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markwu4铜虫 (著名写手)
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[求助]
请有comsol license的人提供我Knowledgebase 103/952 已有2人参与
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有license的人请提供我Knowledgebase 103, 952内容 http://www.comsol.com/support/knowledgebase/103/ http://www.comsol.com/support/knowledgebase/952/ 我算出负的浓度 听说里面有一些技巧可以解决这类问题 |
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albertwowwow
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【答案】应助回帖
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markwu4: 金币+10, ★★★★★最佳答案, 谢谢 因为一半已经分给第一个应助者 2014-10-16 06:48:48
markwu4: 金币+10, ★★★★★最佳答案, 谢谢 因为一半已经分给第一个应助者 2014-10-16 06:48:48
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Description Stationary models with high reaction rates, Ri, or more generally, large source terms, may result in convergence problems. You can for instance get error messages such as "No convergence, even when using the minimum damping factor", "NaN repeatedly found in solution", or "Error: Failed to find a solution". Now what could you do to get around this problem? Try to solve the problem using reduced source terms, and then gradually increase them, using the previous solution when solving, until you reach the solution to your original problem. The following approach uses the parametric solver to gradually increase the source term. COMSOL Multiphysics 4 and later Multiply the reaction (source) term (Ri) by a multiplication factor variable, for example "k". Click the Stationary node and select the Auxiliary sweep (in version 4.4) or Continuation (in earlier versions) check box. Enter k as the Sweep parameter In Parameter values, enter a range of increasing values, starting at a low value and increasing to unity, for example "1e-3 1e-2 1e-1 1". Click Compute. COMSOL Multiphysics 3.5a and earlier Multiply the reaction (source) term (Ri) by a multiplication factor variable, for example "k". In the *'Solver Parameters** dialog box, select the Parametric Solver and specify Name of Parameter to that of the multiplication factor, k. Enter the List of Parameter Values as a range of increasing values, starting at a low value and increasing to unity, for example "1e-3 1e-2 1e-1 1". Click OK. Click Solve. COMSOL Multiphysics will now start to solve the problem using the first multiplication factor. Then, if that works, the solution will be used as the initial guess for the next parameter value. This process will continue until the last parameter value is reached. Because you specified the last parameter value to be unity, the last solution will correspond to your original problem formulation. Use the time dependent solver. By making the problem time dependent, you usually get a smoother convergence. COMSOL Multiphysics 4 and later Right-click the Model node and select Add Study. Select Time Dependent and click Finish. In the Times edit field, enter a range of times to solve for, for example "0 1e3". Click Compute. COMSOL Multiphysics 3.5a and earlier Open Solver Parameters. Select the Time dependent solver and specify a range of Times to solve for, for example 0 1e3". Click OK, then Solve. Make sure to solve the problem for large enough times, such that the solution does not vary any longer. This implies that the solution has reached steady-state. Thus, COMSOL Multiphysics has calculated the stationary solution! If the solution process never gets past t = 0, see Solution 964 for more information. If none of the previous methods would help, try using them in combination with refining the mesh in regions where the source term is large. 这个是103的 |
4楼2014-10-16 06:14:44
2楼2014-10-14 09:48:38
markwu4
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3楼2014-10-14 16:05:33
albertwowwow
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Numerical errors The most common reason for negative concentrations is numerical noise: when the species concentration approaches zero, the numerical noise becomes significant in comparison to the concentration. If you are seeing negative concentrations of very small magnitude, numerical noise is probably the cause. In a pure convection-diffusion problem, the scale of the concentration does not matter, so in order to avoid the problem, you can add an arbitrary baseline concentration to keep the resulting overall concentration above zero. However, with a reaction term which depends on the concentration, the scale and origin do matter, which means that you need to think of other ways to keep the concentration strictly positive. Discontinuous concentrations Another common cause for slightly negative concentrations is a discontinuity in space or time, for instance in the initial condition. As an example, consider the one dimensional time dependent Convection and Diffusion equation where the convection is in the positive x-direction (i.e. the direction vector u=1), with a uniformly zero initial condition, and boundary conditions which set the concentration at the end nodes to one and zero respectively. The physical interpretation of this PDE is an initially sharp, gradually diffusing front moving in the positive x-direction. However, for the default shape function (second order Lagrange), only continuous functions are admissible as FEM solutions, for which reason the discontinuous initial value is modified before the time-iterations can begin. This often results in a small dip in the solution for t=0, and in the above example, the concentration will locally be slightly negative at t=0, as shown in the figure below. Solutions to the time-dependent Convection and diffusion equation at times t=0, 0.01, 0.1, 0.2, 0.3. This type of behavior can also result in wildly oscillating solutions and convergence problems. This problem can be avoided by using one of COMSOL Multiphysics's built in smoothed step functions in order to smooth out the initial discontinuity in a controlled manner. For example, in the Convection and Diffusion problem described above, you could, instead of the uniformly zero initial condition, use a smoothed step transition as the initial condition in order to avoid negative values for concentration at t=0. For more information please refer to Knowledge Base solution 905. Incorrect reaction term Usually a significantly negative concentration (i.e. not noise around zero) indicates that the underlying mathematical model does not correctly describe the physics. In this case "fixing" the numerics does not take care of the problem. One potential cause is that you have a constant sink in your reaction term, which is an approximation that only works for large concentrations. When the concentration reaches zero, the reaction term continues to consume the species, finally resulting in negative concentration. In order to avoid this problem you need to make sure that your reaction rate is such that when the concentration of the species approaches zero, then so does the species sink. This can be achieved for instance by writing max(eps^2,Q). eps is an internal COMSOL constant that is a very small number in the order or 10-15. This type of expression is also good if you want to avoid Q being 0, for example if you apply the logarithm to it somewhere, or if the symbolic derivative runs a risk of containing division by zero. Remember that COMSOL symbolically differentiates all expressions that contribute to the Jacobian. Mesh resolution One other thing that can be indicated by significantly negative concentrations is the lack of mesh resolution. The resulting convergence problems are often the underlying issue when negative concentrations are observed in high convection regimes (high Peclet number) and in those with large reaction terms or fast kinetics (high Damkohler number). In Knowledge Base entry 103 a few tricks are presented which may alleviate these types of problems without extensively refining the mesh. It can also be useful to investigate whether the negative concentration problem gets better or worse with mesh refinement. If better, then you know in which direction to go. If worse, then the physics of the model probably need to be checked. Formulate logarithmic concentrations A nice way of eliminating mesh resolution problems and negative dips is to use the logarithm of the concentration and not the concentration itself as the dependent variable. The reason for this is that a linearly varying mesh can sometimes not capture the exponential behavior of the concentration changes. In addition, modeling the logarithm of the concentration ensures that the real concentration can never become negative during the solution process. 这个是192的 |
5楼2014-10-16 06:15:31