Curvilinear Coordinates
Introduction
A curvilinear coordinate system is a type of coordinate system where the coordinate lines can be curved. Using a curvilinear coordinate system can make it easier to, for example, define boundary conditions that follow a curved surface. The curvilinear coordinate systems in COMSOL Multiphysics can define a vector field and an associated base vector system using four different methods:
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A diffusion method, which solves Laplace’s equation and computes the vector field as . Solve for the vector field using a Stationary study.
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An adaptive method, which adapts the computed vector field to maintain a constant streamline density on the cross section. Solve for the vector field using a Stationary study.
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An elasticity method, which computes the vector field from the solution with the eigenvalue closest to zero for the following eigenvalue problem:
Solve for the vector field using an Eigenvalue study.
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A flow method, which solves the following equation for u and p, and uses u as the vector field:
Solve for the u and p using a Stationary study.
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A user-defined vector field. No study step is required.
Solve for the curvilinear coordinates (unless they are user-defined) in a separate study or separate study step, which you run before the study or study step where you solve for the physics that make use of the computed curvilinear coordinates. Simultaneously solving for the curvilinear coordinates and the physics that use them does not normally work.