To handle a PDE with two Laplacian terms in COMSOL Multiphysics using the PDE interface, define the equation explicitly in the Equation-Based Modeling section. Include the Laplacian terms using the built-in laplacian operator (e.g., D1⋅laplacian(u) and D2⋅laplacian(v). Specify dependent variables, boundary conditions, and initial conditions, then mesh and solve the model. COMSOL’s postprocessing tools can visualize the results for uu and vv. This approach ensures accurate handling of systems with multiple Laplacian terms.
Thank you for your help. I have one more question. How to calculate strain energy in Laminar Flow module of comsol. In particular for non-newtonian fluid case.
In COMSOL Multiphysics, handling two Laplacian terms in a Partial Differential Equation (PDE) within the Equation-Based Modeling interface can be done by directly specifying the equation with the Laplacian terms. Here's a step-by-step approach:
Set up the PDE interface:Go to Model Builder → Component → PDE → General Form (or any other PDE interface depending on your problem). Choose Equation-Based Modeling and set the PDE type to General Form.
Define the equation:In the PDE interface, you can specify the equation in the form: ∂u∂t+∇⋅F(u,∇u)=Q\frac{\partial u}{\partial t} + \nabla \cdot \mathbf{F}(u, \nabla u) = Q∂t∂u+∇⋅F(u,∇u)=Q where F(u,∇u)\mathbf{F}(u, \nabla u)F(u,∇u) is your flux term, and QQQ is a source term.
Include the Laplacian terms:If you have two Laplacian terms (say ∇2u\nabla^2 u∇2u and ∇2v\nabla^2 v∇2v), they would appear as: ∇2u+∇2v=0\nabla^2 u + \nabla^2 v = 0∇2u+∇2v=0 To represent these Laplacians in COMSOL:For ∇2u\nabla^2 u∇2u, you can add it as a term directly in the equation. In the PDE settings, under Equation, enter the term for the Laplacian, which is typically written as diff(u,2) (for the second derivative of uuu). Similarly, for ∇2v\nabla^2 v∇2v, you can add another term diff(v,2).
Input the coefficients:Ensure that the coefficients for both Laplacian terms are defined properly. You may need to add specific coefficients under Coefficient Form PDE for the corresponding terms.
Boundary and initial conditions:Set appropriate boundary conditions for both uuu and vvv, depending on whether the problem is Dirichlet, Neumann, or Robin. Initialize the values for both fields (e.g., u0u_0u0 and v0v_0v0) at t=0t = 0t=0.
Solve the system:Once the equation is set up, you can solve the system numerically using Time-Dependent or Stationary solvers, depending on whether your problem is time-dependent or steady-state.
By setting up the terms for the Laplacians manually in this way, COMSOL will treat the equation with two Laplacian terms and solve it accordingly.