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January 14, 2014. Lyngby . Tingyu Su . Thank you for your reply. For general product information, contact COMSOL at info@comsol.com. 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. The reason why you would want to use a fully coupled solver are described here: 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. 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. It seems that you define u = rho, where rho is a function of x and y. Global Equations. -- Discussion Closed This discussion was created more than 6 months ago and has been closed. This model example illustrates applications of this type that would nominally be built using the following products: however, additional products may be required to completely define and model it. 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. listed if standards is not an option). The Global Equation interface, as well as the appropriate solver settings. Note that this is why it is helpful to have a nondimensionalized residual equation. (If you want to build a model of all the airflow in your room, please see this example of Displacement Ventilation in a Room to get started.). Good luck The short answer is that a Global Equation cannot contain terms that are spatially-dependent. Global equation as follows .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) . Well also assume that the ground underneath is at a constant temperature. 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. If you try to solve it by hand, the issue will become immediately apparent. This second step does require an adjustment to the default solver settings. R, C and R_c are constants while P is the pressure, Pt is its 1st time derivative. listed if standards is not an option). 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. 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. Discussion Closed This discussion was created more than 6 months ago and has been closed. Now it works good, but it seems like equation from Global ODEs and DAEs module is solved on . Dear Walter, ?r/?rp ?r/?thetap Global Constraint: Global Equations: Pointwise Constraint: Weak Constraint: Weak Contribution: Weak Contribution on Mesh Boundaries: Coordinate Systems : Base Vector System: Boundary System: . This means that the global equation introduces a zero on the diagonal of the Jacobian, but many nonzero terms in the corresponding row. Introducing a Global Equation within a physics interface. Dear YongweiL, There is no interior wall with a thermal insulation to override here. 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. To provide this flexibility, COMSOL Multiphysics uses a built-in interpreter that interprets equations, expressions, and other mathematical descriptions before producing a model. In the New window, click Model Wizard. 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. u/p2 in the right hand side previously lacked the factor 1/p2 , where p is the porosity. We know the outside temperature, ground temperature, and all heat transfer coefficients, so this problem is almost solvable. That will lead to a matrix form representation of equations. Particular functionality may be common to several products. Why is that? 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. 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. 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. Here, we will introduce an alternative approach, wherein the equation for the input is updated based upon an equation that lets the software symbolically compute derivatives. The electric and thermal conductivities of the material are nonlinear with temperature. It seems that you define u = rho, where rho is a function of x and y. Using Global Equations to Satisfy Constraints, http://www.comsol.com/blogs/solving-multiphysics-problems/, https://www.comsol.com/video/simulate-thermoelectric-devices-tecs, Multiscale Modeling in High-Frequency Electromagnetics. 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. Lets modify our previous example to demonstrate. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version COMSOL Moderator. 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. 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. most probably because "rho" is defined alread inside COMSOl for the material density. There are two ways to introduce a nonzero gradient in the electric potential. To start a new discussion with a link back to this one, click here. Thanks for your reply. The equation is entered in the global equations box as follows, what am I missing? The simplest way is to specify a spatially varying initial condition, as shown in the screenshot below, in the Electric Currents physics. 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. 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. 2. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version Suggested Products Dear Walter: 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. This affects the kind of linear system solver that we will have to use within the nonlinear iterations. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version The equation that we enter is: Where intop() is an integration operator defined over the inclusion. ?theta/?rp ?theta/?thetap 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. I cant find a reason for it. The problem here is that global equations and variables cannot depend on space coordinates such as x and y. This approach requires more changes to the settings, but will require less memory to solve. There is, however, a cost to these additional terms. In addition, you can use tools like the Physics Builder to create your own physics interfaces, or the Application Builder to create entire new user interfaces. Import libraries 2. COMSOL Multiphysics is a general-purpose software platform, based on advanced numerical methods, for modeling and simulating physics-based problems. where r=sqrt(x^2+y^2) and theta=angle(x+i*y) are the polar coordinates in certain domain, respectively. 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'. Using Heat Transfer in solids, choose Stationary and the geometry is 1m*1m square , 2. 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. The field being solved for is the temperature of the walls and we are assuming steady state conditions. Good luck With COMSOL Multiphysics, you will be able to account for coupled or multiphysics phenomena. You can define rho using a domain variable (in version 4) or a subdomain expression variable (in version 3.5) without any equation. There is a fan circulating air, mixing it thoroughly, so we can assume the inside air temperature is constant. Send Private Message Flag post as spam. or 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. Please login with a confirmed email address before reporting spam Hi, I'm having a problem in defining an ODE by using Global Equations. I had a simulation with AC/DC which simulates Three-phase electric power and it wokrd. 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,. What's wrong? I am using a parametric segregated solver to solve. I have: the state u: [0,T] for the system , the adjoint state : [T,0 . Posted 31 aot 2022, 22:59 UTC+2 Electromagnetics, Structural & Acoustics 0 Replies . Your internet explorer is in compatibility mode and may not be displaying the website correctly. You can define rho using a domain variable (in version 4) or a subdomain expression variable (in version 3.5) without any equation. 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. |?y/?xp ?y/?yp| Best regards, 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. More for me to play with in the coming days . Introducing an additional Global Equation to find an initial value. Unfortunately, I see many of my colleague engineers that are using COMSOL as a classical click and solve tool, and not using the advantages of the global approach you propose. Let us consider a small house with a person inside, as shown below. We would like to find out the air temperature inside of the house, and the temperature gradient through the walls. 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. . The average person at rest dissipates about 75 W of heat. Build learner 4. Dear Enzo, It may be less obvious that you can also solve algebraic and even . Interior wall Overrided by Thermal Insulation is not applicable In Comsol 4.4 ,How did you implement Boundary Selection of Heat Flux ? Customize COMSOL Multiphysics to meet your simulation needs with application-specific modules. To start Comsol Multiphysics 5.0 open the Terminal and enter comsol -ckl Model Wizard. The temperature solution can still be solved in a segregated fashion using an iterative solver. This is simple to do, at least in this case, but might not always work, since we do introduce a nonphysical initial value. You also use. The trick for COMSOL to adapt your equation to their models, i.e. This consent may be withdrawn. 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. The COMSOL Sales and Support teams are available for answering any questions you may have regarding this. If I add a Gloal Equation as separate physic, can I use a segregated stationary solver / iterative linear solver? How can I use TMY3 temperature data instead of ASHRAE ? 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. 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. In the approach presented, a hydrostatic pressure load is applied to a Named Selection of exterior nodes that are located below a liquid surface. If you want u as a dependent variable, you can solve u = rho as a very simple PDE in the domain. f and g are known nonlinear functions. 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. The boundaries conditions you are applying here are not *interior* to the modeling domain. 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. Lets first look at how to implement this method, and then address the relative merits. are parameters defined in 'global expressions'. 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 . That is, within the first study step, we simply specify V_applied, and in the second step, V_applied is solved for such that there is the desired dissipation within the inclusion. To do so, we add a Global Equation feature within the Electric Currents physics. 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. listed if standards is not an option). An automatic notification and a case number are sent to you by email. I have couple of questions: 1. Since this is a steady state problem, it doesn't matter what initial conditions we give for this variable. 5. How can I combine a TEC app to the other components of a model. Global equations are a way of adding an additional equation to a model. |?x/?xp ?x/?yp| These terms tell the nonlinear solver how to update V_applied such that our global equation will equal zero. In this post, we will look at using global equations to introduce an additional degree of freedom to a model. 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.. Using Global Equations: Modeling Room Air Temperature in a House, Using Global Equations to Introduce Fully Coupled Goal Seeking. If you still need help with COMSOL and have an on-subscription license, please visit our Support Center for help. 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. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version The problem here is that global equations and variables cannot depend on space coordinates such as x and y. Ivar Ed Low Theres a stiff breeze outside, and we know the outside air temperature. Hello Chin Neng Leong . 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. Modifying the model configuration for the first study step, where the Global Equation for the initial value is solved. The problem here is that global equations and variables cannot depend on space coordinates such as x and y. This consent may be withdrawn. Your internet explorer is in compatibility mode and may not be displaying the website correctly. Send Private Message Flag post as spam. 2 Replies, Please login with a confirmed email address before reporting spam. In addition, the derivatives shown above have to be nonzero at the initial conditions, otherwise the entire row of the Jacobian would be zero. Solving Algebraic Field Equations. View the specification chart to find your ideal combination. We can also write out what this residual equation represents: When computing the Jacobian contribution, we take the symbolic derivative of this with respect to all of the unknowns in the model. Best, 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. That is, if we take a surface integral of the heat flux between the interior walls and air, and add the heat contribution from the person, this should equal zero: Lets take a look at the Global Equation interface, which gives us a list of variable names to enter well use Tair and the equation to satisfy. That is, the software figures out the update to V_applied automatically. by Bjorn Sjodin. Start Comsol Multiphysics. Global Equations: u: a11 . 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. This additional degree of freedom will represent something we do not want to model explicitly. 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. Here, we explain how to create a global model fully coupled with the BE in the two-term approximation using the COMSOL Multiphysics software. 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. Global equation or constraint . In the Model Wizard window, click 0D in the Select Space Dimension menu. 1. 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. -- Chin Neng Leong . 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 Double click on General Form PDE (g) four times. 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. 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.) 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. 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. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version Please share some documentation, how we can use equation directly. I can help with COMSOL. This is shown in the screenshot below. Adding a Global equation to a PDE in COMSOL Multiphysics, Accumulation of Heat example. 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. It is these additional terms that are the really interesting and useful contribution. 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. Since this is a steady state problem, it doesnt matter what initial conditions we give for this variable. Train model. To remedy this problem, the theory is extended with the effects of induced polarization. And if youre familiar with heat transfer modeling, you know that there are tabulated heat transfer coefficients, h, for vertical and horizontal walls that relate the inward heat flux, q'', to the wall temperature, T, and the air temperature, T_{air} via the equation: q''=h(T_{air}-T). 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. listed if standards is not an option). They do require that we simultaneously solve for the global equation and the electric potential equations, and, since they introduce both off-diagonal terms and a zero on the diagonal, they require that the fully coupled approach use a direct linear system solver when solving for the electric potential field and the global equation. 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. Yes, you can click "Equation View" to edit equation. (Recall in our previous approach we had to construct our own update equation based upon some knowledge of the physics.). To do so, we add a Global Equation feature within the Electric Currents physics. Solving Algebraic and Transcendental Equations: An Example Adding ODEs, DAEs, and Other Global Equations Global ODEs and DAEs Toolbar Is there any way to use an app for a 2D model ? Hello Carl, Global Equations The global equations that you can solve have the following form: with the initial conditions u(t0) = u0 and ut(t0) = ut,0 (where the subscript t indicates the time derivative). 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. should also have taught about that one, you have told me that before Magnus ;) Since we have four equations for four variables, you can choose Number of dependent variables 4. 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 the Select Physics tree, select Mathematics>ODE and DAE interfaces>Global ODEs and DAEs (ge . Posted Dec 9, 2010, 3:27 p.m. GMT+1 If the air is hotter than the wall, heat will flow into the wall and vice versa. Global equations are a way of adding an additional equation to a model. Note that we are entering a residual equation that must equal zero at the solution point. In the second step, the opposite settings are applied. Low-Frequency Electromagnetics, Parameters, Variables, & Functions, Studies & Solvers In general, there are 3 main ways to classify time series, based on the input to the neural network: raw data. r=f(rp,thetap,theta) I am amature in using COMSOL. 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 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. (How can I import a table into COMSOL). 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. Possible uses include: Controllers Rigid-body mechanics Nonlinear eigenvalue problems Continuation Integral constraints Basically, you cannot solve one equation without the other. 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. 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. Version 3.5a, Version 4.3b 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). But I might be wrong, it's just my first guess ;) 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. 5 Replies, Please login with a confirmed email address before reporting spam. 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. When solving it, an error message says: failed to evaluate u. great information you provide in this blog! 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. There are two choices: The global equation and the electric potential must be solved simultaneously and using a direct solver. This approach can be much more robust and general, but does come with a computational cost. 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). Prodotti consigliati 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. But we do not know the air temperature inside the room, T_{air}. In case of using several TEC module for cooling a surface, the modules are electrically in series ? This technique, along with the ones discussed previously, are great tools for an analyst to have in their toolbelt. The information provided may be out of date. 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. How to Convert Point Cloud Data to Surfaces and Solids, How to Customize Your Model Builder Workflow Using Add-Ins, Hi Walter, 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. In the 'global equations' interface, I set 'name' as v, 'equation' as f and 'initial' as v0. 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. To determine the right combination of products for your modeling needs, review the Specification Chart and make use of a free evaluation license. Although I still have a question on .., you will want to use a Fully Coupled Stationary Solver with a Direct Linear System Solver. Here, we will use an equation that contributes terms to the Jacobian matrix when solved simultaneously with the affected physics. A transient structural simulation is run by looping through many load step solves, with the surface. Note that we are entering a residual equation that must equal zero at the solution point. If you still need help with COMSOL and have an on-subscription license, please visit our Support Center for help. How can I define a TEC app for a heat sink or a hot surface? The equations is actually a transformation from (rp,thetap) to (r,theta). Along with the unknown, we need to know what equation this variable must satisfy. Jeff. http://bit.ly/fGRVIa In this example, a structural mechanics model of a spring is augmented by a global equation which solves for the load to . listed if standards is not an option). So the air temperature is the one additional unknown that we need to add to this finite element model. The first time derivative of u is written ut, and the second time derivative of u is utt. Posted Sep 12, 2021, 6:21 a.m. GMT+1



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