In COMSOL Multiphysics, there are actually two possible implementations of a Dirichlet condition. And with the constraint expression being 0, there is no constraint. In that case, the symbolic algebra during assembly will reduce the expression to ht.Tvar-ht.Tvar, and further to zero. This constrains the temperature to be equal to the given value, unless the given value happens to be the string ht.Tvar. The second term is just the temperature degree of freedom cast into a variable. The first term is the prescribed temperature, which you enter as input. The constraint is formulated as ht.T0-ht.Tvar, which implicitly means ht.T0-ht.Tvar = 0. The Equation View for the Temperature node. In order to understand how this works, enable the Equation View, and look at the implementation of the Dirichlet condition (in this case, a prescribed temperature):

Settings for a conditional Dirichlet condition.Īnimation of the temperature distribution as the prescribed temperature spot travels along the bar.

If you instead enter if(r < R,450,ht.Tvar) as the prescribed value, you will get the intended behavior (shown in the following animation). The intention is, however, to switch off the Dirichlet condition outside of the hot spot. If you were to add a Temperature node and enter a similar expression ( if(r < R,450,0)), it would mean setting the temperature to absolute zero on the part of the boundary that is not covered by the hot spot. This may be a bit artificial, but it displays an important difference between the Neumann condition and the Dirichlet condition. When looking in the Equation View of COMSOL Multiphysics, these conditions will appear as constraints.Īssume that you want the traveling spot to prescribe the temperature as exactly 450 K. Dirichlet conditions therefore change the structure of the stiffness matrix. Equations for such degrees of freedom can thus be eliminated from the problem. Where a Dirichlet condition is given, the dependent variable is prescribed, so there is no need to solve for it. A mathematical description of this load could beĪnimation of the temperature distribution as the heat source travels along the bar. Its intensity has a parabolic distribution with a peak value q_0. Let’s consider a heat transfer problem where a circular heat source with a radius R is traveling in the x direction with a velocity v. As the Neumann conditions are purely additive contributions to the right-hand side, they can contain any function of variables: time, coordinates, or parameter values. In COMSOL Multiphysics, you can see them as weak contributions in the Equation View. The Neumann conditions are “loads” and appear in the right-hand side of the system of equations. Within the context of the finite element method, these types of boundary conditions will have different influences on the structure of the problem that is being solved. The following table features some examples from various physics fields that show the corresponding physical interpretation. A Robin condition is a mixture of the two previous boundary condition types, where a relation between the variable and its gradient is prescribed. A Neumann condition, meanwhile, is used to prescribe a flux, that is, a gradient of the dependent variable. With a Dirichlet condition, you prescribe the variable for which you are solving. In the mathematical treatment of partial differential equations, you will encounter boundary conditions of the Dirichlet, Neumann, and Robin types. In this blog post, we’ll discuss how you can utilize the flexibility of COMSOL Multiphysics to handle such situations. In these cases, among other instances, you may want to apply a boundary condition to only part of the geometrical boundary or only under certain conditions. Say you are working on a modeling case where loads are moving in such a way that they cross over different mesh elements and boundaries during the simulation.

Field continuity in comsol 5.3