Visualize uniform flow, point source, vortex, dipole, and custom F(x,y) fields in real time. Streamlines, divergence, and curl color maps. Click to trace streamlines from any point.
The divergence of a 2D vector field $\mathbf{F}= (F_x, F_y)$ quantifies the net flux (outflow minus inflow) per unit area at a point. It tells you if the point is a source, a sink, or neither.
$$\nabla \cdot \mathbf{F}= \frac{\partial F_x}{\partial x}+ \frac{\partial F_y}{\partial y}$$Where $F_x(x,y)$ and $F_y(x,y)$ are the vector components you can type into the simulator's input boxes. A positive result means net outflow; negative means net inflow; zero means what flows in also flows out.
The curl (specifically its z-component in 2D) measures the tendency of the field to rotate or circulate around a point. It's a measure of local angular velocity of the field.
$$(\nabla \times \mathbf{F})_z = \frac{\partial F_y}{\partial x}- \frac{\partial F_x}{\partial y}$$A positive curl indicates counter-clockwise rotation, negative indicates clockwise rotation, and zero indicates an irrotational (curl-free) field, like the uniform flow or a pure source.
Aerodynamic Design: Engineers use potential flow visualization (like the fields in this simulator) to model airflow over wings or car bodies in early design stages. Streamlines show how air will flow, helping to predict lift and drag before running costly CFD simulations.
Electromagnetic Field Sketching: Before setting up complex Finite Element Method (FEM) simulations, analysts sketch field lines. The "Dipole" field in the simulator, for instance, is a fundamental model for the magnetic field around a bar magnet or an electric dipole.
Heat Transfer Analysis: The vector field can represent heat flux. A "Source" could be a heat-generating component on a circuit board. Divergence in this context relates to points where heat is being generated or absorbed.
Structural Stress Analysis: In solid mechanics, the principal stress directions within a material form a vector field. Plotting these stress trajectories helps identify potential failure paths, like around a hole in a loaded plate, which is crucial for safe structural design.
When you start using this tool, there are a few points that are easy to misunderstand, so be careful. First, while "arrow length = vector magnitude," the arrows are automatically scaled for visibility. Near the center of a gravity well, the values theoretically approach infinity, but in the tool they are clipped to a maximum length. Therefore, comparing magnitudes reliably is best done using the color map. For example, the areas near the charges of an electric dipole that turn bright red are the regions where the field is actually strongest.
Next, the point that "divergence and curl values depend on the calculation range (the Δx for differentiation)". The tool calculates these via numerical differentiation using a few pixels around the cursor position. Therefore, for fields with very sharp variations, the value can fluctuate significantly just by moving the cursor one pixel. Always keep in mind that when using CAE software in practice, the mesh coarseness also determines the accuracy of these differential values.
Finally, understand the limitations of 2D visualization. This tool is only visualizing a 2D slice. Almost all real physical phenomena are three-dimensional. For example, a uniform flow (uniform field) filling the screen might actually be a "helical flow" with vortices in the depth direction. It's common for a field to appear divergence-free in 2D, but have a non-zero $ \frac{\partial F_z}{\partial z} $ term in 3D, making the overall divergence non-zero.