However, it is usually not possible to know this ahead of time. That is, the material property changes instantaneously from 10W/m/K to 20W/m/K at 400K. Common Mistakes: Not assigning materials to all the domains. Starting from zero initial conditions, the nonlinear solver will most likely converge if a sufficiently small load is applied. That is: It is also possible to compute the derivative of the solution with respect to the continuation parameter and use that derivative (evaluated at the iteration) to compute a new initial value: where is the stepsize of the continuation parameter. The issue here has do with the iterative algorithm used to solve nonlinear stationary models. Again, introduce a Global Parameter that gets ramped from exactly zero to one. Such problems must solved in the time domain. To switch between these solver types, go to the Stationary Solver node within the Study sequence. That is, start by first solving a model with a small, but non-zero, load. This involves a systematic reduction in the model complexity. Click the link in the email we sent to to verify your email address and activate your job alert. listed if standards is not an option). Under Initial values of variables solved for, the default value of the Settingslist is Physics controlled. Ramping the nonlinearities over time is not as strongly motivated, but step changes in nonlinearities should be smoothed out throughout the simulation. comp1.u2, comp1.v2, and comp1.w2 are usually variables associated with the x,y, and z component of deformation in COMSOL. See Knowledge Base 1240: Manually Setting the Scaling of Variables. Multiphysics problems are often nonlinear. Any trademarks referenced in this document are the property of their respective owners. Near the top of the Stationary Solver log, the software will report if a linear or nonlinear solver is being used. How can I use it? That is: It is also possible to compute the derivative of the solution with respect to the continuation parameter and use that derivative (evaluated at the iteration) to compute a new initial value: where is the stepsize of the continuation parameter. listed if standards is not an option). Reply . As P is ramped up, the continuation method uses the previous solutions to compute initial conditions for the more nonlinear cases. Discussion Closed This discussion was created more than 6 months ago and has been closed. The nature of simulating nature: A Q&A with IBM Quantum researcher Dr. Jamie We've added a "Necessary cookies only" option to the cookie consent popup. We have also introduced meshing considerations for linear static problems, as well as how to identify singularities and what to do about them when meshing. The segregated approach, on the other hand, solves sets of unknowns separately. Not assigning proper boundary conditions: Especially if you have ports. Sometimes, reducing the model complexity can be quite challenging and it can be better to start from as simple a case as possible and gradually increase the complexity. I highly recommend this flower shop. Thanks, Andres. P&S: COMSOL Design Tool for Photonic Devices. Why? In many physics areas there exist alternative physics formulations specifically meant for solving cases where the geometry has an extreme aspect ratio. 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. Second, the continuation method will automatically take smaller load increments if a solution cannot be found. Iterative , Direct . Ideally, one would use small elements in regions where the solution varies quickly in space, and larger elements elsewhere. Sometimes, reducing the model complexity can be quite challenging and it can be better to start from as simple a case as possible and gradually increase the complexity. Here, we begin an overview of the algorithms used for solving nonlinear static finite element problems. Wrong ordering of study steps. Convergence can be poor when the initial values do not provide a good starting point for this iterative approach. Such a large difference in the materials properties can be challenging. Any trademarks referenced in this document are the property of their respective owners. This approach is used by default for most 1D, 2D, and 2D-axisymmetric models. Minimising the environmental effects of my dyson brain. - Posted Sep 9, 2020, 1:44 p.m. EDT Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. Your internet explorer is in compatibility mode and may not be displaying the website correctly. k(T,P) = 10[W/m/K]*((1-P)+P*exp(-(T-293[K])/100[K])) Using the first order optimality. Cooling and Solidification of Metal. The continuation method will again backtrack and try intermediate values of the ramping parameter, thus giving you the nearest approximation to the abrupt transition that is solvable. It is quite rare that changing these settings is superior to using a combination of the other techniques in this Knowledgebase, although it is possible to tune these settings to reduce solution time and memory requirements, once a model is already converging. What are some highly rated cards & stationery in Brea, CA? At low flow speeds the flow solution will be time invariant, but at higher flow rates there will be vortex shedding, a time-varying change in the flow field behind the cylinder. The stationary solver is used both for Stationary (time-invariant) and Frequency Domain (time-harmonic) study types. Dr.S.Ravindran Cite 1 Recommendation Popular answers (1). It is thus always advised to start this procedure with a simplified 2D, or 2D-axisymmetric model. Solve the stationary study then the time dependent study. You can unsubscribe from these emails at any time. If this was solved using the Solid Mechanics physics interface the thin walls of the container would need to be explicitly modeled, but the wall thickness is much smaller than the overall can dimensions. k(T,P) = 10[W/m/K]*((1-P)+P*exp(-(T-293[K])/100[K])) However, it is usually not possible to know this ahead of time. Leverage your professional network, and get hired. The fully coupled and segregated approaches are discussed below. Your Discussion has gone 30 days without a reply. The other low-level default settings within the Stationary Solver are chosen for robustness. This algorithm was also useful for understanding what happens near a failure load. The "Values for dependent values" in study step settings should be set to the default ("Physics-controlled" in 5.2). Alternatively, delete and re-create the study. replace it with the expression: Once a simplified solvable version of the model has been found, gradually increase the model complexity again, re-introducing nonlinearities and multiphysics couplings. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. Within either of these features, it can also be helpful to enable the Results While Solving option, as shown in the screenshot below, to visualize the iterations being taken during the solution. One can say that, in general, if the loads on a nonlinear system are zero, the system will be at rest; that is, the solution will be zero. Sign in to create your job alert for Stationary Engineer jobs in Brea, California, United States. Extending this logic, if one wants to solve for any arbitrary load on a nonlinear system, it makes sense to solve a sequence of intermediate problems with gradually increasing load values and using the solutions from each previous step as the initial condition for the next step. If it is not clear that any of the above strategies are working, it is useful to take a more general approach to verifying the general validity of the model. COMSOL does not assume any legal liability for the accuracy of the data disclosed. When the difference in the computed solutions between successive iterations is sufficiently small, or when the residual is sufficiently small, the problem is considered converged to within the specified tolerance. If all of the above approaches have been tried and you are certain that the problem itself is well-posed, consider that the nonlinear problem may not, in fact, have a stationary (time-invariant) solution. Here we introduce a more robust approach to solving nonlinear problems. Stationary Solver Iterative Direct . Linear solvers. What is \newluafunction? Thanks for contributing an answer to Stack Overflow! If the model is nonlinear, see: Improving Convergence of Nonlinear Stationary Models. Load ramping and nonlinearity ramping can be used in combination, but start with only one or a few of the loads or nonlinearities being ramped. It is also possible to manually refine the mesh. The algorithm is, generally speaking, a Newton's method approach. First, it is physically intuitive, often matching how one would perform an experiment. Within either of these features, it can also be helpful to enable the Results While Solving option, as shown in the screenshot below, to visualize the iterations being taken during the solution. If the material properties entered are incorrect for the governing equation, the model will generate an error at runtime, usually a Singular Matrix error. Feature: Stationary Solver 1 (sol1/s1)" . With the exception of some thermal problems however, it is often difficult to estimate the solution, so alternative approaches are needed. In the extreme case, suppose one wants to model an instantaneous change in properties, such as: See Knowledge Base 1240: Manually Setting the Scaling of Variables. If both load ramping and nonlinearity ramping are still leading to slow convergence, refine the mesh. Knowledgebase 1260: What to do when a linear stationary model is not solving, Knowledge Base 1240: Manually Setting the Scaling of Variables, What to do when a linear stationary model is not solving, Knowledge Base 1254: Controlling the Time Dependent solver timesteps, Galleria dei Modelli e delle App di Simulazione, 2023 da COMSOL. Once a simplified solvable version of the model has been found, gradually increase the model complexity again, re-introducing nonlinearities and multiphysics couplings. You can write the discrete form of the equations as f(U) = 0, where f(U) is the residual vector and U is the solution vector. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. In this post, we will delve deeper into how to choose an appropriate mesh to start your mesh convergence studies for linear static finite element problems. Please dont hesitate to post comments below or send emails to us if you experience any other problems. Not meshing all the domains. The advantages of the continuation method are two-fold. Note: there is no way to couple this . From there, if an additional small load increment is applied, the previously computed solution is a reasonable initial condition. Examine the model and identify all terms that introduce nonlinearities, such as multiphysics couplings, nonlinear materials relationships, and nonlinear boundary conditions. The coupling terms between the different groups are thus neglected. Convergence can be poor when the initial values do not provide a good starting point for this iterative approach.
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