, we add a Global Equation feature within the Electric Currents physics. Yes, you can click "Equation View" to edit equation. What's wrong? Globally Ill say that you should probably propose more COMSOL training courses on the solver settings, for such sets of particular cases, since these are really the strength of COMSOLs multiphysics approach These terms tell the nonlinear solver how to update V_applied such that our global equation will equal zero. Lets first look at how to implement this method, and then address the relative merits. Note that this technique can also be using in the time domain, as long as the global equation can be satisfied at each time step. 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. If you think that using global equations will be helpful for your modeling and are interested in learning more about COMSOL Multiphysics, please contact us. 5 Replies, Please login with a confirmed email address before reporting spam. 2. Ivar Ed Low Global equations are a way of adding an additional equation to a model. Good luck This approach requires more changes to the settings, but will require less memory to solve. In this post, we will look at using global equations to introduce an additional degree of freedom to a model. 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. 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. This approach takes advantage of the segregated solution approach, solving one part of the problem after another (solving all of the various physics) and then updating the input via the global equation. We know the outside temperature, ground temperature, and all heat transfer coefficients, so this problem is almost solvable. segregated approach we introduced previously, blog post on introducing goal seeking into the segregated solver, fully coupled approach use a direct linear system solver, Multiscale Modeling in High-Frequency Electromagnetics. 1. The boundaries conditions you are applying here are not *interior* to the modeling domain. But I might be wrong, it's just my first guess ;) Ivar, Hi, Magnus 4. Although I still have a question on .., you will want to use a Fully Coupled Stationary Solver with a Direct Linear System Solver. Send Private Message Flag post as spam. To do so, we add a Global Equation feature within the Electric Currents physics. I am amature in using COMSOL. The trick for COMSOL to adapt your equation to their models, i.e. So the air temperature is the one additional unknown that we need to add to this finite element model. http://bit.ly/fGRVIa 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. 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. Basically, you cannot solve one equation without the other. Start Comsol Multiphysics. There's a comsol model with 1 module with unknown u and there's another unknown v satisfying an equation f (u,v,a,b,c,d,. 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. Train model. Prepare data 3. But we do not know the air temperature inside the room, T_{air}. 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. Thanks for your reply. Best, : Hi The temperature solution can still be solved in a segregated fashion using an iterative solver. It is simpler to keep the scalar form of representation, and to keep the default value 1 in the window. I have: the state u: [0,T] for the system , the adjoint state : [T,0 . Jeff. The problem here is that global equations and variables cannot depend on space coordinates such as x and y. Several equations can be added and the equation can be coupled. 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. Magnus Ringh, COMSOL, Hi Setting Up a Global Model of a Non-Maxwellian Discharge The equations in a global model are greatly simplified because the spatial information of the different quantities in the plasma reactor is . When solving it, an error message says: failed to evaluate u. most probably because "rho" is defined alread inside COMSOl for the material density. 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. With COMSOL Multiphysics, you will be able to account for coupled or multiphysics phenomena. 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. In this example, a structural mechanics model of a spring is augmented by a global equation which solves for the load to . Note that this segregation will lead to the, Using a parametric sweep and manually identifying the approximate target value, Augmenting the segregated solver with an additional update equation.
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